(not actually a fractal?)
A neat pattern from "The New Turing Omnibus by A. Dewdney":
And the algorithm for generating it is very simple!
I've implemented the algorithm, mostly as a small project to learn ClojureScript: click here to see it in action.
The display will choose random values every 20 seconds, and has an animation of smoothly changing one of the parameters.
Clickto go fullcreen
Enterto generate a new pattern
Spaceto pause animation