(It even made the Knittyspin front page! Ooooh!)
You may remember my previous experiment with fractals- I figured out why that one didn't work. The key is to pick something with nice, loooooong color segments. If they're not long enough, it won't be a noticable difference.
You can really see the striping on the brim of the Mandelbrot:
...and in case you were wondering, this is what it looks like when I try to walk two dogs:
I wonder where our blue leash went...hmmm....