From 53c96fc692cda2089aba4b316a66a626d475d053 Mon Sep 17 00:00:00 2001 From: nilsberglund-orleans <83530463+nilsberglund-orleans@users.noreply.github.com> Date: Fri, 12 Nov 2021 16:25:56 +0100 Subject: [PATCH] Add files via upload --- Parameters.md | 2241 +++++------------------- Parameters_November21.md | 3520 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 3933 insertions(+), 1828 deletions(-) create mode 100644 Parameters_November21.md diff --git a/Parameters.md b/Parameters.md index a5188e8..ab2640e 100644 --- a/Parameters.md +++ b/Parameters.md @@ -10,12 +10,11 @@ updated gradually. - -### 24 October 21 - Dante's 7th circle: a heptagonal parabolic resonator ### +### 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(0.0, 0.0, phi, psi, xy_in);` +**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 */ @@ -38,17 +37,17 @@ updated gradually. /* Choice of the billiard table */ -#define B_DOMAIN 32 /* choice of domain shape, see list in global_pdes.c */ +#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 0.0 /* parameter controlling the dimensions of domain */ +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ #define MU 1.0 /* parameter controlling the dimensions of domain */ -#define NPOLY 7 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -62,11 +61,11 @@ updated gradually. #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 */ +#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 */ @@ -99,8 +98,9 @@ updated gradually. /* Parameters for length and speed of simulation */ -#define NSTEPS 5000 /* number of frames of movie */ -#define NVID 50 /* number of iterations between images displayed on screen */ +// #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 */ @@ -115,27 +115,27 @@ updated gradually. /* Parameters of initial condition */ #define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength 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 1 +#define PLOT 0 -#define PLOT_B 3 /* plot type for second movie */ +#define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#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 0.15 /* sensitivity of color on wave amplitude */ +#define SLOPE 0.25 /* 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 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 */ @@ -145,6 +145,8 @@ updated gradually. #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 */ @@ -154,21 +156,17 @@ updated gradually. ``` -### 23 October 21 - Avoiding a laser in a room of mirrors, with moving shooter and target ### +### 11 November 21 - Stringer Bell's demise: trajectories in a Tokarsky room with a moving shooter ### -**Program:** `particle_trajectory.c` (variant of `particle_billiard.c`) +**Program:** `particle_trajectory.c` **Initial condition in function `animation()`:** -``` -time = (double)i/(double)NSTEPS; -x_shooter = -0.2 - 0.3*sin(DPI*time); -y_shooter = -0.6*cos(DPI*time); -x_target = 0.4 + 0.4*sin(DPI*time); -y_target = 0.7*cos(DPI*time); -init_circle_config(); -alpha = argument(x_target - x_shooter, y_target - y_shooter); -compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, trajectory, traj_length); +``` + 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); ``` ``` @@ -186,20 +184,22 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje /* Choice of the billiard table, see global_particles.c */ -#define B_DOMAIN 21 /* choice of domain shape */ +#define B_DOMAIN 30 /* choice of domain shape */ -#define CIRCLE_PATTERN 11 /* pattern of circles */ +#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 NCX 30 /* number of circles in x direction */ +#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 1.0 /* parameter controlling shape of domain */ -#define MU 0.02 /* second parameter controlling shape of billiard */ +#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 */ @@ -212,16 +212,17 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje /* Simulation parameters */ -#define NPART 5000 /* number of particles */ +#define NPART 10000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 25 /* length of trajectory */ +#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 3200 /* number of frames of movie */ +#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 */ @@ -259,15 +260,21 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje ``` -### 22 October 21 - Moving widdershins: A rotating parabolic resonator ### +### 10 November 21 - The power of Inti: Four waves in a rotating four-sided parabolic resonator ### -**Program:** `wave_billiard_rotate.c` (variant of `wave_billiard.c`) +**Program:** `wave_billiard_rotate.c` -**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` +**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 0 /* set to 1 to produce movies for wave height and energy simultaneously */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ /* General geometrical parameters */ @@ -294,9 +301,9 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje #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 8 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -305,7 +312,7 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje #define NGRIDX 16 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ -#define ROTATION 0.0025 /* rotation angle per frame */ +#define ROTATION 0.0015 /* rotation angle per frame */ #define X_SHOOTER -0.2 #define Y_SHOOTER -0.6 @@ -349,7 +356,7 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje /* Parameters for length and speed of simulation */ -#define NSTEPS 4400 /* number of frames of movie */ +#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 */ @@ -365,18 +372,18 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje /* Parameters of initial condition */ #define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength 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 3 /* plot type for second movie */ +#define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ @@ -395,6 +402,8 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje #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 */ @@ -404,1111 +413,11 @@ compute_trajectories_xy(x_shooter, y_shooter, alpha, alpha + DPI, configs, traje ``` -### 21 October 21 - Statistics for a Sinai billiard on the torus with Poisson-distributed obstacles ### +### 9 November 21 - Particles stating off center in a parabolic resonator ### -**Program:** `particle_pinball.c` +**Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ - -#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 23 /* choice of domain shape */ - -#define CIRCLE_PATTERN 6 /* 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 44 /* number of circles in x direction */ -#define NCY 10 /* number of circles in y direction */ - -#define NPOISSON 350 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ - -#define LAMBDA 3.8105 /* parameter controlling shape of domain */ -#define MU 0.05 /* 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 0.5 /* 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 1 /* 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 0 /* set to 1 to test whether particle is in billiard */ - -#define NSTEPS 11700 /* number of frames of movie */ -#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* 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 48 /* number of colors */ -#define COLORSHIFT 2 /* hue of initial color */ -#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ -#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */ -#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 0.1 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ - -#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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ - - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1000 /* final sleeping time */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 2.5 /* max free path on graph */ - -``` - -### 20 October 21 - Octarine Dream: Two eccentric waves in an octagonal-parabolic resonator ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave(0.5, 0.5, phi, psi, xy_in); - add_circular_wave(-1.0, -0.5, 0.5, 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 8 /* 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 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 -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 2700 /* 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 0.0005 /* 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 10 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 1 /* 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 0.15 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 250.0 /* 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 200.