Tom Beddard of subblue created this nifty little Flash application where you can draw your own mathematical butterfly:

Taken from Clifford Pickover's book, Computers and the Imagination, is this experiment that creates butterfly like curves.

The formula is expressed in polar coordinates as:

By changing the A, B, a, b and c parameters you can get some nice results.

It's fun to change the parameters to see what you get: Link - via Cliff Pickover's Reality Carnival