If you allow branching, there's a body-diagonal fractal that gives the "Sierpinski carpet": 0: / 1: /\/ \ \ /\/ 2: /\/\/\/\/ \ \/ /\ \ /\/\/\/\/ \/\ \/\ / / / / \/\ \/\ /\/\/\/\/ \ \/ /\ \ /\/\/\/\/ 3: /\/\/\/\/\/\/\/\/\/\/\/\/\/ \ \/ /\ \/ /\ \/ /\ \/ /\ \ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \/\ \/\/\/ /\/\/\ \/\ / / / /\ \ \ \/ / / / \/\ \/\/\/ /\/\/\ \/\ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \ \/ /\ \/ /\ \/ /\ \/ /\ \ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \/\/\/\/\ \/\/\/\/\ / /\ \/ / / /\ \/ / \/\/\/\/\ \/\/\/\/\ /\/ /\/ /\/ /\/ \ \ \ \ \ \ \ \ /\/ /\/ /\/ /\/ \/\/\/\/\ \/\/\/\/\ / /\ \/ / / /\ \/ / \/\/\/\/\ \/\/\/\/\ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \ \/ /\ \/ /\ \/ /\ \/ /\ \ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \/\ \/\/\/ /\/\/\ \/\ / / / /\ \ \ \/ / / / \/\ \/\/\/ /\/\/\ \/\ /\/\/\/\/\/\/\/\/\/\/\/\/\/ \ \/ /\ \/ /\ \/ /\ \/ /\ \ /\/\/\/\/\/\/\/\/\/\/\/\/\/ There's a fairly obvious version of this that does the Menger sponge (Sierpinski cube), though I've never seen it rendered. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com