From dfa14850c7e0534c14bd99f8cdbec4a43b4d6837 Mon Sep 17 00:00:00 2001
From: Nils Berglund <83530463+nilsberglund-orleans@users.noreply.github.com>
Date: Sun, 22 Jan 2023 16:50:00 +0100
Subject: [PATCH] Add files via upload

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 Parameters_November22.md | 7380 ++++++++++++++++++++++++++++++++++++++
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+### Parameter values for YouTube simulations ###
+
+Created by **Nils Berglund** and optimized by **Marco Mancini**
+
+C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
+
+Below are parameter values used for different simulations, as well as initial conditions used in 
+function animation. Some simulations use variants of the published code. The list is going to be 
+updated gradually. 
+
+
+### 31 December 22 - Explosive lensing ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave(2.0*LAMBDA*cos(APOLY*PID), 2.0*LAMBDA*sin(APOLY*PID), phi, psi, xy_in);
+    angle = DPI/(double)NPOLY;
+    for (j=1; j<NPOLY; j++)
+        add_circular_wave(1.0, 2.0*LAMBDA*cos((double)j*angle + APOLY*PID), 2.0*LAMBDA*sin((double)j*angle + APOLY*PID), phi, psi, xy_in);
+        
+    if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
+    for (j=0; j<NPOLY; j++)
+        add_circular_wave(sign, 2.0*LAMBDA*cos((double)j*angle + APOLY*PID), 2.0*LAMBDA*sin((double)j*angle + APOLY*PID), phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 1   /* set to 1 to save memory when writing tiff images */
+#define NO_EXTRA_BUFFER_SWAP 1    /* some OS require one less buffer swap when recording images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1150  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2300          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.197916667
+#define YMAX 1.197916667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 59        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.5	    /* parameter controlling the dimensions of domain */
+#define MU 0.5              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.1        /* Courant number */
+#define COURANTB 0.04658753  /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800       /* number of frames of movie */
+#define NVID 9           /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 1
+
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 18     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 40.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 3.5     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e3    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 0.75     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 0.05   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 30 December 22 - Yet another, only marginally successful attempt to solve a maze with an incompressible fluid ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_laminar_flow(flow_speed_schedule(0), LAMINAR_FLOW_MODULATION, 0.5, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 1           /* set to 1 to save memory when writing tiff images */
+#define NO_EXTRA_BUFFER_SWAP 1    /* some OS require one less buffer swap when recording images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1150  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 575          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.197916667
+#define YMAX 1.197916667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 3       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 541          /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.5	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65  
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+#define CHANGE_FLOW_SPEED 0     /* set to 1 to change speed of laminar flow */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define IN_OUT_FLOW_BC 1         /* set to 1 to add in-flow/out-flow boundary conditions (for Euler equation) */
+#define IN_OUT_FLOW_MIN_AMP 0.35  /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) */
+#define IN_OUT_FLOW_AMP 0.35      /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) */
+#define LAMINAR_FLOW_MODULATION 0.3     /* asymmetry of laminar flow */
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1600           /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 50
+#define CPLOT_B 54
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+#define PRINT_FLOW_SPEED 1      /* set to 1 to print speed of flow */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 11     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.7      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+#define VSCALE_PRESSURE 0.5      /* additional scaling factor for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_SHIFT 50.0        /* shift for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_LOG_SHIFT -2.0     /* shift for color scheme Z_EULER_PRESSURE */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 1000.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 29 December 22 - Are circular mazes unilluminable? ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-0.1, 0.1, 0.0, DPI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define SAVE_MEMORY 1           /* set to 1 to save memory when writing tiff images */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 31     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 13  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.005          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000    /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles on left and right side */
+#define PRINT_CIRCLE_PARTICLE_NUMBER 1 /* set to 1 to print number of particles outside circular maze */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 7200      /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 18     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 250      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define COLOR_HUEMIN 30  /* minimal color hue */
+#define COLOR_HUEMAX 330 /* maximal color hue */
+#define RAINBOW_COLOR 1  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.01       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 8      /* width of maze */
+#define NYMAZE 32      /* height of maze */
+#define MAZE_MAX_NGBH 5     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+#define MAZE_RANDOM_FACTOR 0.1     /* randomization factor for S_MAZE_RANDOM */
+#define MAZE_CORNER_RADIUS 0.5     /* radius of tounded corners in maze */
+
+```
+
+### 28 December 22 - A rainbow sprinkler ###
+
+**Program:** `lennardjones.c` postprocessed with `ljones_movie.c` 
+
+```
+#define MOVIE 0         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 1   /* set to 1 to save memory while saving frames */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+#define SAVE_TIME_SERIES 1  /* set to 1 to save time series of particle positions */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -0.1
+#define INITXMAX 0.1	/* x interval for initial condition */
+#define INITYMIN 1.1
+#define INITYMAX 1.2	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.3	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 1     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.009          /* parameter controlling radius of particles of second type */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 0.66           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 1            /* number of grid point for grid of disks */
+#define NGRIDY 1           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 4000       /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 0   /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 8
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 2.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 20.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 40.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 20.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU_B */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 1    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 2      /* time interval between adding further particles */
+#define N_ADD_PARTICLES 20   /* number of particles to add */
+#define FINAL_NOADD_PERIOD 700  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 0       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 1   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 1     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 150   /* size of hashgrid in x direction */
+#define HASHY 75    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 27 December 22 - Turbulence (possibly numerical) in a flow of increasing speed around an obstacle ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_laminar_flow(flow_speed_schedule(0), LAMINAR_FLOW_MODULATION, 0.5, -0.1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+
+#define XMIN -1.0
+#define XMAX 3.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 3       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 199          /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.5	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+#define CHANGE_FLOW_SPEED 1     /* set to 1 to change speed of laminar flow */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define IN_OUT_FLOW_BC 1         /* set to 1 to add in-flow/out-flow boundary conditions (for Euler equation) */
+#define IN_OUT_FLOW_MIN_AMP 0.3  /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) */
+#define IN_OUT_FLOW_AMP 1.4      /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) */
+#define LAMINAR_FLOW_MODULATION 0.5     /* asymmetry of laminar flow */
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1600           /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 50
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+#define PRINT_FLOW_SPEED 1      /* set to 1 to print speed of flow */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.0      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+#define VSCALE_PRESSURE 0.5      /* additional scaling factor for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_SHIFT 10.0        /* shift for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_LOG_SHIFT -2.5     /* shift for color scheme Z_EULER_PRESSURE */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 1.7   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 1000.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 26 December 22 - Shining a rotating laser beam into a 16 by 16 maze with rounded corners ###
+
+**Program:** `particle_trajectory.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    x = -1.65;
+    y = 0.03;
+    alpha = angle_schedule(time);        
+    period = compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length, &xmax);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+#define SAVE_MEMORY 1   /* set to 1 to save memory when writing tiff images */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 31     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 50000        /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 50000        /* total number of sides of polygonal line */   
+#define NCX 9             /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 2            /* Sierpinski gastket depth */
+
+#define LAMBDA -1.1	/* parameter controlling shape of domain */
+#define MU 0.1          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 1         /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define TRAJ_LENGTH 10000 /* length of trajectory */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 0    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+#define PRINT_TRAJECTORY_LENGTH 1   /* set to 1 to print length of trajectory 0 */
+#define PRINT_TRAJECTORY_ANGLE 1    /* set to 1 to print angle of trajectory 0 */
+#define PRINT_TRAJECTORY_PERIOD 0   /* set to 1 to print period of trajectory 0 */
+#define DRAW_LENGTHS_PLOT 1         /* set to 1 to plot trajectory lengths */
+#define LENGTHS_LOG_SCALE 1         /* set to 1 to use log scale for plot of lengths */
+#define MIN_ANGLE 10.0         /* range of angles of trajectory */
+#define MAX_ANGLE 50.0         /* range of angles of trajectory */
+#define TEST_INITIAL_COND 1     /* set to 1 to allow only initial conditions that pass a test */
+
+#define SLOW_AT_LONG_TRAJ 0     /* set to 1 to slow down movie for long trajectories */
+#define ADD_SUCCESS_GALLERY 1   /* set to 1 to add gallery of successful trajectories at end of movie */
+#define SUCCESS_GALLERY_FRAMES 25   /* number of frames per success */
+
+#define NSTEPS 2000      /* number of frames of movie */
+#define TIME 2500         /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00001     /* integration step */
+#define NVID 150         /* number of iterations between images displayed on screen */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 13     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500       /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.03       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+#define GRAPH_HUE 30.0      /* color hue of graph */
+#define SUCCESS_HUE 90.0   /* color hue of success */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 250       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define END_FRAMES  100   /* number of frames at end of movie */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 16     /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1       /* seed of random number generator */
+#define MAZE_XSHIFT -0.5     /* horizontal shift of maze */
+#define MAZE_RANDOM_FACTOR 0.1     /* randomization factor for S_MAZE_RANDOM */
+#define MAZE_CORNER_RADIUS 0.4     /* radius of tounded corners in maze */
+
+```
+
+### 25 December 22 - A refracting star, viewed in 3D ###
+
+**Program:** `wave_3d.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+
+#define HIGHRES 1        /* set to 1 if resolution of grid is double that of displayed image */
+
+#define NX 1440          /* number of grid points on x axis */
+#define NY 1440         /* number of grid points on y axis */
+
+#define XMIN -1.5
+#define XMAX 1.5	/* x interval  */
+#define YMIN -1.5
+#define YMAX 1.5	/* y interval  */
+
+#define JULIA_SCALE 0.8 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 42        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 2   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define VARIABLE_IOR 0      /* set to 1 for a variable index of refraction */
+#define IOR 2               /* choice of index of refraction, see list in global_pdes.c */
+#define MANDEL_IOR_SCALE -0.05   /* parameter controlling dependence of IoR on Mandelbrot escape speed */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.2              /* parameter controlling the dimensions of domain */
+#define NPOLY 24            /* number of sides of polygon */
+#define APOLY 2.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 16           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 3  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.001       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8     /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0       /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1       /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0            /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 100   /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+#define PRECOMPUTE_BC 0     /* set to 1 to compute neighbours for Laplacian in advance */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2150        /* number of frames of movie */
