You want to display a 3d fractal. From my limited knowledge of these mathematical creatures, each point in 3d space is considered to be inside the fractal set, if the specific fractal law you apply with this point as a seed converges - or something like this. Moreover, the color of this point is determined by how fast this covergence occurs.

This is not straightforward to visualize. Imagine you have the mandelbrot set (2d) and you want to visualize on a line. Same problem.

By the way, a voxel (volume element), is the 3d equivalent of a pixel (picture element).

One solution is to use some sort of transparency in your cubes. This is eye candy (or can be), but makes rendering even more complicated. The principle behind this is similar to the way doctors use ultrasounds to see babies before they are born.

May be you’d like to start from the simplified version of the fractal, where a point is either in the fractal set or not, without color info. Then you have 3d regions that belong to the fractal (given a scale), and region that don’t. Being in 3d space, you sort out your voxel connectivity problems I mentioned above in a relative inexpensive way. So, for the shake of rendering, you could get the typical polygonized model to display.

If you implement this, but you still want to see what’s inside and not only on the surface of these region, a cheap trick (which funnaly enough always works for the pro’s) is to display cross-sections, ie. 2d slices of these fractal regions. These should be fractals as well. You could control the position and orientation of the slice from your 3d model.

Can this be done real time? My guess is that you have to try very hard in order to get something decent displayed real time.

May it’s time to start reading all that volume rendering background material after all!

Sorry I can’t be of any more help.

Have fun

madmortigan