Spirograph in Python with matplotlib.

spirograph.py

#!/usr/bin/env python

import sys, os
from pylab import *

gcd = lambda x, y: y and gcd(y, x % y) or x
fx = lambda t, rc, rm, rd: (rc - rm) * cos(t * pi) + rd * cos(t * pi * (rc - rm) / rm)
fy = lambda t, rc, rm, rd: (rc - rm) * sin(t * pi) - rd * sin(t * pi * (rc - rm) / rm)
p = lambda x, rc, rm, rd: plot(fx(x, rc, rm, rd), fy(x, rc, rm, rd))

def spirograph(rc, rm, rd, div=1000):
    p(arange(0.0, 2.0 * rm / gcd(rc, rm), 1.0 / div), rc, rm, rd)
    axis((min(axis()[::2]), max(axis()[1::2])) * 2)
    show()

def main(args):
    if len(args) < 4:
        print >>sys.stderr, "Usage: %s rc rm rd [div=1000]" % os.path.basename(args[0])
        print >>sys.stderr, " Ex. %s 31 16 11" % os.path.basename(args[0])
        sys.exit(1)

    wm = matplotlib.pyplot.get_current_fig_manager()
    wm.window.wm_geometry("500x500+50+50")

    spirograph(*map(int, args[1:]))

if __name__ == "__main__": main(sys.argv)