I was looking back over an old blog post and noticed some code in the comments that I had overlooked. Tom Pollard gives the following code for drawing Spirograph-like curves.

import matplotlib.pyplot as plt from numpy import pi, exp, real, imag, linspace def spiro(t, r1, r2, r3): """ Create Spirograph curves made by one circle of radius r2 rolling around the inside (or outside) of another of radius r1. The pen is a distance r3 from the center of the first circle. """ return r3*exp(1j*t*(r1+r2)/r2) + (r1+r2)*exp(1j*t) def circle(t, r): return r * exp(1j*t) r1 = 1.0 r2 = 52.0/96.0 r3 = 42.0/96.0 ncycle = 13 # LCM(r1,r2)/r2 t = linspace(0, ncycle*2*pi, 1000) plt.plot(real(spiro(t, r1, r2, r3)), imag(spiro(t, r1, r2, r3))) plt.plot(real(circle(t, r1)), imag(circle(t, r1))) fig = plt.gcf() fig.gca().set_aspect('equal') plt.show()

Tom points out that with the r parameters above, this produces the default curve on Nathan Friend’s Inspirograph app.

**Related**: Exponential sum of the day