How did Escher do it?

M. C. Escher is a genius. I was so inspired by his Circle Limit drawings, that I've been working on an iPhone puzzle game.

Early Prototype Here: www.circull.com

The math isn't that difficult to understand. Circle inversions are analogous to reflections about a line in 2d Euclidian geometry. It's fun stuff.

See also http://escherdroste.math.leidenuniv.nl/