+#define NVID 5            /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* set to 1 to print speed of moving source */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 100    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+#define ROTATE_VIEW_WHILE_FADE 1    /* set to 1 to keep rotating viewpoint during fade */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.25         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0005  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.02  /* wavelength of initial condition */
+
+
+/* Plot type, see list in global_pdes.c  */
+
+#define ZPLOT 103     /* wave height */
+#define CPLOT 103     /* color scheme */
+
+#define ZPLOT_B 107 
+#define CPLOT_B 107        /* plot type for second movie */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define FLOOR_ZCOORD 1          /* set to 1 to draw only facets with z not too negative */
+#define DRAW_BILLIARD 0         /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 0   /* set to 1 to draw front of boundary after drawing wave */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw construction lines of certain domains */
+#define FADE_IN_OBSTACLE 1      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental, draw outside of billiard in gray */
+
+#define PLOT_SCALE_ENERGY 0.01         /* vertical scaling in energy plot */
+#define PLOT_SCALE_LOG_ENERGY 0.25       /* vertical scaling in log energy plot */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+#define ROTATE_VIEW 1       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 14      /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13    /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.0   /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define VSCALE_ENERGY 100.0     /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0    /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0      /* scaling factor for energy representation */
+#define LOG_SCALE 0.75     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.5      /* shift of colors on log scale */
+#define LOG_ENERGY_FLOOR -10.0    /* floor value for log of (total) energy */
+#define LOG_MEAN_ENERGY_SHIFT 1.0   /* additional shift for log of mean energy */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 240.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -200.0    /* amplitude of variation of hue for color scheme C_HUE */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 0       /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.5      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0     /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+/* Parameters controlling 3D projection */
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 12.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.6    /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 2.4   /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0         /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1          /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1           /* overall y shift for REP_PROJ_3D representation */
+
+```
+
+### 24 December 22 - A Christmas sandpile ###
+
+**Program:** `lennardjones.c`, postprocessed with `ljones_movie.c`
+
+```
+#define MOVIE 0         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 1   /* set to 1 to save memory while saving frames */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+#define SAVE_TIME_SERIES 1  /* set to 1 to save time series of particle positions */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -0.1
+#define INITXMAX 0.1	/* x interval for initial condition */
+#define INITYMIN 1.1
+#define INITYMAX 1.2	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.3	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 1     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.009          /* parameter controlling radius of particles of second type */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 0.66           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 1            /* number of grid point for grid of disks */
+#define NGRIDY 1           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3300      /* number of frames of movie */
+// #define NSTEPS 1000       /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 0   /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 5
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 2.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 140.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 40.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 20.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU_B */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 1    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 2      /* time interval between adding further particles */
+#define N_ADD_PARTICLES 20   /* number of particles to add */
+#define FINAL_NOADD_PERIOD 700  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 0       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 1   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 1     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 150   /* size of hashgrid in x direction */
+#define HASHY 75    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 23 December 22 - An airfoil in a laminar flow ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_laminar_flow(IN_OUT_FLOW_AMP, 0.2, 0.5, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 3       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 198          /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define IN_OUT_FLOW_BC 1    /* set to 1 to add in-flow/out-flow boundary conditions (for Euler equation) */
+#define IN_OUT_FLOW_AMP 1.0 /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) */
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1500       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 51
+#define CPLOT_B 54
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+#define VSCALE_PRESSURE 0.5      /* additional scaling factor for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_SHIFT 10.0        /* shift for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_LOG_SHIFT -2.5     /* shift for color scheme Z_EULER_PRESSURE */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 1000.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 22 December 22 - Deep impact 8: Dropping heavy particles (mass ratio 20:1) into a Lennard-Jones fluid ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.99
+#define INITXMAX 1.99	/* x interval for initial condition */
+#define INITYMIN -1.1
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 20    /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.009          /* parameter controlling radius of particles of second type */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 1.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 100           /* number of grid point for grid of disks */
+#define NGRIDY 75           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2000      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 5
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 2.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 15.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 40.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 20.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU_B */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 1   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 1     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 75   /* size of hashgrid in x direction */
+#define HASHY 37    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 21 December 22 - Solving a maze with rounded corners using laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, -0.01, 0.15*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 31     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.005          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000    /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 6900      /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 250      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 32      /* width of maze */
+#define NYMAZE 32      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 2        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+#define MAZE_RANDOM_FACTOR 0.1     /* randomization factor for S_MAZE_RANDOM */
+#define MAZE_CORNER_RADIUS 0.4     /* radius of tounded corners in maze */
+
+```
+
+### 20 December 22 - A refracting von Koch snowflake ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave(0.0, 0.0, phi, psi, xy_in);
+    
+    if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
+    add_circular_wave(sign, 0.0, 0.0, phi, psi, xy_in);
+``` 
+    
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 41        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.85	    /* parameter controlling the dimensions of domain */
+#define MU 0.85             /* parameter controlling the dimensions of domain */
+#define NPOLY 24            /* number of sides of polygon */
+#define APOLY 0.333333333   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1       /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 6
+
+#define PLOT_B 7        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 12     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.25     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e3    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 19 December 22 - Bloopers 4: Blow-up in an incompressible Euler flow ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.15, 1, 1, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 3       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 3          /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1400       /* number of frames of movie */
+#define NVID 200          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 54
+#define CPLOT_B 53
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 11     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+#define VSCALE_PRESSURE 0.35      /* additional scaling factor for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_SHIFT 250.0        /* shift for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_LOG_SHIFT -1.8     /* shift for color scheme Z_EULER_PRESSURE */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 1000.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 18 December 22 - Deep impact 7: Dropping heavy particles (mass ratio 5:1) into a Lennard-Jones fluid ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.99
+#define INITXMAX 1.99	/* x interval for initial condition */
+#define INITYMIN -1.1
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 20    /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.009          /* parameter controlling radius of particles of second type */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 1.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 100           /* number of grid point for grid of disks */
+#define NGRIDY 75           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 5
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 2.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 15.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 40.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 5.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU_B */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 1   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 1     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 75   /* size of hashgrid in x direction */
+#define HASHY 37    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 17 December 22 - Mazes with randomized angles are harder to solve with laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, -0.01, 0.15*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 12  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.005          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 20000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 8000      /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 0     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 30      /* width of maze */
+#define NYMAZE 30      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 2        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+#define MAZE_RANDOM_FACTOR 0.1     /* randomization factor for S_MAZE_RANDOM */
+
+```
+
+### 16 December 22 - A refracting star ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave(0.0, 0.0, phi, psi, xy_in);
+    
+    if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
+    add_circular_wave(sign, 0.0, 0.0, phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 42        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.2              /* parameter controlling the dimensions of domain */
+#define NPOLY 24            /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1       /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2400       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 6
+
+#define PLOT_B 7        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 13     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.25     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e3    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 15 December 22 - Pressure of an incompressible Euler flow with a circular obstacle ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.15, 1, 1, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1000  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 500          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+
+#define XMIN -1.0
+#define XMAX 1.0	/* x interval */
+#define YMIN -1.0
+#define YMAX 1.0	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 3       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 3          /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65  
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1000       /* number of frames of movie */
+#define NVID 200          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 54
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+// #define ZPLOT 32     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+#define VSCALE_PRESSURE 0.35      /* additional scaling factor for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_SHIFT 250.0        /* shift for color scheme Z_EULER_PRESSURE */
+#define PRESSURE_LOG_SHIFT -1.8     /* shift for color scheme Z_EULER_PRESSURE */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 1000.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 14 December 22 - Mixing of sticky square grains of sand during a cave-in ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN 0.05
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8  /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 18     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 1         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 2       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 4.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.5  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.014 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 6000      /* number of frames of movie */