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -160.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ - -/* 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 October 21 - A moving light source in a Penrose unilluminable room ### - -**Program:** `particle_trajectory.c` (variant of `particle_billiard.c`) - -**Initial condition in function `animation()`:** -``` -time = DPI*(0.025 + 0.95*(double)i/(double)NSTEPS); -x = 0.6 + 0.6*cos(time); -y = 0.0 + 0.7*sin(time); -init_drop_config(x, y, 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 -1.4 -#define XMAX 1.4 /* x interval */ -#define YMIN -1.4 -#define YMAX 1.4 /* 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 16 /* 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 1.3 /* parameter controlling shape of domain */ -#define MU 0.3 /* 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 15 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 7 /* 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 1250 /* 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 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 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 */ - -``` - -### 18 October 21 - Wave amplitude in two isospectral domains ### - -**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 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 37 /* 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 0.9 /* parameter controlling the dimensions of domain */ -#define MU 0.55 /* parameter controlling the dimensions of domain */ -#define NPOLY 8 /* 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 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 -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 3000 /* 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 0.0005 /* 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 10 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 1 /* 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 0.15 /* 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 210.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ - -/* 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 October 21 - Statistics for an (almost) finite horizon Sinai billiard on the torus ### - -**Program:** `particle_pinball.c` - -**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ - -#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 23 /* choice of domain shape */ - -#define CIRCLE_PATTERN 21 /* 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 44 /* number of circles in x direction */ -#define NCY 10 /* 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 3.8105 /* parameter controlling shape of domain */ -#define MU 0.085 /* 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 0.5 /* 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 1 /* 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 0 /* set to 1 to test whether particle is in billiard */ - -#define NSTEPS 10700 /* number of frames of movie */ -#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* 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 256 /* number of colors */ -#define COLORSHIFT 2 /* hue of initial color */ -#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ -#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */ -#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 0.1 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ - -#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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ - - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1000 /* final sleeping time */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 0.3 /* max free path on graph */ - -``` - -### 16 October 21 - Escaping a laser with finite wavelength in a room of mirrors ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave(X_SHOOTER, Y_SHOOTER, 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 201 /* 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 1.0 /* parameter controlling the dimensions of domain */ -#define MU 0.03 /* parameter controlling the dimensions of domain */ -#define NPOLY 8 /* 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 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 */ - -/* 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 1500 /* 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 0.015 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 1 - -#define PLOT_B 3 /* 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 1 /* 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 0.75 /* 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 190.0 /* 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 */ - -/* 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 October 21 - Average energy of a wave in a Tokarsky unilluminable room ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave(-2.0*ratio, 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 35 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 8 /* 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 0.6 /* parameter controlling the dimensions of domain */ -#define MU 0.6 /* parameter controlling the dimensions of domain */ -#define NPOLY 8 /* 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 16 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -/* 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 0.01 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 3000 /* number of frames of movie */ -#define NVID 100 /* 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 0.0005 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 3 - -#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 1 /* 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 0.5 /* 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 200.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -190.