Solution to: http://www.reddit.com/r/dailyprogrammer/comments/2fkh8u/9052014_challenge_178_hard_regular_expression/

fractal.py

import re, itertools
from PIL import Image

def str2pt(s):
    L = len(s) - 1
    x, y = 1, 1
    for n in s:
        y += 2**L if n in '34' else 0
        x += 2**L if n in '14' else 0
        L -= 1
    return x-1, y-1

def generate(n):
    return map(lambda x: ''.join(x), itertools.product('1234', repeat=n))

def fractal(r, n):
    return map(str2pt, (c for c in generate(n) if re.match(r, c)))

def draw(r, n=10, filename='/tmp/fractal.png'):
    im = Image.new('RGB', (2**n, 2**n), "black")
    for x, y in fractal(r, n):
        im.putpixel((x, y), (255, 255, 255,))
    im.save(filename, 'PNG')

run.md

draw('.*1.*')

Produces: