fluffy September 25, 2000, 09:21 PM 

One thing I've always wondered about quaternion fractals is how, exactly, you calculate the rayset intersection. To me it seems like a VERY nontrivial task. Do you just use brute force to determine approximately where the ray enters the set and then subdivide the region between internal and external until a boundary is found? In that case, what about regions of much complexity where such a naive approach would fail? Or do you just calculate a set of voxels for the set and then refine the visible portions, or what? And then how do you do the surface normal?
I've seen a lot of quaternion fractals out there, and plenty of descriptions of how the iterative process happens, but never anything really explaining how the rayset interesction takes place...
On a similar note, I must take exception to most of the pages out there on quaternion fractals which state that Julia and Mandelbrot sets aren't true 3D. Granted, heightfieldrendered ones aren't  but the sets themselves are actually 4dimensional (you can vary Z0 independently of C and get different 2D planes of the 4D hyperset for Mandelbrot as well as for Julia  and I've never seen a rendering of crosssections of the Julia hyperset). It'd be neat to do raytracing of 3D crosssections of the 4D Mandelbrot hyperset. Actually, aren't Quaternion fractals technically 6D by the same token? Though the Z0=0 crosssection is already difficult enough to grok as a shape... :)
For what it's worth, the Mandelbrot set was originally created as an index into the continuous Julia sets. It's also interesting to note that the 2D crosssection of the Julia hyperset looks very much like the orbits of the Z0=0 Mandelbrot set at that same C.
Also, sorry if I'm munging terminology here. I only did fractal set theory as a hobby back in high school, and back then I didn't really grasp a lot of the mathematical concepts. It's been a while since I've given much thought to it. :)