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ - -/* 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 */ - -``` - -### 14 October 21 - Sinai billiard on a torus with triangular lattice, collisions and free path statistics ### - -**Program:** `particle_pinball.c` - -**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ - -#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 23 /* choice of domain shape */ - -#define CIRCLE_PATTERN 21 /* 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 44 /* number of circles in x direction */ -#define NCY 10 /* 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 3.8105 /* parameter controlling shape of domain */ -#define MU 0.05 /* 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 0.5 /* 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 1 /* 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 0 /* set to 1 to test whether particle is in billiard */ - -#define NSTEPS 11000 /* number of frames of movie */ -#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* 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 48 /* number of colors */ -#define COLORSHIFT 2 /* hue of initial color */ -#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ -#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */ -#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 0.1 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ - -#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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ - - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1000 /* final sleeping time */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 1.5 /* max free path on graph */ - -``` - -### 13 October 21 - One cannot (always) hear the shape of a drum ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(-0.9, 0.0, 0.81, 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 37 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 8 /* 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 0.6 /* parameter controlling the dimensions of domain */ -#define MU 0.6 /* parameter controlling the dimensions of domain */ -#define NPOLY 8 /* 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 16 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define ISO_XSHIFT_LEFT -1.0 -#define ISO_XSHIFT_RIGHT 0.9 -#define ISO_YSHIFT_LEFT 0.05 -#define ISO_YSHIFT_RIGHT 0.05 -#define ISO_SCALE 0.9 /* 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 0.01 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 3000 /* number of frames of movie */ -#define NVID 60 /* 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 0.0005 /* 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 1 /* 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 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 190.0 /* 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 */ - -/* 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 October 21 - Particles in a hexagonal-parabolic resonator ### - -**Program:** `drop_billiard.c` - -**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);` +**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 */ @@ -1523,83 +432,85 @@ init_drop_config(x, y, 0.0, DPI, configs); #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 */ +/* Choice of the billiard table, see global_particles.c */ -#define B_DOMAIN 15 /* choice of domain shape */ +#define B_DOMAIN 15 /* choice of domain shape */ -#define CIRCLE_PATTERN 0 /* pattern of circles */ +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 1 /* pattern of polyline */ -#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ +#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 NCX 15 /* number of circles in x direction */ +#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 billiard */ -#define MU 0.9 /* second parameter controlling shape of billiard */ +#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 6 /* number of sides of polygon */ +#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 1 /* set to 1 to draw additional construction lines for 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 */ -#define NPART 10000 /* number of particles */ +/* Simulation parameters */ + +#define NPART 20000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ - -#define NSTEPS 1440 /* number of frames of movie */ -#define TIME 150 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.0001 /* integration step */ -#define NVID 75 /* 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 */ -/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */ - -/* simulation parameters */ - #define LMAX 0.01 /* minimal segment length triggering resampling */ -#define LPERIODIC 0.1 /* lines longer than this are not drawn (useful for Sinai billiard) */ -#define LCUT 2.0 /* controls the max size of segments not considered as being cut */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */ -#define ORDER_COLORS 1 /* set to 1 if colors should be drawn in order */ +#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 */ -/* color and other graphical parameters */ +#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 */ -#define COLOR_PALETTE 1 /* Color palette, see list in global_pdes.c */ +/* 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 */ -#define NCOLORS 6 /* number of colors */ -#define COLORSHIFT 3 /* hue of initial color */ -#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ -#define NSEG 100 /* number of segments of boundary */ -#define BILLIARD_WIDTH 4 /* width of billiard */ -#define FRONT_WIDTH 4 /* width of wave front */ +/* 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 300.0 /* color outside billiard */ -#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */ -#define PAINT_EXT 0 /* set to 1 to paint exterior of billiard */ +#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 100 /* final sleeping time */ -#define END_FRAMES 0 /* number of frames at end of movie */ - -#define PI 3.141592654 -#define DPI 6.283185307 -#define PID 1.570796327 +#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 */ ``` -### 11 October 21 - The color of magic: An octagonal parabolic resonator ### +### 8 November 21 - Chaotic waves in a diamond resonator ### **Program:** `wave_billiard.c` @@ -1626,17 +537,17 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Choice of the billiard table */ -#define B_DOMAIN 32 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 4 /* choice of domain shape, see list in global_pdes.c */ -#define CIRCLE_PATTERN 8 /* pattern of circles, 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 8 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -1645,6 +556,17 @@ init_drop_config(x, y, 0.0, DPI, configs); #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 */ @@ -1657,9 +579,9 @@ init_drop_config(x, y, 0.0, DPI, configs); #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ -#define COURANTB 0.01 /* Courant number in medium B */ +#define COURANTB 0.02 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 */ @@ -1676,8 +598,8 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Parameters for length and speed of simulation */ -#define NSTEPS 6350 /* number of frames of movie */ -#define NVID 60 /* number of iterations between images displayed on screen */ +#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 */ @@ -1692,36 +614,40 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Parameters of initial condition */ #define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength 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 1 +#define PLOT 0 -#define PLOT_B 0 /* plot type for second movie */ +#define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ -#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 15 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ -#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ +#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 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 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 210.0 /* mean value of hue for color scheme C_HUE */ +#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 */ @@ -1729,204 +655,46 @@ init_drop_config(x, y, 0.0, DPI, configs); ``` -### 10 October 21 - Swaying and repelling mangroves destroyed by the surf ### +### 7 November 21 - Don't s̶h̶u̶t̶ shoot me down (part 2): Particles with trails in a Tokarsky room ### -**Program:** `mangrove.c` +**Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` +**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 */ -/* 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 20 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 8 /* 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 340 /* number of points for Poisson C_RAND_POISSON arrangement */ - -#define