All 256 elementary cellular automata

ca.png

ElementaryCellularAutomata.py

# Generates an image of all 256 1-dimensional cellular automata.

from PIL import Image  # from `pip install Pillow`


def ca1d(rule=90, size=5):
    w, h = 2**size - 1, 2**(size - 1)
    ca = [[0] * w for _ in range(h)]
    ca[0][w//2] = 1
    rules = [(rule >> b) % 2 for b in range(8)]
    for y in range(1, h):
        for x in range(w):
            l, c, r = ca[y-1][x-1], ca[y-1][x], ca[y-1][(x+1) % w]
            ca[y][x] = rules[4*l + 2*c + r]
    return ca


def ca1d_image(rule=90, size=5, fg=(0, 0, 0), bg=(255, 255, 255)):
    ca = ca1d(rule, size)
    w, h = len(ca[0]), len(ca)
    img = Image.new('RGB', (w, h), bg)
    pix = img.load()
    for y in range(h):
        for x in range(w):
            pix[x, y] = fg if ca[y][x] else bg
    return img


def ca1d_tiled(size=5, fg=(0, 0, 0, 255), bg=(255, 255, 255), space=(32, 128, 255), gap=4, scale=4):
    imgs = [ca1d_image(rule, size, fg, bg) for rule in range(256)]
    iw, ih = imgs[0].size
    w, h = 16 * (iw + gap) + gap, 16 * (ih + gap) + gap
    tiled = Image.new('RGB', (w, h), bg if space is None else space)
    i = 0
    for y in range(gap, h, ih + gap):
        for x in range(gap, w, iw + gap):
            tiled.paste(imgs[i], (x, y))
            i += 1
    return tiled.resize((w*scale, h*scale), Image.NEAREST)


img = ca1d_tiled()
img.save('ca.png')
img.show()

# Learn more: https://mathworld.wolfram.com/ElementaryCellularAutomaton.html