3366 lines
135 KiB
Markdown
3366 lines
135 KiB
Markdown
### Parameter values for YouTube simulations ###
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Created by **Nils Berglund** and optimized by **Marco Mancini**
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C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
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Below are parameter values used for different simulations, as well as initial conditions used in
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function animation. Some simulations use variants of the published code. The list is going to be
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updated gradually. Some constants have been moved to global files in later versions.
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### 30 June 21 - #shorts: Working the angle - 60 degrees ###
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**Program:** Variant of `particle_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(-1.5, 1.0, -0.5*PID, -0.25*PID, 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 12 /* 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 D_ANGLE 12 /* angular sector */
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#define LAMBDA 0.3333333333333333333 /* 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 1 /* set to 1 to draw billiard */
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#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
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#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
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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 500 /* 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 700 /* number of frames of movie */
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#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.000006 /* 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 -5 /* 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 0.04 /* 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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### 29 June 21 - #shorts: Wave hitting the Mandelbrot set ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_wave(-0.77, 0.18, phi, psi, xy_in);`
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**In function `init_wave()`:** `phi[i][j] = 0.2*exp(-dist2/0.00025)*cos(-sqrt(dist2)/0.005);`
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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 -1.8
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#define XMAX 0.0 /* x interval */
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#define YMIN 0.0
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#define YMAX 1.0125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.1 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 24 /* 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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#define D_MENGER 15 /* Menger-Sierpinski carpet */
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#define D_JULIA_INT 16 /* interior of Julia set */
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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 D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 0.05 /* parameter controlling the dimensions of domain */
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#define NPOLY 8 /* 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 4 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* 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 below */
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/* Physical parameters of wave equation */
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#define OMEGA 0.9 /* frequency of periodic excitation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* Boundary conditions */
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#define B_COND 2
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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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/* 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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/* Parameters for length and speed of simulation */
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#define NSTEPS 3000 /* number of frames of movie */
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#define NVID 40 /* 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 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 1 /* final sleeping time */
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/* Color schemes */
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#define BLACK 1 /* 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 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 200.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP 220.0 /* 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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### 28 June 21 - #shorts: Working the angle - 90 degrees ###
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**Program:** Variant of `particle_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(-1.5, 1.0, -0.5*PID, -0.25*PID, 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 12 /* 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 D_ANGLE 12 /* angular sector */
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#define LAMBDA 0.5 /* 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 1 /* set to 1 to draw billiard */
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#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
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#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
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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 500 /* 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 700 /* number of frames of movie */
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#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.000006 /* 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 -5 /* 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 0.04 /* 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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### 27 June 21 - More on the importance of mangroves ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_wave(-1.5, 0.0, phi, psi, phi_tmp, psi_tmp, xy_in);`
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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 1.1 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 12 /* 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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#define D_DISK_GRID 12 /* grid of disks */
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#define D_MENGER 15 /* Menger-Sierpinski carpet */
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#define D_JULIA_INT 16 /* interior of Julia set */
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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 D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 0.025 /* parameter controlling the dimensions of domain */
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#define NPOLY 8 /* 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 4 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* 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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#define NGRIDX 15 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define OMEGA 0.9 /* frequency of periodic excitation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* Boundary conditions */
