I've been playing with mandelbulber, a GPL 3D fractal renderer that runs on Linux and Windows. Among other things, it can make animations. I haven't had this much fun since I first discovered fractint in the early 1990s.
The animation is an IFS-type fractal modified by the spherical folding mode. It explores the "alpha", "beta" and "gamma" rotations under General IFS Parameters, ultimately returning to the initial configuration. (too bad I can't figure out how to make the player loop the clip!)
Check it out:
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