Forwarding you to

True 3D mandelbrot type fractal

I've just spent an exhausting week trying to create a TRUE 3D rendition of the Mandelbrot (or whatever the equivalent would turn out to be). It's been a really cumbersome, if somewhat exciting journey. Although you say we should be happy with the 2D version (which I am), I believe that maths can do anything, and that it's just a matter of finding the right equations to find the jackpot.