+#define NVID 150         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 400     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 1
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 11
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 0  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 2.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 4.5e-6    /* time step for particle displacement */
+#define KREPEL 0.5          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 3.5    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 15.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 400.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 750.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.02       /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5        /* radius in which to count neighbours */
+#define GRAVITY 4000.0             /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 1           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 20.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 13 December 22 - Laser beams starting in the center of a 32 by 32 maze ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.05, 0.0, DPI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 40000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 7500     /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 128      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 1  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 32      /* width of maze */
+#define NYMAZE 32      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 2        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
+### 12 December 22 - Randomly started waves refracted on a honeycomb lattice ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+```
+
+```
+    x = XMIN + (XMAX - XMIN)*rand()/RAND_MAX;
+    y = YMIN + (YMAX - YMIN)*rand()/RAND_MAX;
+    init_circular_wave(x, y, phi, psi, xy_in);
+    
+    if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
+    x = XMIN + (XMAX - XMIN)*rand()/RAND_MAX;
+    y = YMIN + (YMAX - YMIN)*rand()/RAND_MAX;
+    add_circular_wave(sign, x, y, phi, psi, xy_in);
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 57        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.1        /* Courant number */
+#define COURANTB 0.05      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1480       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 13     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.25     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e3    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 11 December 22 - Two airfoils on a torus ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.1, 0.2, 1, 1, 0.2, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 58         /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2150       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 10 December 22 - Mixing (or lack thereof) of Lennard-Jones particles during a cave-in ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN 0.05
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8  /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 18     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.008 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 7000      /* number of frames of movie */
+#define NVID 170         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 1
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 11
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 0  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 1.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 4.5e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 3.7    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 15.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 250.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 500.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5        /* radius in which to count neighbours */
+#define GRAVITY 2500.0             /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 180   /* size of hashgrid in x direction */
+#define HASHY 90    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 9 December 22 - Shining a rotating laser beam into a 16 by 16 maze with slanted corners ###
+
+**Program:** `particle_trajectory.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    x = -1.65;
+    y = 0.03;
+    alpha = angle_schedule(time);
+    period = compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length, &xmax); 
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 6   /* pattern of circles */
+#define POLYLINE_PATTERN 11  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 50000        /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 50000        /* total number of sides of polygonal line */   
+#define NCX 9             /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 2            /* Sierpinski gastket depth */
+
+#define LAMBDA -1.1	/* parameter controlling shape of domain */
+#define MU 0.1          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 1         /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define TRAJ_LENGTH 10000 /* length of trajectory */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 0    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+#define PRINT_TRAJECTORY_LENGTH 1   /* set to 1 to print length of trajectory 0 */
+#define PRINT_TRAJECTORY_ANGLE 1    /* set to 1 to print angle of trajectory 0 */
+#define PRINT_TRAJECTORY_PERIOD 0   /* set to 1 to print period of trajectory 0 */
+#define DRAW_LENGTHS_PLOT 1         /* set to 1 to plot trajectory lengths */
+#define LENGTHS_LOG_SCALE 1         /* set to 1 to use log scale for plot of lengths */
+#define MIN_ANGLE 10.0         /* range of angles of trajectory */
+#define MAX_ANGLE 50.0         /* range of angles of trajectory */
+#define TEST_INITIAL_COND 1     /* set to 1 to allow only initial conditions that pass a test */
+
+#define SLOW_AT_LONG_TRAJ 0     /* set to 1 to slow down movie for long trajectories */
+#define ADD_SUCCESS_GALLERY 1   /* set to 1 to add gallery of successful trajectories at end of movie */
+#define SUCCESS_GALLERY_FRAMES 25   /* number of frames per success */
+
+#define NSTEPS 2500      /* number of frames of movie */
+#define TIME 2500         /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00001     /* integration step */
+#define NVID 150         /* number of iterations between images displayed on screen */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 0     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500       /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.03       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+#define GRAPH_HUE 30.0      /* color hue of graph */
+#define SUCCESS_HUE 90.0   /* color hue of success */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 250       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define END_FRAMES  100   /* number of frames at end of movie */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 16     /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1       /* seed of random number generator */
+#define MAZE_XSHIFT -0.5     /* horizontal shift of maze */
+
+```
+
+### 8 December 22 - Energy flux of a wave refracted on a honeycomb lattice ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 57        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 25    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 6
+
+#define PLOT_B 7        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 13     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.25     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e3    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 1.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 7 December 22 - Van Gogh meets Munch: An airfoil in a channel ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.0, 0.1, 1, 1, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 197       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2250       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 14       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.5    /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 6 December 22 - Deep impact 6: Comparing a triangular and a rectangular obstacle ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 0     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 0  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN -1.1
+#define INITYMAX 0.15	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 19    /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 1.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1500      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 250     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 10.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 35.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 5 December 22 - Shooting laser beams at a 16 by 16 maze with slanted corners ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, 0.01, 0.00*PI, 0.3*PI, configs); `
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 11  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 4500     /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 128      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 16      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
+### 4 December 22 - 3D view of a wave refracted on a honeycomb lattice ###
+
+**Program:** `wave_3d.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);
+    add_circular_wave_mod(sign, 0.0, 0.0, phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 2500          /* number of grid points on x axis */
+#define NY 1250          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1        /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 0.8 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 57        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 2   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define VARIABLE_IOR 0      /* set to 1 for a variable index of refraction */
+#define IOR 2               /* choice of index of refraction, see list in global_pdes.c */
+#define MANDEL_IOR_SCALE -0.05   /* parameter controlling dependence of IoR on Mandelbrot escape speed */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 2.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 16           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 3  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.001       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8     /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0       /* damping of periodic excitation */
+#define COURANT 0.05      /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0            /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 100   /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+#define PRECOMPUTE_BC 0     /* set to 1 to compute neighbours for Laplacian in advance */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1400        /* number of frames of movie */
+#define NVID 5            /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* set to 1 to print speed of moving source */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 100    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+#define ROTATE_VIEW_WHILE_FADE 1    /* set to 1 to keep rotating viewpoint during fade */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.25         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0005  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.02  /* wavelength of initial condition */
+
+
+/* Plot type, see list in global_pdes.c  */
+
+#define ZPLOT 103     /* wave height */
+#define CPLOT 103     /* color scheme */
+
+#define ZPLOT_B 107 
+#define CPLOT_B 107        /* plot type for second movie */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define FLOOR_ZCOORD 1          /* set to 1 to draw only facets with z not too negative */
+#define DRAW_BILLIARD 1         /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1   /* set to 1 to draw front of boundary after drawing wave */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw construction lines of certain domains */
+#define FADE_IN_OBSTACLE 1      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental, draw outside of billiard in gray */
+
+#define PLOT_SCALE_ENERGY 0.01         /* vertical scaling in energy plot */
+#define PLOT_SCALE_LOG_ENERGY 0.25       /* vertical scaling in log energy plot */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+#define ROTATE_VIEW 1       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10      /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 14    /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.0   /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define VSCALE_ENERGY 100.0     /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0    /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0      /* scaling factor for energy representation */
+#define LOG_SCALE 0.75     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.5      /* shift of colors on log scale */
+#define LOG_ENERGY_FLOOR -10.0    /* floor value for log of (total) energy */
+#define LOG_MEAN_ENERGY_SHIFT 1.0   /* additional shift for log of mean energy */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 240.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -200.0    /* amplitude of variation of hue for color scheme C_HUE */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1       /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.5      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0     /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+/* Parameters controlling 3D projection */
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.3    /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 2.4   /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0         /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1          /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1           /* overall y shift for REP_PROJ_3D representation */
+
+```
+
+### 3 December 22 - A shear flow with an airfoil-shaped obstacle ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.0, 0.1, 1, 1, 0.0, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 198       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.15	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+#define EULER_GRADIENT_YSHIFT 0.0    /* y-shift in computation of gradient in Euler equation */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2650       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 2 December 22 - Deep inpact 5: Comparing a round and a rectangular obstacle ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 0     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 0  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN -1.1
+#define INITYMAX 0.15	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 19    /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1700      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 250     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 350     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 10.0          /* damping coefficient of particles */
