YouTube-simulations/Parameters.md

### 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. 



### 12 November 21 - Classics revisited: Wave in an ellipse starting from a focus ###

**Program:** `wave_billiard.c` 

**Initial condition in function `animation()`:** `init_circular_wave(sqrt(LAMBDA*LAMBDA - 1.0), 0.0, phi, psi, 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 */

/* General geometrical parameters */

#define WINWIDTH 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 1       /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 1.5	    /* parameter controlling the dimensions of domain */
#define MU 1.0              /* parameter controlling the dimensions of domain */
#define NPOLY 4             /* number of sides of polygon */
#define APOLY 0.5           /* 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 16           /* 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 -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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

// #define NSTEPS 500      /* number of frames of movie */
#define NSTEPS 4200      /* number of frames of movie */
#define NVID 40          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_WAVELENGTH  0.015 /* wavelength of initial condition */
#define INITIAL_VARIANCE 0.0003  /* variance of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 0

#define PLOT_B 1        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 11     /* 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 0.25        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 120.0     /* scaling factor for energy representation */

#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 7.5    /* scale of color scheme bar */
#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 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 November 21 - Stringer Bell's demise: trajectories in a Tokarsky room with a moving shooter ###

**Program:** `particle_trajectory.c` 

**Initial condition in function `animation()`:** 

```
    x = -0.95 - 0.2*time;
    y = 0.5 - 0.5*(1.0 - time);
    alpha = argument(x + 0.95, y) - PI;
    compute_trajectories_xy(x, y, alpha, DPI + alpha, configs, trajectory, traj_length);  
```

```
#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 5   /* pattern of circles */
#define POLYLINE_PATTERN 1  /* pattern of polyline */

#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */

#define NMAXCIRCLES 1000        /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000        /* 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 LAMBDA 1.5	/* parameter controlling shape of domain */
#define MU 0.02        /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 TRAJ_LENGTH 48  /* 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 1      /* set to 1 to show zoom on specific area */
#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#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 14     /* Color palette, see list in global_pdes.c  */

#define NCOLORS 64       /* 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 0.03       /* 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 PAUSE 1000       /* number of frames after which to pause */
#define PSLEEP 1         /* sleep time during pause */
#define SLEEP1  1        /* initial sleeping time */
#define SLEEP2  1000      /* final sleeping time */

```

### 10 November 21 - The power of Inti: Four waves in a rotating four-sided parabolic resonator ###

**Program:** `wave_billiard_rotate.c` 

**Initial condition in function `animation()`:** 
```
    init_circular_wave(0.35, 0.35, phi, psi, xy_in);
    add_circular_wave(-1.0, -0.35, 0.35, phi, psi, xy_in);
    add_circular_wave(1.0, -0.35, -0.35, phi, psi, xy_in);
    add_circular_wave(-1.0, 0.35, -0.35, 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 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 32      /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 0.0	    /* parameter controlling the dimensions of domain */
#define MU 0.9              /* parameter controlling the dimensions of domain */
#define NPOLY 4             /* number of sides of polygon */
#define APOLY -0.02         /* 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 16           /* number of grid point for grid of disks */
#define NGRIDY 20           /* number of grid point for grid of disks */

#define ROTATION 0.0015     /* rotation angle per frame */

#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 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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

#define NSTEPS 2600      /* number of frames of movie */
#define NVID 50          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.00025  /* variance of initial condition */
#define INITIAL_WAVELENGTH  0.03 /* wavelength of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 0

#define PLOT_B 1        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 16     /* 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 0.2        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 100.0     /* scaling factor for energy representation */

#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 7.5    /* scale of color scheme bar */
#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 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 21 - Particles stating off center in a parabolic resonator ###

**Program:** `particle_billiard.c` 

**Initial condition in function `animation()`:** `init_drop_config(0.03, 0.02, 0.0, DPI, configs);`

```
#define MOVIE 1         /* set to 1 to generate movie */

#define WINWIDTH 	720   /* window width */
#define WINHEIGHT 	720   /* window height */

#define XMIN -1.125
#define XMAX 1.125	/* 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 15     /* choice of domain shape */

#define CIRCLE_PATTERN 1    /* pattern of circles */
#define POLYLINE_PATTERN 1  /* pattern of polyline */

#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */

#define NMAXCIRCLES 1000     /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000        /* 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 LAMBDA 0.0	/* parameter controlling shape of domain */
#define MU 1.0          /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 0    /* 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 TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#define NSTEPS 1350      /* number of frames of movie */
#define TIME 1500         /* 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 16     /* Color palette, see list in global_pdes.c  */

#define NCOLORS 16       /* 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 0.025       /* 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 0         /* set to 1 to paint exterior */

