Tonight I made a little patch using Gridflow to generate fractals like this:

The source image for this one was a red circle, but you can use any image provided it has 3 channels (ie, no b/w or grayscale or transparency).

Here's the patch:

Other people have made much cooler stuff than me:

Cyrille Henry - L-systems (Gem)

Ben Bogart - texture feedback (Gem)

Mathieu Bouchard - fractalizing video (Gridflow)

I'd be very interested in seeing more ways of making fractals, so if anyone knows of any, please post them here :-)