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#define B_COND 2
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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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/* 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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/* 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 25 /* 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 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 1 /* final sleeping time */
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/* Plot type */
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#define PLOT 1
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#define P_AMPLITUDE 0 /* plot amplitude of wave */
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#define P_ENERGY 1 /* plot energy of wave */
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/* Color schemes */
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#define BLACK 1 /* 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) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.02 /* 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 250.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -250.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 26 June 21 - Where lightning strikes the Mandelbrot set ###
|
|
|
|
**Program:** 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 0 /* 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 -2.6
|
|
#define XMAX 1.4 /* x interval */
|
|
#define YMIN -1.0
|
|
#define YMAX 1.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 26 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski carpet */
|
|
#define D_JULIA_INT 16 /* interior of Julia set */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
|
|
|
|
#define LAMBDA -1.5 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* 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 */
|
|
|
|
/* 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 */
|
|
|
|
#define B_COND 1
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 6000 /* 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 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 50 /* number of field lines */
|
|
#define FIELD_LINE_FACTOR 100 /* factor controlling precision when computing origin of field lines */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.3 /* 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 240.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -240.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
double julia_x = 0.0, julia_y = 0.0; /* parameters for Julia sets */
|
|
double center_x = -1.5, center_y = -1.0; /* parameters for circle center */
|
|
|
|
```
|
|
|
|
### 25 June 21 - Mystery billiard 7 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.2, 0.2, 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 0.4 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 10 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 2.0 /* parameter controlling shape of billiard */
|
|
#define MU 0.7 /* second parameter controlling shape of billiard */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define NPOLY 8 /* 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 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 NSTEPS 4500 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 -8 /* number of colors */
|
|
#define COLORSHIFT 270 /* hue of initial 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 0.05 /* length of velocity vectors */
|
|
#define BILLIARD_WIDTH 3 /* width of billiard */
|
|
#define PARTICLE_WIDTH 3 /* width of particles */
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
|
|
#define OUTER_COLOR 270.0 /* color outside billiard */
|
|
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
|
|
|
|
|
#define 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
|
|
|
|
```
|
|
|
|
### 24 June 21 - Wave hitting a Sierpinki carpet: evolution of the energy distribution ###
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(-1.5, 0.0, phi, psi, phi_tmp, psi_tmp, xy_in, level);`
|
|
|
|
```
|
|
#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 15 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski gasket */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define OMEGA 0.9 /* frequency of periodic excitation */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
/* 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 */
|
|
|
|
#define B_COND 2
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
|
|
/* 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 */
|
|
|
|
/* 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 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.02 /* 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 240.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -240.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 23 June 21 - Mystery billiard 6 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(-0.0000001, 0.0, 0.0000001, 0.0, -0.6*PID, 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 1.3 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 9 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 2.732050808 /* sin(45°)/sin(15°) for 4-star-shaped billiard with 60° angles */
|
|
#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 0 /* set to 1 to draw billiard */
|
|
#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
|
|
|
|
#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 NSTEPS 2500 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* integration step */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
|
|
/* 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 12 /* number of colors */
|
|
#define COLORSHIFT 0 /* hue of initial 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 0.02 /* length of velocity vectors */
|
|
#define BILLIARD_WIDTH 3 /* width of billiard */
|
|
#define PARTICLE_WIDTH 3 /* width of particles */
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
|
|
#define OUTER_COLOR 270.0 /* color outside billiard */
|
|
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
|
|
|
|
|
#define 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
|
|
|
|
```
|
|
|
|
### 22 June 21 - Zoom on a wave hitting the Mandelbrot set ###
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(-0.77, 0.18, 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 1280 /* number of grid points on x axis */
|
|
#define NY 720 /* number of grid points on y axis */
|
|
|
|
#define XMIN -1.2
|
|
#define XMAX -0.6 /* x interval */
|
|
#define YMIN 0.0
|
|
#define YMAX 0.3375 /* y interval for 9/16 aspect ratio */
|
|
|
|
#define JULIA_SCALE 1.1 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 24 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski carpet */
|
|
#define D_JULIA_INT 16 /* interior of Julia set */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define OMEGA 0.9 /* frequency of periodic excitation */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
/* 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 */
|
|
|
|
#define B_COND 2
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 5000 /* number of frames of movie */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.06 /* 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 180.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP 150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 21 June 21 - Mystery billiard 5 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 1.5*PI, 1.57*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 */
|
|
|
|
