src/examples/life.c

    Conway’s game of life

    We use a cartesian grid and the generic time loop.

    #include "grid/cartesian.h"
    #include "run.h"

    We need two fields to store the old and new states as well as a field to store the age of each cell.

    scalar a[], b[], age[];

    The lower-left corner is at (-0.5,-0.5) (the default box size is one) i.e. the domain spans (-0.5,-0.5) (0.5,0.5) and is discretised using 256^2 cells.

    int main()
    {
      origin (-0.5, -0.5);
      init_grid (256);

    The generic run() function implements the main time loop.

      run();
    }

    We initialise zeros and ones randomly (the noise() function returns random numbers between -1 and 1) in a circle centered on the origin of radius 2.

    event init (i = 0)
    {
      foreach() {
        a[] = (x*x + y*y < sq(0.2))*(noise() > 0.);
        age[] = a[];
      }
      boundary({a});
    }

    Animation

    We generate images of the age field every 5 timesteps for the first 1000 timesteps of the evolution.

    event movie (i += 5; i < 1000)
    {

    We mask out dead cells (i.e. cells for which age is zero).

      scalar m[];
      foreach()
        m[] = age[] ? 1 : -1;
    
      output_ppm (age, mask = m, n = 512, file = "age.gif", opt = "--delay 1");
    }

    Game of life algorithm

    event life (i++)
    {
      foreach() {

    We count the number of live neighbors in a 3x3 neighbourhood.

        int neighbors = - a[];
        for (int i = -1; i <= 1; i++)
          for  (int j = -1; j <= 1; j++)
    	neighbors += a[i,j];

    If a cell is alive and surrounded by 2 or 3 neighbors it carries on living, otherwise it dies. If a cell is dead and surrounded by exactly 3 neighbors it becomes alive.

        b[] = a[] ? (neighbors == 2 || neighbors == 3) : (neighbors == 3);

    The age of live cells is incremented.

        age[] = b[]*(age[] + 1);
      }
      boundary({b});

    Here we swap the old state (a) with the new state (b).

      swap (scalar, a, b);
    }
    Evolution of the age of cells

    Evolution of the age of cells