LAMBDA 0.85 /* parameter controlling the dimensions of domain */ -#define MU 0.03 /* parameter controlling the dimensions of domain */ -#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 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -/* 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 1 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ -#define X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ - -#define OMEGA 0.00133333333 /* frequency of periodic excitation */ -#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ -#define KX_BC 20.0 /* spatial period of periodic excitation in x direction */ -#define KY_BC 6.66666 /* spatial period of periodic excitation in y direction */ -#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ -#define COURANT 0.02 /* Courant number */ -#define COURANTB 0.015 /* Courant number in medium B */ -#define GAMMA 3.0e-6 /* damping factor in wave equation */ -#define GAMMAB 5.0e-4 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPAB 1.0e-6 /* "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 3 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 5500 /* number of frames of movie */ -#define NVID 60 /* number of iterations between images displayed on screen */ -#define NSEG 100 /* number of segments of boundary */ -#define INITIAL_TIME 100 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.2 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 0 - -/* Color schemes */ - -#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 2500.0 /* 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 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 */ - -/* mangrove properties */ - -#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ -#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */ -#define MANGROVE_EMAX 1.5e-3 /* max energy for mangrove to survive */ - -#define RANDOM_RADIUS 1 /* set to 1 for random circle radius */ -#define ERODE_MANGROVES 0 /* set to 1 for mangroves to be eroded */ -#define MOVE_MANGROVES 1 /* set to 1 for mobile mangroves */ -#define DETACH_MANGROVES 1 /* set to 1 for mangroves to be able to detach */ -#define INERTIA 1 /* set to 1 for taking inertia into account */ -#define REPELL_MANGROVES 1 /* set to 1 for mangroves to repell each other */ -#define DT_MANGROVE 0.1 /* time step for mangrove displacement */ -#define KSPRING 0.05 /* spring constant of mangroves */ -#define KWAVE 4.0 /* constant in force due to wave gradient */ -#define KREPEL 5.0 /* constant in repelling force between mangroves */ -#define REPEL_RADIUS 1.1 /* radius in which repelling force acts (in units of mangrove radius) */ -#define DXMAX 0.02 /* max displacement of mangrove in one time step */ -#define L_DETACH 0.25 /* spring length beyond which mangroves detach */ -#define DAMP_MANGROVE 0.1 /* damping coefficient of mangroves */ -#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */ - -#define HASHX 25 /* size of hashgrid in x direction */ -#define HASHY 15 /* size of hashgrid in y direction */ -#define HASHMAX 10 /* maximal number of mangroves per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -/* 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 */ - -``` - -### 9 October 21 - Sinai billiard on a torus with square lattice of obstacles: collision and free path statistics ### - -**Program:** `particle_pinball.c` - -**Initial condition in function `animation()`:** `` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ - #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 23 /* choice of domain shape */ +#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 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 40 /* number of circles in x direction */ -#define NCY 10 /* number of circles in y direction */ +#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 3.8 /* parameter controlling shape of domain */ -#define MU 0.05 /* second parameter controlling shape of billiard */ +#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 0.5 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -1936,17 +704,19 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Simulation parameters */ -#define NPART 1 /* number of particles */ +#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 0 /* set to 1 to keep trails of the particles */ -#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */ +#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 8800 /* number of frames of movie */ -#define TIME 5000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* integration step */ +#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 */ @@ -1957,44 +727,36 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Colors and other graphical parameters */ -#define COLOR_PALETTE 1 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ -#define NCOLORS 48 /* number of colors */ -#define COLORSHIFT 2 /* hue of initial color */ +#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 SINGLE_COLOR 1 /* set to 1 to make all particles a single color */ #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 0.1 /* length of velocity vectors */ +#define LENGTH 0.015 /* length of velocity vectors */ #define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ +#define PARTICLE_WIDTH 2 /* width of particles */ #define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ #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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ +#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 */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 1.5 /* max free path on graph */ +#define SLEEP2 1000 /* final sleeping time */ ``` -### 8 October 21 - Waves in a Tokarsky unilluminable room ### +### 6 November 21 - Wave amplitude and average energy in homophonic drums ### **Program:** `wave_billiard.c` -**Initial condition in function `animation()`:** `init_circular_wave(-2.0*ratio, 0.0, phi, psi, xy_in);` +**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 */ @@ -2017,17 +779,17 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Choice of the billiard table */ -#define B_DOMAIN 35 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 38 /* choice of domain shape, see list in global_pdes.c */ -#define CIRCLE_PATTERN 8 /* pattern of circles, 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 5 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -2036,6 +798,17 @@ init_drop_config(x, y, 0.0, DPI, configs); #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 */ @@ -2048,9 +821,9 @@ init_drop_config(x, y, 0.0, DPI, configs); #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ -#define COURANTB 0.01 /* Courant number in medium B */ +#define COURANTB 0.02 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 */ @@ -2067,8 +840,8 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Parameters for length and speed of simulation */ -#define NSTEPS 3500 /* number of frames of movie */ -#define NVID 60 /* number of iterations between images displayed on screen */ +#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 */ @@ -2083,36 +856,40 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Parameters of initial condition */ #define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength 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 0 #define PLOT_B 3 /* plot type for second movie */ /* Color schemes */ -#define COLOR_PALETTE 1 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ -#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ +#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 0.15 /* sensitivity of color on wave amplitude */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 200.0 /* scaling factor for energy representation */ +#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 260.