#define B_DOMAIN 5 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
#define MU 0.7 /* 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 -1.0 /* 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 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 1500 /* 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 6000 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS 10 /* number of colors */
|
|
#define COLORSHIFT 80 /* hue of initial 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 0.04 /* 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 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
|
|
|
|
```
|
|
|
|
### 20 June 21 - Storm in a fjord: More waves in a Julia set ###
|
|
|
|
**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 */
|
|
|
|
/* 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 1.1 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 16 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski carpet */
|
|
#define D_JULIA_INT 16 /* interior of Julia set */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define OMEGA 0.9 /* frequency of periodic excitation */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
/* 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 */
|
|
|
|
#define B_COND 2
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 4000 /* number of frames of movie */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#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 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 230.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP 50.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
double julia_x = -0.5, julia_y = 0.5; /* parameters for Julia sets */
|
|
|
|
```
|
|
|
|
### 19 June 21 - Mystery billiard 4 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(-0.6, 0.0, -0.7, 0.1, 0.5*PID, 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 2 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 0.15 /* parameter controlling shape of billiard */
|
|
#define MU 0.7 /* 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 2.0 /* 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 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 NSTEPS 4000 /* number of frames of movie */
|
|
#define TIME 600 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -10 /* number of colors */
|
|
#define COLORSHIFT 200 /* hue of initial 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 0.025 /* 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 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
|
|
|
|
```
|
|
|
|
### 18 June 21 - Dropping a stone in a Julia pond ###
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.0, 0.0, phi, psi, xy_in);`
|
|
|
|
```
|
|
#define MOVIE 0 /* 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 0.7 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 16 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski carpet */
|
|
#define D_JULIA_INT 16 /* interior of Julia set */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define OMEGA 0.9 /* frequency of periodic excitation */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
/* 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 */
|
|
|
|
#define B_COND 2
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 4000 /* number of frames of movie */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.5 /* sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP 60.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
double julia_x = 0.33267, julia_y = 0.06395; /* parameters for Julia sets */
|
|
|
|
```
|
|
|
|
### 17 June 21 - Mystery billiard 3 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, -0.4, 0.0, 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 -1.0
|
|
#define YMAX 1.25 /* 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 9 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA -3.346065215 /* sin(60°)/sin(15°) for Reuleaux-type triangle with 90° angles */
|
|
#define MU 0.7 /* 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 -1.0 /* 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 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 25005 /* 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 5000 /* number of frames of movie */
|
|
#define TIME 600 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS 10 /* number of colors */
|
|
#define COLORSHIFT 120 /* hue of initial 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 0.01 /* 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 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
|
|
|
|
```
|
|
|
|
### 16 June 21 - Waves hitting a Sierpinski carpet ###
|
|
|
|
**Program:** `wave_billiard.c` (variant)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(-1.5, 0.0, phi, psi, xy_in);`
|
|
|
|
```
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
#define B_DOMAIN 15 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
#define D_MENGER 15 /* Menger-Sierpinski gasket */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 3 /* 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 */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define KAPPA 5.0e-6 /* "elasticity" term enforcing oscillations */
|
|
/* 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 */
|
|
|
|
#define B_COND 2
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 5000 /* number of frames of movie */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#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 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 150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 15 June 21 - Mystery billiard 2 ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(-0.6, 0.0, -0.7, 0.1, 0.5*PID, 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 7 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 0.07 /* parameter controlling shape of billiard */
|
|
#define MU 0.7 /* 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 2.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
#define DRAW_BILLIARD 0 /* set to 1 to draw billiard */
|
|
|
|
#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 NSTEPS 3000 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -10 /* number of colors */
|
|
#define COLORSHIFT 200 /* hue of initial 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 0.025 /* 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 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
|
|
|
|
```
|
|
|
|
### 14 June 21 - Sticking to the pointy ends: electric field lines in an evolving Julia set capacitor ###
|
|
|
|
**Program:** `heat.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);`
|
|
|
|
```
|
|
void set_Julia_parameters(time, phi, xy_in)
|
|
int time;
|
|
double *phi[NX];
|
|
short int *xy_in[NX];
|
|
{
|
|
double jangle, cosj, sinj, radius = 0.15;
|
|
|
|
jangle = (double)time*DPI/(double)NSTEPS;
|
|
|
|
cosj = cos(jangle);
|
|
sinj = sin(jangle);
|
|
julia_x = -0.9 + radius*cosj;
|
|
julia_y = radius*sinj;
|
|
init_julia_set(phi, xy_in);
|
|
|
|
printf("Julia set parameters : i = %i, angle = %.5lg, cx = %.5lg, cy = %.5lg \n", time, jangle, julia_x, julia_y);
|
|
}
|
|
```
|
|
|
|
|
|
```
|
|
#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 1.1 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 25 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* 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 */
|
|
|
|
/* 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 */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 4500 /* 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 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 0
|
|
|
|
