R-set of a kaleidoscopic IFS

[msltoe]

The R-set idea is that if we have two rotations (X,Y) and (Y,Z) for an octahedral IFS, we can select those rotations based on the phi and theta of the original (x,y,z) position. There's a lot variants possible. Here is one with phi and theta times 1/2:

[knighty]

Nice idea! 
Just wondering, would its DE be continuous?

[msltoe]

knighty: Thanks! With the appropriate function, we could probably get continuity everywhere except the poles. Plenty of non-conformal stretching, though, which is interesting given that fixed-rotation Julias are anti-conformal. Maybe as one zooms in, the stretching becomes less and less since the rotation parameters won't change as much.

[knighty]

Thank you.