+#define INITIAL_DAMPING 35.0  /* damping coefficient of particles during initial phase */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1500.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 750.0    /* mass of segment group */
+#define SEGMENT_GROUP_I 500.0       /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 1 December 22 - 45 degrees are not always optimal: Solving a 16 by 32 maze with laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, 0.01, 0.00*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */ 
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 6000     /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 1  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 32      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
diff --git a/Parameters_November22.md b/Parameters_November22.md
new file mode 100644
index 0000000..a9c1ec3
--- /dev/null
+++ b/Parameters_November22.md
@@ -0,0 +1,7380 @@
+### Parameter values for YouTube simulations ###
+
+Created by **Nils Berglund** and optimized by **Marco Mancini**
+
+C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
+
+Below are parameter values used for different simulations, as well as initial conditions used in 
+function animation. Some simulations use variants of the published code. The list is going to be 
+updated gradually. 
+
+
+### 30 November 22 - 3D view of a wave refracted on a chessboard ###
+
+**Program:** `wave_3d.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);
+    add_circular_wave_mod(sign, 0.0, 0.0, phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 2730          /* number of grid points on x axis */
+#define NY 1500          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1        /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 0.8 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 55        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 2   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define VARIABLE_IOR 0      /* set to 1 for a variable index of refraction */
+#define IOR 2               /* choice of index of refraction, see list in global_pdes.c */
+#define MANDEL_IOR_SCALE -0.05   /* parameter controlling dependence of IoR on Mandelbrot escape speed */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 2.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 16           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 3  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.001       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8     /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0       /* damping of periodic excitation */
+#define COURANT 0.05      /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0            /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50     /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+#define PRECOMPUTE_BC 0     /* set to 1 to compute neighbours for Laplacian in advance */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1200        /* number of frames of movie */
+#define NVID 5            /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* set to 1 to print speed of moving source */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 100    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+#define ROTATE_VIEW_WHILE_FADE 1    /* set to 1 to keep rotating viewpoint during fade */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+
+/* Plot type, see list in global_pdes.c  */
+
+#define ZPLOT 103     /* wave height */
+#define CPLOT 103     /* color scheme */
+
+#define ZPLOT_B 107 
+#define CPLOT_B 107        /* plot type for second movie */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define FLOOR_ZCOORD 1          /* set to 1 to draw only facets with z not too negative */
+#define DRAW_BILLIARD 1         /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1   /* set to 1 to draw front of boundary after drawing wave */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw construction lines of certain domains */
+#define FADE_IN_OBSTACLE 1      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental, draw outside of billiard in gray */
+
+#define PLOT_SCALE_ENERGY 0.01         /* vertical scaling in energy plot */
+#define PLOT_SCALE_LOG_ENERGY 0.25       /* vertical scaling in log energy plot */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+#define ROTATE_VIEW 1       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 17      /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13    /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.0   /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define VSCALE_ENERGY 100.0     /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0    /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.5      /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.5      /* shift of colors on log scale */
+#define LOG_ENERGY_FLOOR -10.0    /* floor value for log of (total) energy */
+#define LOG_MEAN_ENERGY_SHIFT 1.0   /* additional shift for log of mean energy */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 240.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -200.0    /* amplitude of variation of hue for color scheme C_HUE */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1       /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0     /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+/* Parameters controlling 3D projection */
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.35    /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 2.4   /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0         /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1          /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1           /* overall y shift for REP_PROJ_3D representation */
+
+```
+
+### 29 November 22 - A shear flow with an elliptical obstacle ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.02, 0.05, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 199       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.2	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2500       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 28 November 22 - A cave-in with square grains of sand ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN 0.05
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8  /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 18     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 1         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 2       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 4.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.5  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.014 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 4000      /* number of frames of movie */
+#define NVID 75         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 1
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 4
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 0  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 17     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 2.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 4.5e-6    /* time step for particle displacement */
+#define KREPEL 0.5          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 3.5    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 15.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 200.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.5      /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5        /* radius in which to count neighbours */
+#define GRAVITY 4000.0             /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 1           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 20.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 27 November 22 - Shining a rotating laser beam into a 16 by 16 maze ###
+
+**Program:** `particle_trajectory.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    x = -1.65;
+    y = 0.07;
+    alpha = angle_schedule(time);        
+    period = compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length, &xmax); 
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 6   /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 50000        /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 50000        /* total number of sides of polygonal line */   
+#define NCX 9             /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 2            /* Sierpinski gastket depth */
+
+#define LAMBDA -1.1	/* parameter controlling shape of domain */
+#define MU 0.1          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 3             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 1         /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define TRAJ_LENGTH 10000 /* length of trajectory */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 0    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+#define PRINT_TRAJECTORY_LENGTH 1   /* set to 1 to print length of trajectory 0 */
+#define PRINT_TRAJECTORY_ANGLE 1    /* set to 1 to print angle of trajectory 0 */
+#define PRINT_TRAJECTORY_PERIOD 0   /* set to 1 to print period of trajectory 0 */
+#define DRAW_LENGTHS_PLOT 1         /* set to 1 to plot trajectory lengths */
+#define LENGTHS_LOG_SCALE 1         /* set to 1 to use log scale for plot of lengths */
+#define MIN_ANGLE 40.0         /* range of angles of trajectory */
+#define MAX_ANGLE 50.0         /* range of angles of trajectory */
+#define TEST_INITIAL_COND 1     /* set to 1 to allow only initial conditions that pass a test */
+
+#define SLOW_AT_LONG_TRAJ 0     /* set to 1 to slow down movie for long trajectories */
+#define ADD_SUCCESS_GALLERY 1   /* set to 1 to add gallery of successful trajectories at end of movie */
+#define SUCCESS_GALLERY_FRAMES 25   /* number of frames per success */
+
+#define NSTEPS 3500      /* number of frames of movie */
+#define TIME 2500         /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00001     /* integration step */
+#define NVID 150         /* number of iterations between images displayed on screen */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500       /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.03       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+#define GRAPH_HUE 100.0     /* color hue of graph */
+#define SUCCESS_HUE 150.0   /* color hue of success */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 250       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define END_FRAMES  100   /* number of frames at end of movie */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 16     /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1       /* seed of random number generator */
+#define MAZE_XSHIFT -0.5     /* horizontal shift of maze */
+
+```
+
+### 26 November 22 - Refraction of a wave on a honeycomb lattice with inverted wave speeds ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_circular_wave(0.0, 0.0, phi, psi, xy_in);`
+    add_circular_wave(sign, 0.0, 0.0, phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 57        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1700       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 13     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 18     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 100.0     /* scaling factor for energy representation */
+#define LOG_SCALE 0.25     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 7.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 25 November 22 - An incompressible flow in a maze ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_laminar_flow(1.0, 1.0, 1.0, 0.5, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 53       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.2	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3800       /* number of frames of movie */
+#define NVID 80           /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 14       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 0        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 24 November 22 - Modeling a cave-in with Lennard-Jones particles, version with stronger damping ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN 0.05
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8  /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 18     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.008 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 6000      /* number of frames of movie */
+#define NVID 150         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 1
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 0  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 1.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 4.5e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 3.7    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 15.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 250.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5        /* radius in which to count neighbours */
+#define GRAVITY 2500.0             /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 180   /* size of hashgrid in x direction */
+#define HASHY 90    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 23 November 22 - Solving a 48 by 48 maze with laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, -0.01, 0.15*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 10700     /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 17     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 500      /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 48      /* width of maze */
+#define NYMAZE 48      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
+### 22 November 22 - Refraction of a wave on a honeycomb lattice ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** 
+
+```
+    init_circular_wave(0.0, 0.0, phi, psi, xy_in);
+    add_circular_wave(sign, 0.0, 0.0, phi, psi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 57        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.25	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.1        /* Courant number */
+#define COURANTB 0.05      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0         /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50    /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.35         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 14     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 12     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 200.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 7.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 21 November 22 - A shear flow with an obstacle ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.15, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 3       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.2	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2700       /* number of frames of movie */
+#define NVID 60           /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 10       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 20 November 22 - Modeling a cave-in with Lennard-Jones particles ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN 0.05
+#define INITYMAX 1.1	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8  /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 18     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.008 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 5000      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 1
