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@ -1816,22 +1816,250 @@ double julia_x = 0.33267, julia_y = 0.06395; /* parameters for Julia sets */
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### 14 June 21 - Sticking to the pointy ends: electric field lines in an evolving Julia set capacitor ###
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**Program:** `xxx.c`
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**Program:** `heat.c`
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**Initial condition in function `animation()`:** `xxx`
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**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);`
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```
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void set_Julia_parameters(time, phi, xy_in)
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int time;
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double *phi[NX];
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short int *xy_in[NX];
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{
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double jangle, cosj, sinj, yshift;
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jangle = pow(1.05 + (double)time*0.00003, 0.333);
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yshift = 0.02*sin((double)time*PID*0.002);
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cosj = cos(jangle);
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sinj = sin(jangle);
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julia_x = 0.5*(cosj*(1.0 - 0.5*cosj) + 0.5*sinj*sinj);
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julia_y = 0.5*sinj*(1.0-cosj) + yshift;
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/* need to decrease 0.05 for i > 2000 */
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init_julia_set(phi, xy_in);
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printf("Julia set parameters : i = %i, angle = %.5lg, cx = %.5lg, cy = %.5lg \n", time, jangle, julia_x, julia_y);
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}
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```
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 1280 /* number of grid points on x axis */
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#define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 0.8 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 25 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_FLAT 6 /* flat interface */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_YOUNG 9 /* Young diffraction slits */
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#define D_GRATING 10 /* diffraction grating */
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#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
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/* Billiard tables for heat equation */
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#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
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#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
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#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
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#define D_MANDELBROT 24 /* Mandelbrot set */
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#define D_JULIA 25 /* Julia set */
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#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
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#define MU 0.1 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 2 /* depth of computation of Menger gasket */
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#define MRATIO 5 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 1.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard in sub_wave.c */
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/* Physical patameters of wave equation */
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#define DT 0.000004
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#define VISCOSITY 10.0
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#define T_OUT 2.0 /* outside temperature */
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#define T_IN 0.0 /* inside temperature */
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#define SPEED 0.0 /* speed of drift to the right */
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/* Boundary conditions */
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#define B_COND 0
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#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
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#define BC_PERIODIC 1 /* periodic boundary conditions */
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#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
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/* Parameters for length and speed of simulation */
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#define NSTEPS 5000 /* number of frames of movie */
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#define NVID 50 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define PAUSE 100 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 2 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* Field representation */
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#define FIELD_REP 1
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#define F_INTENSITY 0 /* color represents intensity */
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#define F_GRADIENT 1 /* color represents norm of gradient */
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#define DRAW_FIELD_LINES 1 /* set to 1 to draw field lines */
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#define FIELD_LINE_WIDTH 1 /* width of field lines */
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#define N_FIELD_LINES 200 /* number of field lines */
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#define FIELD_LINE_FACTOR 100 /* factor controlling precision when computing origin of field lines */
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/* Color schemes */
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#define BLACK 1 /* black background */
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#define COLOR_SCHEME 1 /* choice of color scheme */
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#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
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#define C_HUE 1 /* color scheme modifies hue */
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#define C_PHASE 2 /* color scheme shows phase */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 0.1 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -240.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* Basic math */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 13 June 21 - A mystery billiard ###
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**Program:** `xxx.c`
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**Program:** Variant of `particle_billiard.c`
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**Initial condition in function `animation()`:** `xxx`
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**Initial condition in function `animation()`:** `init_line_config(-0.5, -0.25, -0.5, 0.25, 0.0, configs);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
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/* Choice of the billiard table */
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#define B_DOMAIN 11 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_REULEAUX 9 /* Reuleaux and star shapes */
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#define D_FLOWER 10 /* Bunimovich flower */
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#define D_ALT_REU 11 /* alternating between star and Reuleaux */
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#define LAMBDA 3.0 /* parameter controlling shape of billiard */
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#define MU 0.1 /* second parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NPOLY 6 /* number of sides of polygon */
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#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define DRAW_BILLIARD 0 /* set to 1 to draw billiard */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define DEBUG 0 /* draw trajectories, for debugging purposes */
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/* Simulation parameters */
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#define NPART 20000 /* number of particles */
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#define NPARTMAX 100000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 6000 /* number of frames of movie */
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#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.00002 /* integration step */
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#define NVID 150 /* number of iterations between images displayed on screen */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
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/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
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/* Colors and other graphical parameters */
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#define NCOLORS -10 /* number of colors */
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#define COLORSHIFT 200 /* hue of initial color */
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#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.025 /* length of velocity vectors */
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#define BILLIARD_WIDTH 3 /* width of billiard */
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#define PARTICLE_WIDTH 2 /* width of particles */
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#define FRONT_WIDTH 3 /* width of wave front */
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#define BLACK 1 /* set to 1 for black background */
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#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
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#define OUTER_COLOR 270.0 /* color outside billiard */
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#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1000 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 12 June 21 - Julia set capacitors 2: field lines reflecting the charge density ###
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