#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  1000      /* final sleeping time */

```

### 8 November 21 - Chaotic waves in a diamond resonator ###

**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 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 4      /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 2.0	    /* parameter controlling the dimensions of domain */
#define MU 0.5              /* parameter controlling the dimensions of domain */
#define NPOLY 4             /* number of sides of polygon */
#define APOLY 0.5           /* 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 16           /* 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 -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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

#define NSTEPS 2300      /* number of frames of movie */
#define NVID 40          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_WAVELENGTH  0.015 /* wavelength of initial condition */
#define INITIAL_VARIANCE 0.0003  /* variance of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 0

#define PLOT_B 1        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 15     /* 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 0.25        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 120.0     /* scaling factor for energy representation */

#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 7.5    /* scale of color scheme bar */
#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 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 November 21 - Don't s̶h̶u̶t̶  shoot me down (part 2): Particles with trails in a Tokarsky room ###

**Program:** `particle_billiard.c` 

**Initial condition in function `animation()`:** `init_drop_config(-0.95, 0.0, -0.1, -0.1 + 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 1  /* pattern of polyline */

#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */

#define NMAXCIRCLES 1000     /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000        /* 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 LAMBDA 1.5	/* parameter controlling shape of domain */
#define MU 0.0035        /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 16        /* 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 1      /* set to 1 to show zoom on specific area */
#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles */
#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#define NSTEPS 3000      /* number of frames of movie */
#define TIME 1500         /* 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 16     /* Color palette, see list in global_pdes.c  */

#define NCOLORS 64       /* 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 0.015       /* 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 1         /* sleep time during pause */
#define SLEEP1  1        /* initial sleeping time */
#define SLEEP2  1000      /* final sleeping time */

```

### 6 November 21 - Wave amplitude and average energy in homophonic drums ###

**Program:** `wave_billiard.c` 

**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], 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 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 38      /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 1.5	    /* parameter controlling the dimensions of domain */
#define MU 0.5              /* parameter controlling the dimensions of domain */
#define NPOLY 4             /* number of sides of polygon */
#define APOLY 0.5           /* 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 16           /* 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 -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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

#define NSTEPS 3600      /* number of frames of movie */
#define NVID 40          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.0003  /* variance of initial condition */
#define INITIAL_WAVELENGTH  0.02  /* wavelength of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 0

#define PLOT_B 3        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 16     /* 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 0.25        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 150.0     /* scaling factor for energy representation */

#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 7.5    /* scale of color scheme bar */
#define ROTATE_COLOR_SCHEME 1   /* 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 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 21 - Don’t s̶h̶u̶t̶ shoot me down: Particles in a Tokarsky unilluminable room ###

**Program:** `particle_billiard.c` 

**Initial condition in function `animation()`:** `init_drop_config(-0.95, 0.0, PI, 3.0*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 1  /* pattern of polyline */

#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
#define ABSORBING_CORNER_RADIUS 0.0     /* radius of absorbing corners in polygonal line */

#define NMAXCIRCLES 1000     /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000        /* 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 LAMBDA 1.5	/* parameter controlling shape of domain */
#define MU 0.01        /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 5000         /* 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 0    /* set to 1 to keep trails of the particles */
#define SHOWZOOM 1      /* set to 1 to show zoom on specific area */
#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles */
#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#define NSTEPS 1150      /* number of frames of movie */
#define TIME 3000         /* time between movie frames, for fluidity of real-time simulation */ 
#define DPHI 0.000005    /* 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 64       /* 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 0.025       /* length of velocity vectors */
#define BILLIARD_WIDTH 2    /* 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 1         /* sleep time during pause */
#define SLEEP1  1        /* initial sleeping time */
#define SLEEP2  1000      /* final sleeping time */

```

### 4 November 21 - A rotating hexagonal parabolic resonator ###

**Program:** `wave_billiard_rotate.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 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 32      /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 0.0	    /* parameter controlling the dimensions of domain */
#define MU 1.0              /* parameter controlling the dimensions of domain */
#define NPOLY 6             /* number of sides of polygon */
#define APOLY -0.02         /* 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 16           /* number of grid point for grid of disks */
#define NGRIDY 20           /* number of grid point for grid of disks */

#define ROTATION 0.00275      /* rotation angle per frame */

#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 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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

#define NSTEPS 4350      /* number of frames of movie */
#define NVID 50          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.00025  /* variance of initial condition */
#define INITIAL_WAVELENGTH  0.02 /* wavelength of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 1

#define PLOT_B 0        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 10     /* 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 0.2        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 50.0     /* scaling factor for energy representation */

#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 7.5    /* scale of color scheme bar */

#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */

/* 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 */

```

### 3 November 21 - Trajectories in a triangular billiard ###

**Program:** `particle_trajectory.c` 

**Initial condition in function `animation()`:** 
```
    alpha = PI*1.25;
    x = -1.0 + 0.5*cos(DPI*time + alpha);
    y = LAMBDA - 2.0 + 0.5*sin(DPI*time + alpha);
    alpha = PI/3.0;
    compute_trajectories_xy(x, y, alpha, DPI + alpha, configs, trajectory, traj_length);         