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 0    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 0    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 0  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 1.5e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 3.7    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 15.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 100.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5        /* radius in which to count neighbours */
+#define GRAVITY 2500.0             /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 180   /* size of hashgrid in x direction */
+#define HASHY 90    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 19 November 22 - Solving a 30 by 30 maze with laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, -0.01, 0.15*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 8600      /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 0     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 1024       /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 3    /* width of billiard */
+#define PARTICLE_WIDTH 3    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 30      /* width of maze */
+#define NYMAZE 30      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
+### 18 November 22 - 2D view of an annular waveguide ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave(-0.85, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 0   /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 7        /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.7	    /* parameter controlling the dimensions of domain */
+#define MU 0.0              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.06      /* Courant number */
+#define COURANTB 0.15     /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.015            /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 0        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 1     /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2000       /* number of frames of movie */
+#define NVID 15          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.75         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+
+#define PLOT_B 4        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 17     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 12     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 500.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 20.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 17 November 22 - A visualisation with tracers of interacting vortices in the Euler equation  ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_vortex_state(0.25, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(0.8, 0.3, -0.15, phi, xy_in);
+    add_vortex_state(1.5, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(-0.3, 0.3, -0.15, phi, xy_in);
+    add_vortex_state(-0.75, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(-1.55, 0.3, -0.15, phi, xy_in);
+
+    add_vortex_state(0.3, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(0.75, -0.25, 0.15, phi, xy_in);
+    add_vortex_state(1.55, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(-0.25, -0.25, 0.15, phi, xy_in);
+    add_vortex_state(-0.8, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(-1.5, -0.25, 0.15, phi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.01     /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2800       /* number of frames of movie */
+#define NVID 120          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+// #define ZPLOT 32     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 17       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 16 November 22 - Solving a 16 by 16 maze with laser beams ###
+
+**Program:** `particle_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_drop_config(-1.15, 0.07, -0.3*PI, 0.3*PI, configs);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 30     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 1    /* pattern of circles */
+#define POLYLINE_PATTERN 10  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 100000     /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 100000        /* total number of sides of polygonal line */   
+#define NCX 30            /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 1            /* Sierpinski gastket depth */
+
+#define LAMBDA 1.5	/* parameter controlling shape of domain */
+#define MU 0.5          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define PENROSE_RATIO 2.5    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 0   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 10000     /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 1    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */
+#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */
+#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+
+#define TEST_INITIAL_COND 0     /* set to 1 to allow only initial conditions that pass a test */
+
+#define NSTEPS 7500      /* number of frames of movie */
+#define TIME 1500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00002     /* integration step */
+#define NVID 25          /* number of iterations between images displayed on screen */
+#define END_FRAMES 25    /* number of still frames at the end of the movie */
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 16       /* number of colors */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define RAINBOW_COLOR 1  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.04       /* length of velocity vectors */
+#define BILLIARD_WIDTH 3    /* width of billiard */
+#define PARTICLE_WIDTH 3    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1       /* final sleeping time */
+
+#define NXMAZE 16      /* width of maze */
+#define NYMAZE 16     /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 1        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+```
+
+### 15 November 22 - Rocket comparison 12: Glas-shaped vs trumpet-shaped nozzle, with a background grid  ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -3.3
+#define XMAX 4.7	/* x interval */
+#define YMIN -2.25
+#define YMAX 2.25	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -2.5
+#define INITXMAX 2.5	/* x interval for initial condition */
+#define INITYMIN -1.7
+#define INITYMAX 0.7	/* y interval for initial condition */
+
+#define BCXMIN -5.1
+#define BCXMAX 6.1	/* x interval for boundary condition */
+#define BCYMIN -6.5
+#define BCYMAX 44.0	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 102     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 2        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 4      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3500      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 10     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 20
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define ALTITUDE_LINES 1    /* set to 1 to add horizontal lines to show altitude */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 2.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.5    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 5.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 1        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 15.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 1  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 2000   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1300    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 1       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 1     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 450    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 14 November 22 - A visualisation of a shear flow with tracers ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.03, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+#define SAVE_MEMORY 1           /* set to 1 to save memory when writing tiff images */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.03      /* factor by which to smoothen */
+
+#define ADD_TRACERS 1    /* set to 1 to add tracer particles (for Euler equations) */
+#define N_TRACERS 1000    /* number of tracer particles */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3700       /* number of frames of movie */
+#define NVID 60           /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 11       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 13 November 22 - Energy flux of waves crossing a maze ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave(-1.5, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 1920          /* number of grid points on x axis */
+#define NY 1000          /* number of grid points on x axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 0       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 53       /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 0.3              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 5.0e-3           /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 1     /* period of oscillating source */
+#define ALTERNATE_OSCILLATING_SOURCE 1  /* set to 1 to alternate sign of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2400       /* number of frames of movie */
+#define NVID 20          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.005  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 7
+
+#define PLOT_B 6        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 18     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 5000.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define FLUX_SCALE 1.0e4    /* scaling factor for enegy flux represtnation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 1.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 12 November 22 - Deep impact 4: Dropping a rectangle in a Lennard-Jones fluid ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 0     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 0  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN -1.05
+#define INITYMAX -0.25	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 16    /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.3	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 300     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 15.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1000.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 0.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 0           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 11 November 22 - Several interacting vortices in the Euler equation ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** 
+```
+    init_vortex_state(0.25, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(0.8, 0.3, -0.15, phi, xy_in);
+    add_vortex_state(1.5, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(-0.3, 0.3, -0.15, phi, xy_in);
+    add_vortex_state(-0.75, 0.25, 0.15, phi, xy_in);
+    add_vortex_state(-1.55, 0.3, -0.15, phi, xy_in);
+
+    add_vortex_state(0.3, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(0.75, -0.25, 0.15, phi, xy_in);
+    add_vortex_state(1.55, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(-0.25, -0.25, 0.15, phi, xy_in);
+    add_vortex_state(-0.8, -0.3, -0.15, phi, xy_in);
+    add_vortex_state(-1.5, -0.25, 0.15, phi, xy_in);
+```
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1800       /* number of frames of movie */
+#define NVID 80          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 17       /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 1.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 2.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 3.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 10 November 22 - Refraction of a wave on a grid of triangles ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 56       /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.75	    /* parameter controlling the dimensions of domain */
+#define MU 0.3              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0           /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50     /* period of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2800       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 14     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 200.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 5.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 9 November 22 - Deep impact 3: Dropping a disc in a Lennard-Jones fluid ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 0     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 0  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -1.95
+#define INITXMAX 1.95	/* x interval for initial condition */
+#define INITYMIN -1.05
+#define INITYMAX -0.25	/* y interval for initial condition */
+
+#define BCXMIN -2.0
+#define BCXMAX 2.0	/* x interval for boundary condition */
+#define BCYMIN -1.125
+#define BCYMAX 1.125	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 9     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 3.0  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.2	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1600      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 200     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 300     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 0
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 3.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.0    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 15.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 0        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 1000.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 0  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 0     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 0.0        /* initial position of segments */
+#define SEGMENTS_Y0 0.8        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 0           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 0             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 0      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 0       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 0     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 60    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 8 November 22 - Periodicised view of a 2D shear flow rendered in 3D ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.02, 0.05, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2000       /* number of frames of movie */
+#define NVID 80          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 1    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+#define DRAW_PERIODICISED 1     /* set to 1 to repeat wave periodically in x and y directions */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 11     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0   
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 6.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 5.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.7  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 0       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 7 November 22 - Phase space representation of a Bunimovich flower billiard ###
+
+**Program:** `billiard_phase_space.c` 
+
+**Initial condition in function `animation()`:** `lyap_exponents[i] = draw_phase_portrait(14, 20, 200, 20, 0.1);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.125