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -250.0 /* amplitude of variation of hue for color scheme C_HUE */ +#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 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 */ @@ -2120,11 +897,11 @@ init_drop_config(x, y, 0.0, DPI, configs); ``` -### 7 October 21 - Collision statistics for a “sunflower” Sinai billiard ### +### 5 November 21 - Don’t s̶h̶u̶t̶ shoot me down: Particles in a Tokarsky unilluminable room ### -**Program:** `particle_pinball.c` +**Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_drop_config(0.5, 0.1, -0.5*PID, 0.5*PID, configs);` +**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 */ @@ -2132,36 +909,35 @@ init_drop_config(x, y, 0.0, DPI, configs); #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ +#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 21 /* choice of domain shape */ +#define B_DOMAIN 30 /* choice of domain shape */ -// #define CIRCLE_PATTERN 6 /* pattern of circles */ -#define CIRCLE_PATTERN 4 /* pattern of circles */ +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 1 /* pattern of polyline */ -#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ +#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 5000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NCX 40 /* number of circles in x direction */ -#define NCY 10 /* number of circles in y direction */ +#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 3.8 /* parameter controlling shape of domain */ -#define MU 0.05 /* second parameter controlling shape of billiard */ +#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 0.5 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -2171,17 +947,19 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Simulation parameters */ -#define NPART 1 /* number of particles */ +#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 TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */ +#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 10300 /* number of frames of movie */ -#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* integration step */ +#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 */ @@ -2192,45 +970,42 @@ init_drop_config(x, y, 0.0, DPI, configs); /* 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 SINGLE_COLOR 1 /* set to 1 to make all particles a single color */ #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 0.1 /* length of velocity vectors */ +#define LENGTH 0.025 /* length of velocity vectors */ #define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ +#define PARTICLE_WIDTH 3 /* width of particles */ #define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ #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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ +#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 */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 1.5 /* max free path on graph */ +#define SLEEP2 1000 /* final sleeping time */ ``` -### 6 October 21 - "Energy evolution in a triangular grid wave protection" ### +### 4 November 21 - A rotating hexagonal parabolic resonator ### -**Program:** `wave_energy.c` +**Program:** `wave_billiard_rotate.c` -**Initial condition in function `animation()`:** `int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);` +**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 */ @@ -2247,48 +1022,58 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Choice of the billiard table */ -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ -#define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 32 /* choice of domain shape, see list in global_pdes.c */ -#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */ -#define CIRCLE_PATTERN_B 11 /* pattern of circles, 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 0.75 /* parameter controlling the dimensions of domain */ -#define MU 0.03 /* parameter controlling the dimensions of domain */ -#define MUB 0.03 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 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 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 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 0.0 /* frequency of periodic excitation */ -#define AMPLITUDE 0.025 /* amplitude of periodic excitation */ +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ -#define COURANTB 0.004 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-8 /* damping factor in wave equation */ +#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-6 /* 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 */ +#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 */ @@ -2296,100 +1081,111 @@ init_drop_config(x, y, 0.0, DPI, configs); /* Boundary conditions, see list in global_pdes.c */ -#define B_COND 3 +#define B_COND 2 /* Parameters for length and speed of simulation */ -#define NSTEPS 3750 /* number of frames of movie */ -#define NVID 25 /* number of iterations between images displayed on screen */ +#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 200 /* time after which to start saving frames */ -#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ +#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 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 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 0.2 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength 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 1 /* choice of color scheme, see list in global_pdes.c */ +#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 50.0 /* sensitivity of color on wave amplitude */ +#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 500.0 /* scaling factor for energy representation */ +#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 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */ +#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 5.0 /* max value of wave amplitude */ +#define VMAX 10.0 /* max value of wave amplitude */ ``` +### 3 November 21 - Trajectories in a triangular billiard ### -### 5 October 21 - Particles with trails in a Penrose unilluminable room ### - -**Program:** `particle_billiard.c` - -**Initial condition in function `animation()`:** `` +**Program:** `particle_trajectory.c` +**Initial condition in function `animation()`:** ``` -init_partial_drop_config(0.0, 0.0, 0.0, DPI, 0, 2*NPART/5, 0, configs, color, newcolor); -init_partial_drop_config(0.0, 0.8, 0.0, DPI, 2*NPART/5, 4*NPART/5, 10, configs, color, newcolor); -init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, color, newcolor); + 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 720 /* window width */ +#define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ -#define XMIN -1.4 -#define XMAX 1.4 /* x interval */ -#define YMIN -1.4 -#define YMAX 1.4 /* y interval for 9/16 aspect ratio */ +#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 16 /* choice of domain shape */ +#define B_DOMAIN 5 /* choice of domain shape */ -#define CIRCLE_PATTERN 2 /* pattern of circles */ +#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 NCX 30 /* number of circles in x direction */ +#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 1.3 /* parameter controlling shape of domain */ -#define MU 0.3 /* second parameter controlling shape of billiard */ +#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 */ @@ -2402,15 +1198,16 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Simulation parameters */ -#define NPART 100 /* number of particles */ +#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 1 /* set to 1 to keep trails of the particles */ +#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 1300 /* number of frames of movie */ +#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 */ @@ -2423,6 +1220,8 