logistic_map.c

/* This program uses SDL.
 * To install:
 *
 *   sudo apt-get install libsdl1.2-dev
 *
 * To compile:
 *
 *   gcc -lSDL filename.c
 *
 */
#include <SDL/SDL.h>

// The size of the window
#define SIZE 800

// number of iterations to do
#define ITERATIONS 1000000

// start drawing after this many iterations
#define START_DRAWING (ITERATIONS - 100)

// the lower bound for a
#define LEFTMOST 3.45

// the initial value of X
// note that this value doesn't actually matter that much,
// so long as it is between 0 and 1
#define INITIAL_X 0.0001

void plot_pixel(SDL_Surface * surface, int x, int y){
  *((Uint32*)surface->pixels + y * surface->w + x) =
    SDL_MapRGB(surface->format, 0, 0, 0);
}

void render(SDL_Surface * screen){
  int i, j;
  double a;
  double x;

  SDL_FillRect(screen, NULL, SDL_MapRGB(screen->format, 255, 255, 255));

  for (i = 0; i < SIZE; i++){
    x = INITIAL_X;
    // a goes from LEFTMOST to 4
    a = LEFTMOST + (double)i / (double)SIZE * (4.0 - LEFTMOST);

    for (j = 0; j < ITERATIONS; j++){
      x = a * x * (1 - x);

      if (j > START_DRAWING){
        plot_pixel(screen, i, SIZE - (int)(x * SIZE) - 1);
      }
    }
  }

  SDL_UpdateRect(screen, 0, 0, 0, 0);
}

int main(){
  SDL_Surface * screen;
  SDL_Event evt;

  SDL_Init(SDL_INIT_VIDEO);

  screen = SDL_SetVideoMode(SIZE, SIZE, 32, SDL_HWSURFACE);

  render(screen);
  while(1){
    if (SDL_PollEvent(&evt)){
      if(evt.type == SDL_QUIT) break;
    }
    SDL_Delay(1);
  }
  SDL_Quit();
}