+#define YMAX 1.125	/* y interval for 9/16 aspect ratio */
+
+#define XPHASEMAX 0.0   /* max x coordinate of phase portrait */
+
+#define PIXELIZE 0      /* set to 1 to pixelize phase portrait (beta) */
+#define NGRID 200       /* size of grid to draw orbits with positive Lyapunov exponent */
+
+#define SYMMETRIZE_S 1  /* set to 1 to symmetrize orbits wrt s */
+
+#define SCALING_FACTOR 1.0       /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
+
+/* Choice of the billiard table, see global_particles.c */
+
+#define B_DOMAIN 10     /* choice of domain shape */
+
+#define CIRCLE_PATTERN 6   /* pattern of circles */
+#define POLYLINE_PATTERN 4  /* pattern of polyline */
+
+#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
+
+#define NMAXCIRCLES 50000        /* total number of circles (must be at least NCX*NCY for square grid) */
+#define NMAXPOLY 50000        /* total number of sides of polygonal line */   
+#define NCX 9             /* number of circles in x direction */
+#define NCY 20            /* number of circles in y direction */
+#define NPOISSON 500        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define NGOLDENSPIRAL 2000  /* max number of points for C_GOLDEN_SPIRAL arrandement */
+#define SDEPTH 2            /* Sierpinski gastket depth */
+
+#define LAMBDAMIN 0.5	/* parameter controlling shape of domain */
+#define LAMBDA 1.2	/* parameter controlling shape of domain */
+#define MU 0.1          /* second parameter controlling shape of billiard */
+#define FOCI 1          /* set to 1 to draw focal points of ellipse */
+#define NPOLY 7             /* number of sides of polygon */
+#define APOLY -1.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define DRAW_BILLIARD 1     /* set to 1 to draw billiard */
+#define DRAW_CONSTRUCTION_LINES 1   /* set to 1 to draw additional construction lines for billiard */
+#define PERIODIC_BC 0       /* set to 1 to enforce periodic boundary conditions when drawing particles */
+#define PENROSE_RATIO 1.0    /* parameter controlling the shape of small ellipses in Penrose room */
+
+#define RESAMPLE 0      /* set to 1 if particles should be added when dispersion too large */
+#define DEBUG 0         /* draw trajectories, for debugging purposes */
+
+/* Simulation parameters */
+
+#define NPART 1         /* number of particles */
+#define NPARTMAX 100000	/* maximal number of particles after resampling */
+#define TRAJ_LENGTH 10000 /* length of trajectory */
+#define LMAX 0.01       /* minimal segment length triggering resampling */ 
+#define DMIN 0.02       /* minimal distance to boundary for triggering resampling */ 
+#define CYCLE 1         /* set to 1 for closed curve (start in all directions) */
+#define SHOWTRAILS 0    /* set to 1 to keep trails of the particles */
+#define SHOWZOOM 0      /* set to 1 to show zoom on specific area */
+#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */
+#define PRINT_TRAJECTORY_LENGTH 0   /* set to 1 to print length of trajectory 0 */
+#define PRINT_TRAJECTORY_PERIOD 0   /* set to 1 to print period of trajectory 0 */
+#define DRAW_LENGTHS_PLOT 0         /* set to 1 to plot trajectory lengths */
+#define LENGTHS_LOG_SCALE 1         /* set to 1 to use log scale for plot of lengths */
+#define MAX_ANGLE 90.0         /* range of angles of trajectory */
+
+#define NSTEPS 3400      /* number of frames of movie */
+// #define NSTEPS 500       /* number of frames of movie */
+#define TIME 2500        /* time between movie frames, for fluidity of real-time simulation */ 
+#define DPHI 0.00001     /* integration step */
+#define NVID 150         /* number of iterations between images displayed on screen */
+#define SYMMETRIC_PARAMETER 1    /* set to 1 if parameters depend symmetrically on time */ 
+
+/* Decreasing TIME accelerates the animation and the movie                               */
+/* For constant speed of movie, TIME*DPHI should be kept constant                        */
+/* However, increasing DPHI too much deterioriates quality of simulation                 */
+/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
+/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100    */
+
+/* Colors and other graphical parameters */
+
+#define COLOR_PALETTE 17     /* Color palette, see list in global_pdes.c  */
+
+#define NCOLORS 64       /* number of colors */
+#define CFACTOR 3        /* color step */
+#define COLORSHIFT 0     /* hue of initial color */ 
+#define LYAP_PLOT_COLOR 100.0   /* color hue of Lyapunov exponent plot */
+#define RAINBOW_COLOR 0  /* set to 1 to use different colors for all particles */
+#define FLOWER_COLOR 0   /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
+#define NSEG 100         /* number of segments of boundary */
+#define LENGTH 0.03       /* length of velocity vectors */
+#define BILLIARD_WIDTH 2    /* width of billiard */
+#define PARTICLE_WIDTH 2    /* width of particles */
+#define FRONT_WIDTH 3       /* width of wave front */
+
+#define BLACK 1             /* set to 1 for black background */
+#define COLOR_OUTSIDE 0     /* set to 1 for colored outside */ 
+#define OUTER_COLOR 270.0   /* color outside billiard */
+#define PAINT_INT 0         /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
+#define PAINT_EXT 1         /* set to 1 to paint exterior */
+
+#define PRINT_LAMBDA 1      /* set to 1 to print value of lambda */
+#define PRINT_MU 0          /* set to 1 to print value of mu */
+#define PRINT_PENROSE_RATIO 0      /* set to 1 to print value of the Penrose billiard ratio */
+#define PRINT_LYAPUNOV 1    /* set to 1 to print mean Lyapunov exponent */
+#define PLOT_LYAPUNOV 1     /* set to 1 to add plot of Lyapunov exponents */
+#define LOGSCALEX_LYAP 0    /* set to 1 to use log scale on parameter axis of Lyapunov exponents */
+#define LYAP_MAX 0.7        /* maximal Lyapunov exponent */
+
+#define PAUSE 1000       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define END_FRAMES  100   /* number of frames at end of movie */
+
+```
+
+### 6 November 22 - Refraction of a wave on a chessboard ###
+
+**Program:** `wave_billiard.c` 
+
+**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 3840          /* number of grid points on x axis */
+#define NY 2000          /* number of grid points on y axis */
+
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval  */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+#define HIGHRES 1       /* set to 1 if resolution of grid is double that of displayed image */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 55       /* choice of domain shape, see list in global_pdes.c */
+
+#define CIRCLE_PATTERN 1   /* pattern of circles or polygons, see list in global_pdes.c */
+
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.5	    /* parameter controlling the dimensions of domain */
+#define MU 0.3              /* parameter controlling the dimensions of domain */
+#define NPOLY 6             /* number of sides of polygon */
+#define APOLY 0.0           /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 6            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 12           /* number of grid point for grid of disks */
+#define NGRIDY 15           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -2.9
+#define ISO_XSHIFT_RIGHT 1.4
+#define ISO_YSHIFT_LEFT -0.15
+#define ISO_YSHIFT_RIGHT -0.15 
+#define ISO_SCALE 0.5           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define TWOSPEEDS 1          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OSCILLATE_LEFT 0     /* set to 1 to add oscilating boundary condition on the left */
+#define OSCILLATE_TOPBOT 0   /* set to 1 to enforce a planar wave on top and bottom boundary */
+#define OSCILLATION_SCHEDULE 1  /* oscillation schedule, see list in global_pdes.c */
+
+#define OMEGA 0.0005       /* frequency of periodic excitation */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.25        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COURANT 0.05        /* Courant number */
+#define COURANTB 0.1      /* Courant number in medium B */
+#define GAMMA 0.0          /* damping factor in wave equation */
+#define GAMMAB 0.0           /* damping factor in wave equation */
+#define GAMMA_SIDES 1.0e-4      /* damping factor on boundary */
+#define GAMMA_TOPBOT 1.0e-7     /* damping factor on boundary */
+#define KAPPA 0.0           /* "elasticity" term enforcing oscillations */
+#define KAPPA_SIDES 5.0e-4  /* "elasticity" term on absorbing boundary */
+#define KAPPA_TOPBOT 0.0    /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+#define ADD_OSCILLATING_SOURCE 1        /* set to 1 to add an oscillating wave source */
+#define OSCILLATING_SOURCE_PERIOD 50     /* period of oscillating source */
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 2
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2100       /* number of frames of movie */
+#define NVID 12          /* number of iterations between images displayed on screen */
+#define NSEG 1000         /* number of segments of boundary */
+#define INITIAL_TIME 0      /* time after which to start saving frames */
+#define BOUNDARY_WIDTH 2    /* width of billiard boundary */
+#define PRINT_SPEED 0       /* print speed of moving source */
+
+#define PAUSE 200       /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Parameters of initial condition */
+
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.01  /* wavelength of initial condition */
+
+/* Plot type, see list in global_pdes.c  */
+
+#define PLOT 0
+
+#define PLOT_B 5        /* plot type for second movie */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 17     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 13     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_pdes.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define PHASE_FACTOR 1.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 200.0     /* scaling factor for energy representation */
+#define LOG_SCALE 1.0     /* scaling factor for energy log representation */
+#define LOG_SHIFT 0.0     /* shift of colors on log scale */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 180.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -180.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+#define DRAW_COLOR_SCHEME 1    /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 1.5     /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 5.5    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+/* for compatibility with sub_wave and sub_maze */
+#define ADD_POTENTIAL 0
+#define POT_MAZE 7
+#define POTENTIAL 0
+/* end of constants only used by sub_wave and sub_maze */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+```
+
+### 5 November 22 - Rocket comparison 11: Bell-shaped vs narrow straight nozzle, with higher moments of inertia ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -3.3
+#define XMAX 4.7	/* x interval */
+#define YMIN -2.25
+#define YMAX 2.25	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -2.5
+#define INITXMAX 2.5	/* x interval for initial condition */
+#define INITYMIN -1.7
+#define INITYMAX 0.7	/* y interval for initial condition */
+
+#define BCXMIN -5.1
+#define BCXMAX 6.1	/* x interval for boundary condition */
+#define BCYMIN -6.5
+#define BCYMAX 44.0	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 102     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3300      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 10     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 20
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 2.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.5    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 5.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 1        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 15.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 1  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 1000.0      /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 1       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 1     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 450    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 4 November 22 - A 2D shear flow rendered in 3D ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.02, 0.05, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.05      /* factor by which to smoothen */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1600       /* number of frames of movie */
+#define NVID 100          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 1    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 11     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+#define LOG_MIN 1.0e-3   /* floor value for log vorticity plot */
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 6.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 5.0   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.08  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.8  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.1          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 2       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 3 November 22 - Rocket comparison 10: Bell-shaped vs narrow straight nozzle ###
+
+**Program:** `lennardjones.c` 
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 0  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+#define TIME_LAPSE 1     /* set to 1 to add a time-lapse movie at the end */
+                         /* so far incompatible with double movie */
+#define TIME_LAPSE_FACTOR 3    /* factor of time-lapse movie */
+#define TIME_LAPSE_FIRST 1  /* set to 1 to show time-lapse version first */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define XMIN -3.3
+#define XMAX 4.7	/* x interval */
+#define YMIN -2.25
+#define YMAX 2.25	/* y interval for 9/16 aspect ratio */
+
+#define INITXMIN -2.5
+#define INITXMAX 2.5	/* x interval for initial condition */
+#define INITYMIN -1.7
+#define INITYMAX 0.7	/* y interval for initial condition */
+
+#define BCXMIN -5.1
+#define BCXMAX 6.1	/* x interval for boundary condition */
+#define BCYMIN -6.5
+#define BCYMAX 44.0	/* y interval for boundary condition */
+
+#define OBSXMIN -2.0
+#define OBSXMAX 2.0     /* x interval for motion of obstacle */
+
+#define CIRCLE_PATTERN 8   /* pattern of circles, see list in global_ljones.c */
+
+#define ADD_FIXED_OBSTACLES 0   /* set to 1 do add fixed circular obstacles */
+#define OBSTACLE_PATTERN 3  /* pattern of obstacles, see list in global_ljones.c */
+
+#define ADD_FIXED_SEGMENTS 1    /* set to 1 to add fixed segments as obstacles */
+#define SEGMENT_PATTERN 102     /* pattern of repelling segments, see list in global_ljones.c */
+#define ROCKET_SHAPE 2        /* shape of rocket combustion chamber, see list in global_ljones.c */
+#define ROCKET_SHAPE_B 2      /* shape of second rocket */
+#define NOZZLE_SHAPE 1        /* shape of nozzle, see list in global_ljones.c */
+#define NOZZLE_SHAPE_B 0      /* shape of nozzle for second rocket, see list in global_ljones.c */
+
+#define TWO_TYPES 0         /* set to 1 to have two types of particles */
+#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */
+#define SYMMETRIZE_FORCE 1  /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */
+#define CENTER_PX 0         /* set to 1 to center horizontal momentum */
+#define CENTER_PY 0         /* set to 1 to center vertical momentum */