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* 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 */ @@ -2446,12 +1245,11 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo ``` - -### 4 October 21 - Mean energy in a Penrose unilluminable room, starting behind a mushroom ### +### 2 November 21 - Classics revisited: circular wave starting from the center of an ellipse ### **Program:** `wave_billiard.c` -**Initial condition in function `animation()`:** `init_wave_plus(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);` +**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 */ @@ -2474,17 +1272,17 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Choice of the billiard table */ -#define B_DOMAIN 33 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ -#define CIRCLE_PATTERN 8 /* pattern of circles, 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 0.3 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -2493,6 +1291,17 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo #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 */ @@ -2505,9 +1314,9 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ -#define COURANTB 0.01 /* Courant number in medium B */ +#define COURANTB 0.02 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 */ @@ -2524,8 +1333,8 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Parameters for length and speed of simulation */ -#define NSTEPS 3500 /* number of frames of movie */ -#define NVID 40 /* number of iterations between images displayed on screen */ +#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 */ @@ -2539,259 +1348,39 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Parameters of initial condition */ -#define INITIAL_AMP 0.2 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength 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 3 - -#define PLOT_B 0 /* plot type for second movie */ - -/* Color schemes */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 1 /* 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 200.0 /* 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 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* 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 October 21 - Mystery billiard 9 ### - -**Program:** `mystery_billiard.c` - -**Initial condition in function `animation()`:** `init_line_config(0.0, -0.2, 0.0, 0.2, 0.0, 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 */ - -#define B_DOMAIN 15 /* choice of domain shape */ - -#define CIRCLE_PATTERN 0 /* pattern of circles */ - -#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NCX 40 /* number of circles in x direction */ -#define NCY 10 /* 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 billiard */ -#define MU 0.8 /* 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 0 /* 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 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 4001 /* 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 NSTEPS 4000 /* number of frames of movie */ -#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.000015 /* integration step */ -#define NVID 50 /* 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 NCOLORS 15 /* 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 3 /* 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 in other color */ - - -#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 */ - -#define PI 3.141592654 -#define DPI 6.283185307 -#define PID 1.570796327 - -``` - - -### 2 October 21 - A pentagonal-parabolic resonator ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_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 8 /* 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 5 /* 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 16 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -/* 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 0.01 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* 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 5600 /* number of frames of movie */ -#define NVID 60 /* 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 0.2 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 0 +#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 1 /* choice of color scheme, see list in global_pdes.c */ +#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 0.15 /* sensitivity of color on wave amplitude */ +#define SLOPE 0.35 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 200.0 /* scaling factor for energy representation */ +#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 210.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -210.0 /* amplitude of variation of hue for color scheme C_HUE */ +#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 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 */ @@ -2800,11 +1389,17 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo ``` -### 1 October 21 - Statistics for a Sinai billiard with Poisson disc obstacles ### +### 1 November 21 - Particles in a four-sided eccentric parabolic resonator ### -**Program:** `particle_pinball.c` +**Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_drop_config(0.5, 0.1, -0.5*PID, 0.5*PID, configs); ` +**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 */ @@ -2812,36 +1407,32 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ -#define XMIN -4.0 -#define XMAX 4.0 /* x interval */ -#define YMIN -1.25 -#define YMAX 3.25 /* y interval for 9/16 aspect ratio */ - -#define BOXYMIN -1.0 -#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */ +#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 21 /* choice of domain shape */ +#define B_DOMAIN 15 /* choice of domain shape */ -#define CIRCLE_PATTERN 7 /* pattern of circles */ +#define CIRCLE_PATTERN 2 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ -#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NCX 40 /* number of circles in x direction */ -#define NCY 10 /* number of circles in y direction */ +#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 3.8 /* parameter controlling shape of domain */ -#define MU 0.05 /* second parameter controlling shape of billiard */ -// #define MU 0.034 /* second parameter controlling shape of billiard */ +#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 0.5 /* angle by which to turn polygon, in units of Pi/2 */ +#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 */ @@ -2851,17 +1442,17 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Simulation parameters */ -#define NPART 1 /* number of particles */ +#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 0 /* set to 1 to test whether particle is in billiard */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define NSTEPS 10900 /* number of frames of movie */ -#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00007 /* integration step */ +#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 */ @@ -2872,33 +1463,27 @@ init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, colo /* Colors and other graphical parameters */ -#define NCOLORS 32 /* number of colors */ +#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 1 /* set to 1 to use different colors for all particles */ -#define SINGLE_COLOR 1 /* set to 1 to make all particles a single 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 0.1 /* length of velocity vectors */ +#define LENGTH 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 4 /* width of particles */ +#define PARTICLE_WIDTH 1 /* width of particles */ #define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_TRAJECTORY 8 /* hue for single color */ #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 in other color */ -#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 500 /* number of frames after which to pause */ -#define PSLEEP 5 /* sleep time during pause */ +#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 */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -#define NPATHBINS 200 /* number of bins for path length histogramm */ -#define PATHLMAX 2.5 /* max free path on graph */ +#define SLEEP2 1000 /* final sleeping time */ ``` diff --git a/Parameters_November21.md b/Parameters_November21.md new file mode 100644 index 0000000..60cea13 --- /dev/null +++ b/Parameters_November21.md @@ -0,0 +1,3520 @@ +### 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. + + +### 29 November 21 - ### + +**Program:** `` + +**Initial condition in function `animation()`:** `` + +``` + +``` + +### 28 November 21 - Quantum snowflake: Schrödinger’s equation in a von Koch fractal ### + +**Program:** `schrodinger.