#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 200 /* number of field lines */
|
|
#define FIELD_LINE_FACTOR 100 /* factor controlling precision when computing origin of field lines */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 0.3 /* 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 280.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -110.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 13 June 21 - A mystery billiard ###
|
|
|
|
**Program:** Variant of `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(-0.5, -0.25, -0.5, 0.25, 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 11 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
|
|
|
#define LAMBDA 3.0 /* parameter controlling shape of billiard */
|
|
#define MU 0.1 /* 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 2.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
#define DRAW_BILLIARD 0 /* set to 1 to draw billiard */
|
|
|
|
#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 NSTEPS 6000 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -10 /* number of colors */
|
|
#define COLORSHIFT 200 /* hue of initial 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 0.025 /* 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 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
|
|
```
|
|
|
|
### 12 June 21 - Julia set capacitors 2: field lines reflecting the charge density ###
|
|
|
|
**Program:** Variant of `heat.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);`
|
|
|
|
```
|
|
void set_Julia_parameters(time, phi, xy_in)
|
|
int time;
|
|
double *phi[NX];
|
|
short int *xy_in[NX];
|
|
{
|
|
double jangle, cosj, sinj, yshift;
|
|
|
|
jangle = pow(1.05 + (double)time*0.00003, 0.333);
|
|
yshift = 0.02*sin((double)time*PID*0.002);
|
|
|
|
cosj = cos(jangle);
|
|
sinj = sin(jangle);
|
|
julia_x = 0.5*(cosj*(1.0 - 0.5*cosj) + 0.5*sinj*sinj);
|
|
julia_y = 0.5*sinj*(1.0-cosj) + yshift;
|
|
init_julia_set(phi, xy_in);
|
|
|
|
printf("Julia set parameters : i = %i, angle = %.5lg, cx = %.5lg, cy = %.5lg \n", time, jangle, julia_x, julia_y);
|
|
}
|
|
```
|
|
|
|
```
|
|
#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 0.8 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 25 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
#define MANDELLIMIT 1.0 /* limit value for approximation of Mandelbrot set */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* 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 */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* 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 NSEG 100 /* number of segments of 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 200 /* number of field lines */
|
|
#define FIELD_LINE_FACTOR 100 /* factor controlling precision when computing origin of field lines */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 -240.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 11 June 21 - More chaos in a 5-petaled elliptical flower billiard ###
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 1.82, PI, 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 0.6 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 10 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling shape of billiard */
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define NPOLY 5 /* number of sides of polygon */
|
|
#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
#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 25000 /* 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 6000 /* number of frames of movie */
|
|
#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -50 /* number of colors */
|
|
#define COLORSHIFT 200 /* hue of initial color */
|
|
#define FLOWER_COLOR 1 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.04 /* length of velocity vectors */
|
|
#define BILLIARD_WIDTH 3 /* width of billiard */
|
|
#define PARTICLE_WIDTH 2 /* width of particles */
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
#define COLOR_OUTSIDE 1 /* set to 1 for colored outside */
|
|
#define OUTER_COLOR 270.0 /* color outside billiard */
|
|
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
|
|
|
|
|
#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
|
|
|
|
```
|
|
|
|
### 10 June 21 - A family of Julia set capacitors ###
|
|
|
|
**Program:** Variant of `heat.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);`
|
|
|
|
```
|
|
void set_Julia_parameters(time, phi, xy_in)
|
|
int time;
|
|
double *phi[NX];
|
|
short int *xy_in[NX];
|
|
{
|
|
double jangle, cosj, sinj;
|
|
|
|
jangle = pow(0.05 + (double)time*0.00003, 0.333);
|
|
|
|
cosj = cos(jangle);
|
|
sinj = sin(jangle);
|
|
julia_x = 0.5*(cosj*(1.0 - 0.5*cosj) + 0.5*sinj*sinj);
|
|
julia_y = 0.5*sinj*(1.0-cosj);
|
|
init_julia_set(phi, xy_in);
|
|
|
|
printf("Julia set parameters : i = %i, angle = %.5lg, cx = %.5lg, cy = %.5lg \n", time, jangle, julia_x, julia_y);
|
|
}
|
|
```
|
|
|
|
```
|
|
#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 0.7 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 25 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
#define D_JULIA 25 /* Julia set */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
#define MANDELLIMIT 1.0 /* limit value for approximation of Mandelbrot set */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* 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 0.000002
|
|
#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 */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 10000 /* 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 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 9 June 21 - The narcissus, a Bunimovich elliptical flower billiard with 6 petals ###
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 1.0, -PID, 3.0*PID, configs); `
|
|
|
|
```
|
|
#define MOVIE 0 /* 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 0.6 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 10 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
#define MU 0.1 /* 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 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
#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 NSTEPS 6000 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -50 /* number of colors */
|
|
#define COLORSHIFT 200 /* hue of initial color */
|
|
#define FLOWER_COLOR 1 /* 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 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
|
|
|
|
```
|
|
|
|
### 8 June 21 - The Mandelbrot capacitor with field lines ###
|
|
|
|
**Program:** `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 */
|
|
|
|
#define XMIN -1.5
|
|
#define XMAX 2.5 /* x interval */
|
|
#define YMIN -1.125
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 24 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
#define MANDELLIMIT 1.0 /* limit value for approximation of Mandelbrot set */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* 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 0.000002
|
|
#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 */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 4000 /* number of frames of movie */
|
|
#define NVID 100 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 1000 /* 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 */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 230.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 7 June 21 - A Bunimovich elliptical flower billiard ###
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_sym_drop_config(-0.99*r, 0.0, -PID, PID, 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 0.7 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 10 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