+#define CENTER_PANGLE 0     /* set to 1 to center angular momentum */
+
+#define INTERACTION 1       /* particle interaction, see list in global_ljones.c */
+#define INTERACTION_B 1     /* particle interaction for second type of particle, see list in global_ljones.c */
+#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */
+#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 100        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define PDISC_DISTANCE 2.7  /* minimal distance in Poisson disc process, controls density of particles */
+#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 0.8	    /* parameter controlling the dimensions of domain */
+#define MU 0.009 	    /* parameter controlling radius of particles */
+#define MU_B 0.018          /* parameter controlling radius of particles of second type */
+#define NPOLY 25            /* number of sides of polygon */
+#define APOLY 0.666666666   /* angle by which to turn polygon, in units of Pi/2 */ 
+#define MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000    /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0    /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 90           /* number of grid point for grid of disks */
+#define NGRIDY 100           /* number of grid point for grid of disks */
+#define EHRENFEST_RADIUS 0.9    /* radius of container for Ehrenfest urn configuration */
+#define EHRENFEST_WIDTH 0.035     /* width of tube for Ehrenfest urn configuration */
+#define TWO_CIRCLES_RADIUS_RATIO 0.8    /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */
+#define DAM_WIDTH 0.05       /* width of dam for S_DAM segment configuration */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 3300      /* number of frames of movie */
+#define NVID 100         /* number of iterations between images displayed on screen */
+#define NSEG 250         /* number of segments of boundary */
+#define INITIAL_TIME 10     /* time after which to start saving frames */
+#define OBSTACLE_INITIAL_TIME 200     /* time after which to start moving obstacle */
+#define BOUNDARY_WIDTH 1    /* width of particle boundary */
+#define LINK_WIDTH 2        /* width of links between particles */
+#define CONTAINER_WIDTH 4   /* width of container boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+#define MID_FRAMES 20    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 100   /* number of still frames at end of movie */
+
+/* Boundary conditions, see list in global_ljones.c */
+
+#define BOUNDARY_COND 20
+
+/* Plot type, see list in global_ljones.c  */
+
+#define PLOT 0
+#define PLOT_B 8        /* plot type for second movie */
+
+#define DRAW_BONDS 0    /* set to 1 to draw bonds between neighbours */
+#define COLOR_BONDS 1   /* set to 1 to color bonds according to length */
+#define FILL_TRIANGLES 1    /* set to 1 to fill triangles between neighbours */
+#define COLOR_SEG_GROUPS 1  /* set to 1 to collor segment groups differently */
+
+/* Color schemes */
+
+#define COLOR_PALETTE 10     /* Color palette, see list in global_ljones.c  */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme, see list in global_ljones.c  */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 0.5        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 220.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -50.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* particle properties */
+
+#define ENERGY_HUE_MIN 330.0        /* color of original particle */
+#define ENERGY_HUE_MAX 50.0         /* color of saturated particle */
+#define PARTICLE_HUE_MIN 359.0      /* color of original particle */
+#define PARTICLE_HUE_MAX 0.0        /* color of saturated particle */
+#define PARTICLE_EMAX 2.0e2         /* energy of particle with hottest color */
+#define HUE_TYPE0 70.0     /* hue of particles of type 0 */
+#define HUE_TYPE1 280.0      /* hue of particles of type 1 */
+#define HUE_TYPE2 .0      /* hue of particles of type 2 */
+#define HUE_TYPE3 210.0     /* hue of particles of type 3 */
+
+#define RANDOM_RADIUS 0     /* set to 1 for random circle radius */
+#define DT_PARTICLE 3.0e-6    /* time step for particle displacement */
+#define KREPEL 12.0          /* constant in repelling force between particles */
+#define EQUILIBRIUM_DIST 4.5    /* Lennard-Jones equilibrium distance */
+#define EQUILIBRIUM_DIST_B 3.5  /* Lennard-Jones equilibrium distance for second type of particle */
+#define REPEL_RADIUS 20.0    /* radius in which repelling force acts (in units of particle radius) */
+#define DAMPING 5.0          /* damping coefficient of particles */
+#define PARTICLE_MASS 1.0    /* mass of particle of radius MU */
+#define PARTICLE_MASS_B 1.0   /* mass of particle of radius MU */
+#define PARTICLE_INERTIA_MOMENT 0.2     /* moment of inertia of particle */
+#define PARTICLE_INERTIA_MOMENT_B 0.02     /* moment of inertia of second type of particle */
+#define V_INITIAL 0.0        /* initial velocity range */
+#define OMEGA_INITIAL 10.0        /* initial angular velocity range */
+
+#define THERMOSTAT 1        /* set to 1 to switch on thermostat */
+#define VARY_THERMOSTAT 0   /* set to 1 for time-dependent thermostat schedule */
+#define SIGMA 5.0           /* noise intensity in thermostat */
+#define BETA 0.02          /* initial inverse temperature */
+#define MU_XI 0.01           /* friction constant in thermostat */
+#define KSPRING_BOUNDARY 1.0e7    /* confining harmonic potential outside simulation region */
+#define KSPRING_OBSTACLE 1.0e11    /* harmonic potential of obstacles */
+#define NBH_DIST_FACTOR 7.5       /* radius in which to count neighbours */
+#define GRAVITY 15.0            /* gravity acting on all particles */
+#define GRAVITY_X 0.0        /* horizontal gravity acting on all particles */
+#define INCREASE_GRAVITY 0     /* set to 1 to increase gravity during the simulation */
+#define GRAVITY_SCHEDULE 2     /* type of gravity schedule, see list in global_ljones.c */
+#define GRAVITY_FACTOR 100.0    /* factor by which to increase gravity */
+#define GRAVITY_INITIAL_TIME 200    /* time at start of simulation with constant gravity */
+#define GRAVITY_RESTORE_TIME 700    /* time at end of simulation with gravity restored to initial value */
+
+#define ROTATION 0           /* set to 1 to include rotation of particles */
+#define COUPLE_ANGLE_TO_THERMOSTAT 0    /* set to 1 to couple angular degrees of freedom to thermostat */
+#define DIMENSION_FACTOR 1.0  /* scaling factor taking into account number of degrees of freedom */  
+#define KTORQUE 100.0          /* force constant in angular dynamics */
+#define KTORQUE_B 10.0        /* force constant in angular dynamics */
+#define KTORQUE_DIFF 150.0    /* force constant in angular dynamics for different particles */
+#define DRAW_SPIN 0           /* set to 1 to draw spin vectors of particles */
+#define DRAW_SPIN_B 0         /* set to 1 to draw spin vectors of particles */
+#define DRAW_CROSS 1          /* set to 1 to draw cross on particles of second type */
+#define SPIN_RANGE 7.0       /* range of spin-spin interaction */
+#define SPIN_RANGE_B 5.0     /* range of spin-spin interaction for second type of particle */
+#define QUADRUPOLE_RATIO 0.6  /* anisotropy in quadrupole potential */ 
+
+#define INCREASE_BETA 1  /* set to 1 to increase BETA during simulation */
+#define BETA_FACTOR 0.025   /* factor by which to change BETA during simulation */
+#define N_TOSCILLATIONS 1.5   /* number of temperature oscillations in BETA schedule */
+#define NO_OSCILLATION 1        /* set to 1 to have exponential BETA change only */
+#define MIDDLE_CONSTANT_PHASE 1600   /* final phase in which temperature is constant */
+#define FINAL_DECREASE_PHASE 1500    /* final phase in which temperature decreases */ 
+#define FINAL_CONSTANT_PHASE -1     /* final phase in which temperature is constant */
+
+#define DECREASE_CONTAINER_SIZE 0   /* set to 1 to decrease size of container */
+#define SYMMETRIC_DECREASE 0        /* set tp 1 to decrease container symmetrically */
+#define COMPRESSION_RATIO 0.3       /* final size of container */
+#define RESTORE_CONTAINER_SIZE 1    /* set to 1 to restore container to initial size at end of simulation */
+#define RESTORE_TIME 700            /* time before end of sim at which to restore size */
+
+#define MOVE_OBSTACLE 0     /* set to 1 to have a moving obstacle */
+#define CENTER_VIEW_ON_OBSTACLE 0   /* set to 1 to center display on moving obstacle */
+#define RESAMPLE_Y 0         /* set to 1 to resample y coordinate of moved particles (for shock waves) */
+#define NTRIALS 2000         /* number of trials when resampling */
+#define OBSTACLE_RADIUS 0.12  /* radius of obstacle for circle boundary conditions */
+#define FUNNEL_WIDTH  0.25   /* funnel width for funnel boundary conditions */
+#define OBSTACLE_XMIN 0.0    /* initial position of obstacle */
+#define OBSTACLE_XMAX 3.0    /* final position of obstacle */
+#define RECORD_PRESSURES 0   /* set to 1 to record pressures on obstacle */
+#define N_PRESSURES 100      /* number of intervals to record pressure */
+#define N_P_AVERAGE 100      /* size of pressure averaging window */
+#define N_T_AVERAGE 50       /* size of temperature averaging window */
+#define MAX_PRESSURE 3.0e10  /* pressure shown in "hottest" color */
+#define PARTIAL_THERMO_COUPLING 0   /* set to 1 to couple only particles to the right of obstacle to thermostat */
+#define PARTIAL_THERMO_REGION 1     /* region for partial thermostat coupling (see list in global_ljones.c) */
+#define PARTIAL_THERMO_SHIFT 0.2    /* distance from obstacle at the right of which particles are coupled to thermostat */
+#define PARTIAL_THERMO_WIDTH 0.5    /* vertical size of partial thermostat coupling */
+#define PARTIAL_THERMO_HEIGHT 0.2   /* vertical size of partial thermostat coupling */
+
+#define INCREASE_KREPEL 0   /* set to 1 to increase KREPEL during simulation */
+#define KREPEL_FACTOR 1000.0   /* factor by which to change KREPEL during simulation */
+
+#define PART_AT_BOTTOM 0     /* set to 1 to include "seed" particles at bottom */
+#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */
+#define NPART_BOTTOM 100     /* number of particles at the bottom */
+
+#define ADD_PARTICLES 0    /* set to 1 to add particles */
+#define ADD_TIME 0       /* time at which to add first particle */
+#define ADD_PERIOD 10000       /* time interval between adding further particles */
+#define FINAL_NOADD_PERIOD 200  /* final period where no particles are added */
+#define SAFETY_FACTOR 2.0  /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */
+
+#define TRACER_PARTICLE 0   /* set to 1 to have a tracer particle */
+#define N_TRACER_PARTICLES 3    /* number of tracer particles */
+#define TRAJECTORY_LENGTH 8000   /* length of recorded trajectory */
+#define TRACER_PARTICLE_MASS 4.0    /* relative mass of tracer particle */
+#define TRAJECTORY_WIDTH 3      /* width of tracer particle trajectory */
+
+#define ROTATE_BOUNDARY 0           /* set to 1 to rotate the repelling segments */
+#define SMOOTH_ROTATION 1           /* set to 1 to update segments at each time step (rather than at each movie frame) */
+#define PERIOD_ROTATE_BOUNDARY 1000  /* period of rotating boundary */
+#define ROTATE_INITIAL_TIME 0       /* initial time without rotation */
+#define ROTATE_FINAL_TIME 100       /* final time without rotation */
+#define ROTATE_CHANGE_TIME 0.33     /* relative duration of acceleration/deceleration phases */
+#define OMEGAMAX 100.0              /* maximal rotation speed */
+#define PRINT_OMEGA 0               /* set to 1 to print angular speed */
+#define PRINT_PARTICLE_SPEEDS 0     /* set to 1 to print average speeds/momenta of particles */
+#define PRINT_SEGMENTS_SPEEDS 1     /* set to 1 to print velocity of moving segments */
+
+#define MOVE_BOUNDARY 0        /* set to 1 to move repelling segments, due to force from particles */
+#define SEGMENTS_MASS 40.0     /* mass of collection of segments */
+#define DEACTIVATE_SEGMENT 1    /* set to 1 to deactivate last segment after a certain time */
+#define SEGMENT_DEACTIVATION_TIME 200   /* time at which to deactivate last segment */
+#define RELEASE_ROCKET_AT_DEACTIVATION 1    /* set to 1 to limit segments velocity before segment release */
+#define SEGMENTS_X0 1.5        /* initial position of segments */
+#define SEGMENTS_Y0 0.0        /* initial position of segments */
+#define SEGMENTS_VX0 0.0       /* initial velocity of segments */
+#define SEGMENTS_VY0 0.0      /* initial velocity of segments */
+#define DAMP_SEGS_AT_NEGATIVE_Y 0   /* set to 1 to dampen segments when y coordinate is negative */
+
+#define MOVE_SEGMENT_GROUPS 1       /* set to 1 to group segments into moving units */
+#define SEGMENT_GROUP_MASS 1000.0   /* mass of segment group */
+#define SEGMENT_GROUP_I 100.0        /* moment of inertia of segment group */
+#define SEGMENT_GROUP_DAMPING 0.0   /* damping of segment groups */
+#define GROUP_REPULSION 1           /* set to 1 for groups of segments to repel each other */
+#define KSPRING_GROUPS 1.0e11       /* harmonic potential between segment groups */
+#define GROUP_WIDTH 0.05            /* interaction width of groups */
+#define GROUP_G_REPEL 1             /* set to 1 to add repulsion between centers of mass of groups */
+#define GROUP_G_REPEL_RADIUS 1.2    /* radius within which centers of mass of groups repel each other */
+#define TRACK_SEGMENT_GROUPS 1      /* set to 1 for view to track group of segments */
+#define TRACK_X_PADDING 2.0         /* distance from x boundary where tracking starts */
+
+#define POSITION_DEPENDENT_TYPE 0   /* set to 1 to make particle type depend on initial position */
+#define POSITION_Y_DEPENDENCE 0     /* set to 1 for the separation between particles to be horizontal */
+#define PRINT_ENTROPY 0     /* set to 1 to compute entropy */
+
+#define REACTION_DIFFUSION 0    /* set to 1 to simulate a chemical reaction (particles may change type) */
+#define RD_TYPES 3              /* number of types in reaction-diffusion equation */
+#define REACTION_PROB 0.0045      /* probability controlling reaction term */ 
+
+#define PRINT_PARTICLE_NUMBER 0     /* set to 1 to print total number of particles */
+#define PRINT_LEFT 0        /* set to 1 to print certain parameters at the top left instead of right */
+#define PLOT_SPEEDS 1       /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */
+#define PLOT_TRAJECTORIES 1     /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */
+#define VMAX_PLOT_SPEEDS 0.6    /* vertical scale of plot of obstacle speeds */
+
+#define EHRENFEST_COPY 0    /* set to 1 to add equal number of larger particles (for Ehrenfest model) */
+
+#define LID_MASS 1000.0     /* mass of lid for BC_RECTANGLE_LID b.c. */
+#define LID_WIDTH 0.1       /* width of lid for BC_RECTANGLE_LID b.c. */
+#define WALL_MASS 2000.0    /* mass of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_FRICTION 0.0   /* friction on wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_WIDTH 0.1      /* width of wall for BC_RECTANGLE_WALL b.c. */
+#define WALL_VMAX 100.0     /* max speed of wall */
+#define WALL_TIME 0         /* time during which to keep wall */
+
+#define NXMAZE 10      /* width of maze */
+#define NYMAZE 10      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 200      /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define FLOOR_FORCE 1      /* set to 1 to limit force on particle to FMAX */
+#define FMAX 1.0e12         /* maximal force */
+#define FLOOR_OMEGA 0      /* set to 1 to limit particle momentum to PMAX */