```

```
#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 5     /* choice of domain shape */

#define CIRCLE_PATTERN 5   /* pattern of circles */
#define POLYLINE_PATTERN 1  /* pattern of polyline */

#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */

#define NMAXCIRCLES 1000        /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000        /* 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 LAMBDA 1.732050808	/* sqrt(3) - parameter controlling shape of domain */
#define MU 0.04          /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 24      /* number of particles */
#define NPARTMAX 100000	/* maximal number of particles after resampling */
#define TRAJ_LENGTH 48  /* 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 TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#define NSTEPS 3000      /* 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 14     /* Color palette, see list in global_pdes.c  */

#define NCOLORS 64       /* 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 0.03       /* 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 PAUSE 1000       /* number of frames after which to pause */
#define PSLEEP 1         /* sleep time during pause */
#define SLEEP1  1        /* initial sleeping time */
#define SLEEP2  1000      /* final sleeping time */

```

### 2 November 21 - Classics revisited: circular wave starting from the center of an ellipse ###

**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 0  /* set to 1 to produce movies for wave height and energy simultaneously */

/* General geometrical parameters */

#define WINWIDTH 	1280  /* window width */
#define WINHEIGHT 	720   /* window height */

#define NX 1280          /* number of grid points on x axis */
#define NY 720          /* number of grid points on y axis */

#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 JULIA_SCALE 1.0 /* scaling for Julia sets */

/* Choice of the billiard table */

#define B_DOMAIN 1      /* choice of domain shape, see list in global_pdes.c */

#define CIRCLE_PATTERN 7   /* 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 LAMBDA 1.5	    /* parameter controlling the dimensions of domain */
#define MU 0.5              /* parameter controlling the dimensions of domain */
#define NPOLY 4             /* number of sides of polygon */
#define APOLY 0.5           /* 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 16           /* 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 -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 OMEGA 0.002        /* frequency of periodic excitation */
#define AMPLITUDE 1.0      /* amplitude of periodic excitation */ 
#define COURANT 0.02       /* Courant number */
#define COURANTB 0.02      /* 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 */

/* Boundary conditions, see list in global_pdes.c  */

#define B_COND 2

/* Parameters for length and speed of simulation */

#define NSTEPS 4600      /* number of frames of movie */
#define NVID 50          /* number of iterations between images displayed on screen */
#define NSEG 100         /* 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 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 */

/* Parameters of initial condition */

#define INITIAL_AMP 0.75         /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.0003  /* variance of initial condition */
#define INITIAL_WAVELENGTH  0.02  /* wavelength of initial condition */

/* Plot type, see list in global_pdes.c  */

#define PLOT 1

#define PLOT_B 1        /* plot type for second movie */

/* Color schemes */

#define COLOR_PALETTE 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 0.35        /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 100.0     /* scaling factor for energy representation */

#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 0     /* set to 1 to plot the color scheme */

#define SAVE_TIME_SERIES 0      /* set to 1 to save wave time series at a point */

/* 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 */

```


### 1 November 21 - Particles in a four-sided eccentric parabolic resonator ###

**Program:** `particle_billiard.c` 

**Initial condition in function `animation()`:** 
```
    init_partial_drop_config(LAMBDA, 0.0, 0.0, DPI, 0, NPART/4, 0, configs, color, newcolor);
    init_partial_drop_config(-LAMBDA, 0.0, 0.0, DPI, NPART/4, NPART/2, 0, configs, color, newcolor);
    init_partial_drop_config(0.0, LAMBDA, 0.0, DPI, NPART/2, 3*NPART/4, 0, configs, color, newcolor);
    init_partial_drop_config(0.0, -LAMBDA, 0.0, DPI, 3*NPART/4, NPART, 0, configs, color, newcolor);
```

```
#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 15     /* choice of domain shape */

#define CIRCLE_PATTERN 2    /* pattern of circles */

#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */

#define NMAXCIRCLES 1000        /* total number of circles (must be at least NCX*NCY for square grid) */
#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 LAMBDA 0.3	/* parameter controlling shape of domain */
#define MU 0.7          /* second parameter controlling shape of billiard */
#define FOCI 1          /* set to 1 to draw focal points of ellipse */
#define NPOLY 4             /* 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 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 0    /* set to 1 to keep trails of the particles */
#define TEST_ACTIVE 1   /* set to 1 to test whether particle is in billiard */

#define NSTEPS 4600      /* number of frames of movie */
#define TIME 2500         /* time between movie frames, for fluidity of real-time simulation */ 
#define DPHI 0.0000025    /* 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 1     /* Color palette, see list in global_pdes.c  */

#define NCOLORS 64       /* 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 0.02       /* length of velocity vectors */
#define BILLIARD_WIDTH 2    /* width of billiard */
#define PARTICLE_WIDTH 1    /* 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 1         /* sleep time during pause */
#define SLEEP1  1        /* initial sleeping time */
#define SLEEP2  1000      /* final sleeping time */

```