import numpy as np

import matplotlib

import matplotlib.pyplot as plt

def iterate(Z):

# Count neighbours

N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +

Z[1:-1,0:-2] + Z[1:-1,2:] +

Z[2: ,0:-2] + Z[2: ,1:-1] + Z[2: ,2:])

# Apply rules

birth = (N==3) & (Z[1:-1,1:-1]==0)

survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)

Z[...] = 0

Z[1:-1,1:-1][birth | survive] = 1

return Z

Z = np.random.randint(0,2,(256,256)).astype(int)

U = np.zeros((2*128,2*128), dtype=int)

for i in range(100):

iterate(Z)

U = .999*U + Z

size = np.array(Z.shape)

dpi = 72.0

figsize= size[1]/float(dpi),size[0]/float(dpi)

fig = plt.figure(figsize=figsize, dpi=dpi, facecolor="white")

fig.add_axes([0.0, 0.0, 1.0, 1.0], frameon=False)

plt.imshow(U,interpolation='nearest', cmap=plt.cm.Purples)

plt.xticks([]), plt.yticks([])

plt.savefig('trace.png')

plt.show()