|
#define D_FLOWER 10 /* Bunimovich flower */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define NPOLY 7 /* number of sides of polygon */
|
|
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
#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 NSTEPS 8000 /* number of frames of movie */
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00002 /* 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 NCOLORS -14 /* number of colors */
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.05 /* 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 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
|
|
|
|
```
|
|
|
|
### 6 June 21 - Phase dynamics in the quantum stadium billiard ###
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 0.0, 10.0, 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 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 2 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
|
|
#define LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
#define DT 0.00000002
|
|
#define HBAR 1.0
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 6000 //7500 /* number of frames of movie */
|
|
#define NVID 750 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Plot type */
|
|
|
|
#define PLOT 1
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
#define P_REAL 2 /* plot real part */
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 5 June 21 - The Mandelbrot capacitor ###
|
|
|
|
**Program:** 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 */
|
|
|
|
#define XMIN -1.5
|
|
#define XMAX 2.5 /* x interval */
|
|
#define YMIN -1.125
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 24 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
#define D_MANDELBROT 24 /* Mandelbrot set */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
#define MANDELLIMIT 1.0 /* limit value for approximation of Mandelbrot set */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* 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 0.000002
|
|
#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 */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 1000 /* number of frames of movie */
|
|
#define NVID 300 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 1000 /* 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 */
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 230.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 4 June 21 - Water flowing through a heated Sierpinski-type carpet ###
|
|
|
|
**Program:** Variant of `heat.c`
|
|
|
|
**Initial condition in function `animation()`:** ` init_gaussian(0.7, 0.7, 0.0, 0.1, phi, xy_in, mdepth);`
|
|
|
|
```
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 23 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* 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 0.000002
|
|
#define VISCOSITY 10.0
|
|
#define T_OUT 0.0 /* outside temperature */
|
|
#define T_IN 2.0 /* inside temperature */
|
|
#define SPEED 0.2 /* speed of drift to the right */
|
|
|
|
/* Boundary conditions */
|
|
|
|
#define B_COND 0
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 1500 /* number of frames of movie */
|
|
#define NVID 100 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 1000 /* 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 */
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 230.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 3 June 21 - Billiard in a 9-pointed star ###
|
|
|
|
**Program:** `xxx.c`
|
|
|
|
**Initial condition in function `animation()`:** `xxx`
|
|
|
|
```
|
|
|
|
```
|
|
|
|
### 2 June 21 - The quantum Ehrenfest model 2: Shooting the particle straight at the channel ###
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 10.0, 0.0, 0.08, 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 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 11 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
#define D_TRIANGLE 5 /* triangular billiard */
|
|
#define D_FLAT 6 /* flat interface */
|
|
#define D_ANNULUS 7 /* annulus */
|
|
#define D_POLYGON 8 /* polygon */
|
|
#define D_YOUNG 9 /* Young diffraction slits */
|
|
#define D_GRATING 10 /* diffraction grating */
|
|
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
|
|
|
/* Billiard tables for heat equation */
|
|
|
|
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
|
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
|
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
|
|
|
|
|
#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.05 /* 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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
#define DT 0.00000002
|
|
#define HBAR 1.0
|
|
|
|
/* 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 */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 5230 //7500 /* number of frames of movie */
|
|
#define NVID 1000 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of 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 */
|
|
|
|
/* Plot type */
|
|
|
|
#define PLOT 0
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
#define P_REAL 2 /* plot real part */
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
/* Boundary conditions */
|
|
|
|
#define B_COND 1
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions */
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* 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 1 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* 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 150.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -150.0 /* 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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### 1 June 21 - Heat equation in a Menger-Sierpinski carpet ###
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**Program:** Variant of `heat.c`
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**Initial condition in function `animation()`:** `init_gaussian(0.7, 0.7, 0.0, 0.1, phi, xy_in, mdepth);`
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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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/* Choice of the billiard table */
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#define B_DOMAIN 22 /* 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 LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.1 /* parameter controlling the dimensions of domain */
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|
#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 2 /* depth of computation of Menger gasket */
|
|
#define MRATIO 5 /* ratio defining Menger gasket */
|
|
#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 */
|
|
/* 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 0.000002
|
|
#define VISCOSITY 10.0
|
|
#define T_OUT 0.0 /* outside temperature */
|
|
#define T_IN 2.0 /* inside temperature */
|
|
|
|
/* Boundary conditions */
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|
|
|
#define B_COND 1
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|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 2000 /* number of frames of movie */
|
|
#define NVID 100 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 1000 /* 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 */
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
#define BLACK 1 /* black background */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
#define C_PHASE 2 /* color scheme shows phase */
|
|
|
|
#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 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 230.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|