Something I've mentioned before is that if we look at generalized cubics of the form z = z^3 + k z + c (eliminating the z^2 term by moving the origin), we get a collection of Julia sets Jkc for these maps. And the cubic mandebrots Mk are the set of all c such that Jkc is connected.

I recently implemented these guys in Ultra Fractal, see my public formula and parameter files rvr.ufm and rvr.upr. Also see my blog post

http://www.rudyrucker.com/blog/2010/04/02/the-rudy-set-fractal/.

My belief is that we could make a nice 3D Mandelbulb-style shape by stacking up a sequence of the Mk. To suggest what I'm getting at, here's a YouTube video that scans forward and back through some of the Mk. [I updated the video on April 16, 2010].