+#define PMAX 1000.0        /* maximal force */
+
+#define HASHX 120   /* size of hashgrid in x direction */
+#define HASHY 450    /* size of hashgrid in y direction */
+#define HASHMAX 100  /* maximal number of particles per hashgrid cell */
+#define HASHGRID_PADDING 0.1    /* padding of hashgrid outside simulation window */
+
+#define DRAW_COLOR_SCHEME 0     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 8.0    /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 12.0    /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+```
+
+### 2 November 22 - A shear flow at 60 fps ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.03, 1, 1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+#define NX 960          /* number of grid points on x axis */
+#define NY 500          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 6  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 1   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65 
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.0000012
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.015     /* factor by which to smoothen */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 1
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 4000       /* number of frames of movie */
+#define NVID 50           /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 0    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Plot type - color scheme */
+
+#define CPLOT 52
+#define CPLOT_B 51
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 52     /* z coordinate in 3D plot */
+#define ZPLOT_B 51    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 11     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 17     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 0.5      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.5   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 0.25  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.8  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.0          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 2       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+
+### 1 November 22 - A quantum particle tunneling through a maze ###
+
+**Program:** `rde.c` 
+
+**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.35, 5.0, -2.0, 0.1, phi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+#define DOUBLE_MOVIE 1  /* set to 1 to produce movies for wave height and energy simultaneously */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1920  /* window width */
+#define WINHEIGHT 	1000  /* window height */
+
+#define NX 480          /* number of grid points on x axis */
+#define NY 250          /* number of grid points on y axis */
+ 
+#define XMIN -2.0
+#define XMAX 2.0	/* x interval */
+#define YMIN -1.041666667
+#define YMAX 1.041666667	/* y interval for 9/16 aspect ratio */
+
+/* Choice of simulated equation */
+
+#define RDE_EQUATION 5  /* choice of reaction term, see list in global_3d.c */
+#define NFIELDS 2       /* number of fields in reaction-diffusion equation */
+#define NLAPLACIANS 2   /* number of fields for which to compute Laplacian */
+
+#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodinger equation) */
+#define ADD_MAGNETIC_FIELD 0    /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
+#define POTENTIAL 7     /* type of potential or vector potential, see list in global_3d.c  */
+
+#define ANTISYMMETRIZE_WAVE_FCT 0   /* set tot 1 to make wave function antisymmetric */
+
+#define JULIA_SCALE 0.5 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 999       /* choice of domain shape, see list in global_pdes.c  */
+
+#define CIRCLE_PATTERN 99    /* pattern of circles, see list in global_pdes.c */
+
+#define P_PERCOL 0.25       /* probability of having a circle in C_RAND_PERCOL arrangement */
+#define NPOISSON 300        /* number of points for Poisson C_RAND_POISSON arrangement */
+#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 1.0	            /* parameter controlling the dimensions of domain */
+#define NPOLY 5             /* number of sides of polygon */
+#define APOLY 2.0          /* angle by which to turn polygon, in units of Pi/2 */
+#define MDEPTH 7            /* depth of computation of Menger gasket */
+#define MRATIO 5            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+#define X_SHOOTER -0.2
+#define Y_SHOOTER -0.6
+#define X_TARGET 0.4
+#define Y_TARGET 0.7        /* shooter and target positions in laser fight */
+
+#define ISO_XSHIFT_LEFT -1.65  
+#define ISO_XSHIFT_RIGHT 0.4
+#define ISO_YSHIFT_LEFT -0.05
+#define ISO_YSHIFT_RIGHT -0.05 
+#define ISO_SCALE 0.85           /* coordinates for isospectral billiards */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.00000002
+
+#define VISCOSITY 2.0
+
+#define RPSA 0.75         /* parameter in Rock-Paper-Scissors-type interaction */
+#define RPSLZB 0.75       /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
+
+#define EPSILON 0.8     /* time scale separation */
+#define DELTA 0.1       /* time scale separation */
+#define FHNA 1.0        /* parameter in FHN equation */
+#define FHNC -0.01      /* parameter in FHN equation */
+#define K_HARMONIC 1.0  /* spring constant of harmonic potential */
+#define K_COULOMB 0.5   /* constant in Coulomb potential */
+#define V_MAZE 0.4      /* potential in walls of maze */
+#define BZQ 0.0008      /* parameter in BZ equation */
+#define BZF 1.2         /* parameter in BZ equation */
+#define B_FIELD 10.0    /* magnetic field */
+#define AB_RADIUS 0.2   /* radius of region with magnetic field for Aharonov-Bohm effect */
+#define K_EULER 50.0    /* constant in stream function integration of Euler equation */
+
+#define SMOOTHEN_VORTICITY 1    /* set to 1 to smoothen vorticity field in Euler equation */
+#define SMOOTHEN_PERIOD 10      /* period between smoothenings */
+#define SMOOTH_FACTOR 0.015     /* factor by which to smoothen */
+
+#define T_OUT 2.0       /* outside temperature */
+#define T_IN 0.0        /* inside temperature */
+#define SPEED 0.0       /* speed of drift to the right */
+
+#define ADD_NOISE 0     /* set to 1 to add noise, set to 2 to add noise in right half */
+#define NOISE_INTENSITY 0.005      /* noise intensity */
+#define CHANGE_NOISE 1      /* set to 1 to increase noise intensity */
+#define NOISE_FACTOR 40.0   /* factor by which to increase noise intensity */
+#define NOISE_INITIAL_TIME 100  /* initial time during which noise remains constant */
+
+#define CHANGE_VISCOSITY 0      /* set to 1 to change the viscosity in the course of the simulation */
+#define ADJUST_INTSTEP 0       /* set to 1 to decrease integration step when viscosity increases */
+#define VISCOSITY_INITIAL_TIME 10  /* initial time during which viscosity remains constant */
+#define VISCOSITY_FACTOR 100.0   /* factor by which to change viscosity */
+#define VISCOSITY_MAX 2.0        /* max value of viscosity beyond which NVID is increased and integration step is decrase, 
+                                    for numerical stability */
+                                        
+#define CHANGE_RPSLZB 0         /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
+#define RPSLZB_CHANGE 0.75      /* factor by which to rpslzb parameter */
+#define RPSLZB_INITIAL_TIME 0   /* initial time during which rpslzb remains constant */
+#define RPSLZB_FINAL_TIME 500   /* final time during which rpslzb remains constant */
+                                      
+/* Boundary conditions, see list in global_pdes.c  */
+
+#define B_COND 0
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 2500       /* number of frames of movie */
+#define NVID 500          /* number of iterations between images displayed on screen */
+#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
+#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation  */
+#define MAX_DT 0.024     /* maximal value of integration step */
+#define NSEG 100         /* number of segments of boundary */
+#define BOUNDARY_WIDTH 5    /* width of billiard boundary */
+
+#define PAUSE 100       /* number of frames after which to pause */
+#define PSLEEP 2         /* sleep time during pause */
+#define SLEEP1  2        /* initial sleeping time */
+#define SLEEP2  1        /* final sleeping time */
+#define INITIAL_TIME 0  /* initial still time */
+#define MID_FRAMES 50    /* number of still frames between parts of two-part movie */
+#define END_FRAMES 50    /* number of still frames at end of movie */
+#define FADE 1           /* set to 1 to fade at end of movie */
+
+/* Visualisation */
+
+#define PLOT_3D 1    /* controls whether plot is 2D or 3D */
+
+#define ROTATE_VIEW 0       /* set to 1 to rotate position of observer */
+#define ROTATE_ANGLE 360.0  /* total angle of rotation during simulation */
+
+/* Plot type - color scheme */
+
+#define CPLOT 30
+#define CPLOT_B 31
+
+/* Plot type - height of 3D plot */
+
+#define ZPLOT 30     /* z coordinate in 3D plot */
+#define ZPLOT_B 30    /* z coordinate in second 3D plot */
+
+#define AMPLITUDE_HIGH_RES 1    /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
+#define SHADE_3D 1              /* set to 1 to change luminosity according to normal vector */
+#define NON_DIRICHLET_BC 0      /* set to 1 to draw only facets in domain, if field is not zero on boundary */
+#define WRAP_ANGLE 1            /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
+#define FADE_IN_OBSTACLE 0      /* set to 1 to fade color inside obstacles */
+#define DRAW_OUTSIDE_GRAY 0     /* experimental - draw outside of billiard in gray */
+#define ADD_POTENTIAL_TO_Z 1    /* set to 1 to add the external potential to z-coordinate of plot */
+#define ADD_POT_CONSTANT 0.35   /* constant in front of added potential */
+
+#define PLOT_SCALE_ENERGY 0.05      /* vertical scaling in energy plot */
+
+#define PRINT_TIME 0        /* set to 1 to print running time */
+#define PRINT_VISCOSITY 0   /* set to 1 to print viscosity */
+#define PRINT_RPSLZB 0      /* set to 1 to print rpslzb parameter */
+#define PRINT_PROBABILITIES 0   /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
+#define PRINT_NOISE 0       /* set to 1 to print noise intensity */
+
+#define DRAW_FIELD_LINES 0  /* set to 1 to draw field lines */
+#define FIELD_LINE_WIDTH 1  /* width of field lines */
+#define N_FIELD_LINES 120   /* number of field lines */
+#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
+#define DRAW_BILLIARD 1     /* set to 1 to draw boundary */
+#define DRAW_BILLIARD_FRONT 1     /* set to 1 to draw boundary */
+#define FILL_BILLIARD_COMPLEMENT 1  /* set to 1 to fill complement of billiard (for certain shapes only) */
+
+/* 3D representation */
+
+#define REPRESENTATION_3D 1     /* choice of 3D representation */ 
+
+#define REP_AXO_3D 0        /* linear projection (axonometry) */
+#define REP_PROJ_3D 1       /* projection on plane orthogonal to observer line of sight */
+
+/* Color schemes, see list in global_pdes.c  */
+
+#define COLOR_PALETTE 11     /* Color palette, see list in global_pdes.c  */
+#define COLOR_PALETTE_B 0     /* Color palette, see list in global_pdes.c  */
+
+#define BLACK 1          /* black background */
+
+#define COLOR_SCHEME 3   /* choice of color scheme */
+
+#define COLOR_PHASE_SHIFT 0.0   /* phase shift of color scheme, in units of Pi */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define VSCALE_AMPLITUDE 30.0      /* additional scaling factor for color scheme P_3D_AMPLITUDE */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define CURL_SCALE 0.000015   /* scaling factor for curl representation */
+#define RESCALE_COLOR_IN_CENTER 0   /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
+#define SLOPE_SCHROD_LUM 50.0       /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
+#define MIN_SCHROD_LUM 0.2       /* minimal luminosity in color scheme Z_ARGUMENT*/
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 359.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -359.0    /* amplitude of variation of hue for color scheme C_HUE */
+#define E_SCALE 100.0    /* scaling factor for energy representation */
+#define LOG_SCALE 0.75   /* scaling factor for energy log representation */
+#define LOG_SHIFT 1.0 
+
+#define NXMAZE 7      /* width of maze */
+#define NYMAZE 7      /* height of maze */
+#define MAZE_MAX_NGBH 4     /* max number of neighbours of maze cell */
+#define RAND_SHIFT 24        /* seed of random number generator */
+#define MAZE_XSHIFT 0.0     /* horizontal shift of maze */
+
+#define DRAW_COLOR_SCHEME 1     /* set to 1 to plot the color scheme */
+#define COLORBAR_RANGE 3.0      /* scale of color scheme bar */
+#define COLORBAR_RANGE_B 2.5   /* scale of color scheme bar for 2nd part */
+#define ROTATE_COLOR_SCHEME 0   /* set to 1 to draw color scheme horizontally */
+
+/* only for compatibility with wave_common.c */
+#define TWOSPEEDS 0          /* set to 1 to replace hardcore boundary by medium with different speed */
+#define OMEGA 0.005        /* frequency of periodic excitation */
+#define COURANT 0.08       /* Courant number */
+#define COURANTB 0.03      /* Courant number in medium B */
+#define INITIAL_AMP 0.5         /* amplitude of initial condition */
+#define INITIAL_VARIANCE 0.0002  /* variance of initial condition */
+#define INITIAL_WAVELENGTH  0.1  /* wavelength of initial condition */
+#define VSCALE_ENERGY 200.0       /* additional scaling factor for color scheme P_3D_ENERGY */
+#define PHASE_FACTOR 20.0       /* factor in computation of phase in color scheme P_3D_PHASE */
+#define PHASE_SHIFT 0.0      /* shift of phase in color scheme P_3D_PHASE */
+#define OSCILLATION_SCHEDULE 0  /* oscillation schedule, see list in global_pdes.c */
+#define AMPLITUDE 0.8      /* amplitude of periodic excitation */ 
+#define ACHIRP 0.2        /* acceleration coefficient in chirp */
+#define DAMPING 0.0        /* damping of periodic excitation */
+#define COMPARISON 0        /* set to 1 to compare two different patterns (beta) */
+#define B_DOMAIN_B 20       /* second domain shape, for comparisons */
+#define CIRCLE_PATTERN_B 0  /* second pattern of circles or polygons */
+/* end of constants added only for compatibility with wave_common.c */
+
+
+double u_3d[2] = {0.75, -0.45};     /* projections of basis vectors for REP_AXO_3D representation */
+double v_3d[2] = {-0.75, -0.45};
+double w_3d[2] = {0.0, 0.015};
+double light[3] = {0.816496581, -0.40824829, 0.40824829};      /* vector of "light" direction for P_3D_ANGLE color scheme */
+double observer[3] = {8.0, 8.0, 8.0};    /* location of observer for REP_PROJ_3D representation */ 
+int reset_view = 0;         /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
+
+#define Z_SCALING_FACTOR 1.25  /* overall scaling factor of z axis for REP_PROJ_3D representation */
+#define XY_SCALING_FACTOR 1.8  /* overall scaling factor for on-screen (x,y) coordinates after projection */
+#define ZMAX_FACTOR 1.0        /* max value of z coordinate for REP_PROJ_3D representation */
+#define XSHIFT_3D -0.1         /* overall x shift for REP_PROJ_3D representation */
+#define YSHIFT_3D 0.0          /* overall y shift for REP_PROJ_3D representation */
+#define BORDER_PADDING 2       /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
+
+/* For debugging purposes only */
+#define FLOOR 1         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0        /* max value of wave amplitude */
+#define TEST_GRADIENT 0 /* print norm squared of gradient */
+
+```
+