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 10.0, 0.0, 0.1, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */ +/* but will multiply run time by 4 */ + +#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, see list in global_pdes.c */ + +#define B_DOMAIN 41 /* choice of domain shape */ + +#define CIRCLE_PATTERN 0 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#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 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 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 0.00000001 +#define HBAR 1.0 + +/* 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 1200 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#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 END_FRAMES 100 /* still frames at end of movie */ + +/* 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 */ + + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 11 + + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* 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 2.0 /* 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 21 - A von Koch snowflake resonating cavity with refracting walls ### + +**Program:** `wave_billiard_vonKoch.c` (variant of `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 -2.666666666 +#define XMAX 2.666666666 /* x interval */ +#define YMIN -1.5 +#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ + +#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 2 /* pattern of circles or polygons, 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.06 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MAXDEPTH 5 /* max 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.02 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 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 25 /* 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 0.015 /* 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 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 1.0 /* 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 4.0 /* 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 */ + +#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 */ + +``` + +### 26 November 21 - A von Koch snowflake capacitor with field lines ### + +**Program:** `heat_vonKoch.c` (variant of `heat.c`) + +**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 */ + +/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */ +/* but will multiply run time by 4 */ + +#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 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 27 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 0 /* 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 1.1 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.000004 +#define VISCOSITY 10.0 +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 0 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* 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 BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 1 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define DRAW_FIELD_LINES 1 /* 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 REDISTRIBUTE_FIELD_LINES 0 /* set to 1 to "equidistribute" field lines according to gradient on boundary */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 1 /* choice of color scheme */ + +#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 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 */ + +``` + +### 25 November 21 - Average energy of a wave in a von Koch snowflake fractal ### + +**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 720 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 720 /* number of grid points on x axis */ +#define NY 720 /* number of grid points on y axis */ + +#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 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 2 /* pattern of circles or polygons, 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.06 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1400 /* number of frames of movie */ +#define NVID 60 /* 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 350 /* 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 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 3 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 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 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 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 */ + +#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 */ + +``` + +### 24 November 21 - A lighthouse beam in a von Koch snowflake fractal ### + +**Program:** `particle_trajectory_vonKoch.c` (variant of `particle_trajectory.c`) + +**Initial condition in function `animation()`:** +``` + alpha = ((double)depth + (double)time)*PI/6.0; + compute_trajectories_xy(0.0, 0.0, alpha, alpha + DPI, 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 4 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* 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 5 /* Sierpinski gastket depth */ + +#define LAMBDA 1.0 /* parameter controlling shape of domain */ +#define MU 0.0001 /* 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 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 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 36 /* 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 NSTEPS 1480 /* 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 16 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 36 /* 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 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 */ +#define ENDFRAMES 20 /* still frames at end of animation */ + +``` + +### 23 November 21 - Waves in a von Koch snowflake fractal ### + +**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 41 /* 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 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 0.06 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2900 /* 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 350 /* 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 0.015 /* 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 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 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 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 */ + +#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 */ + +``` + +### 22 November 21 - Billiard in a von Koch snowflake fractal ### + +**Program:** `particle_vonKoch.c` (variant of `particle_billiard.c`) + +**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -PI, 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 4 /* 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 5 /* Sierpinski gastket depth */ + +#define LAMBDA 1.8 /* parameter controlling shape of domain */ +#define MU 0.0001 /* 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 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 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 1000 /* number