Hi, I'm Tom Lowe, I have been experimenting with 3d fractals since reading Daniel White's fascinating web page on his search for a 3d version of the Mandelbrot set.
A great way to collaborate on building fractals is to join fractalforums there are some great ideas and beautiful images here, and many applications for rendering 3d fractals.
This Mandelbox fractal is an attempt to build a 3d fractal that matches the variety of shapes that exist in the 2d Mandelbrot set. I wanted a formula that was continuous and made of shape-preserving transformations, and not too complicated or arbitrary.
To the right is the first image of the scale 2 Mandelbox, and below are the first images I took, which are of a scale=3. Alternatively see the original discussion thread