of frames of movie */ +#define TIME 1500 /* 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 11 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 12 /* 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 0.01 /* length of velocity vectors */ +#define BILLIARD_WIDTH 1 /* 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 */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +``` + +### 21 November 21 - Waves hitting a randomized square grid of hexagons ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.02, 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 40 /* 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 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 0.06 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2200 /* 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 50 /* 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 0.015 /* 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 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 0.1 /* 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 20.0 /* 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 */ + +``` + +### 20 November 21 - A lighthouse beam in a mirrored hexagon ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** +``` + x = 0.0; + y = 0.0; + alpha = (1.0/6.0 + (double)time/3.0)*PI; + compute_trajectories_xy(x, y, alpha, alpha + DPI, 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 8 /* 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 SDEPTH 4 /* Sierpinski gastket depth */ + +#define LAMBDA 1.0 /* 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 6 /* 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 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 36 /* 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 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 16 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 36 /* 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 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 */ + +``` + +### 19 November 21 - Waves starting off center in a four-sided parabolic resonator ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.1, 0.05, 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 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 3350 /* 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 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 0.25 /* 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 */ + +``` + +### 18 November 21 - Mystery billiard 11 ### + +**Program:** `mystery_billiard.c` + +**Initial condition in function `animation()`:** `init_drop_config(-1.5, 0.0, -PI, 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 3 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* 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 4 /* Sierpinski gastket depth */ + +#define LAMBDA 1.8 /* 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 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 0 /* 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 2000 /* 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 5000 /* number of frames of movie */ +#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.0000075 /* 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 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 0.025 /* 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 */ +#define FINALFRAMES 100 /* number of still frames at the end */ + +``` + +### 17 November 21 - Wave meets triangular grid of triangular obstacles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.02, 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 720 /* 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 -1.125 +#define XMAX 1.125 /* 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 40 /* 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 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 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* 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 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* 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 25 /* 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 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 0.04 /* 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 COLORBAR_RANGE 40.0 /* 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 */ + +``` + +### 16 November 21 - Mystery billiard 10 ### + +**Program:** `mystery_billiard.c` + +**Initial condition in function `animation()`:** `init_drop_config(0.75, 0.0, PI-0.1, PI+0.1, 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 2 /* 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 1.2 /* parameter controlling shape of domain */ +#define MU 0.6 /* 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 DRAW_BILLIARD 0 /* 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 1000 /* 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 4500 /* number of frames of movie */ +#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.0000075 /* 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 8 /* 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 */ + +``` + +### 15 November 21 - A fiery wave hitting random obstacles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.02, 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 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* 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 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* 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 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 OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.02 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* 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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3350 /* number of frames of movie */ +#define NVID 35 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define INITIAL_TIME 75 /* 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 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 0.05 /* 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 40.0 /* 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 */ + +``` + +### 14 November 21 - The origin of the xenomorph: wave in a rotating ellipse ### + +**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 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 -3.0 +#define XMAX 3.0 /* x interval */ +#define YMIN -1.6875 +#define YMAX 1.6875 /* 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 0.9 /* 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 0.0014 /* 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 6250 /* 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 0.0005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.04 /* 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 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 1 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.8 /* 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 2.8 /* 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 */ + +``` + +### 13 November 21 - Trajectories on a translation surface of genus 2 ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** +``` + x = -0.5; + y = -0.5; + alpha = time*PI; + compute_trajectories_xy(x, y, alpha, alpha + DPI, 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 13 /* 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 16 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 10 /* 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 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 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 0.03 /* 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 */ + +``` + +### 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 */ + +```