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Here is my first try at volumetrically rendering a 3d nebulabrot.
<a href="http://www.youtube.com/v/rR23UZkik1M&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/rR23UZkik1M&rel=1&fs=1&hd=1</a>

Its just a standard nebulabrot with the z axis manipulating the start value of the x axis. I have done some tests with using Buddha versions of the power 2 mandelbulb also but not gotten any good results so far. For rendering I just pack it into a 512^3 3d texture and more or less brute force it on the graphic card which yields about 10 fps on my 5870. With some optimizations I hope to increase that at least 10x though.

For the future I hope to find some non Buddha (ie locally computable) fractal that generates interesting RGB volumetric data so that one can increase resolution close to the camera on the fly and gain semi infinite resolution. With the Buddha version memory seem to become a bottleneck quite rapidly and my 6GB ram machine will probably never be able to do much above 1024^3 res.

Nice work!

Just out of curiosity, which version(s) of the mandelbulb did you try? I had hoped that the positive sin version would look more interesting when rendered Buddha style, since it seems to make the most sense mathematically (in my opinion).

jehovajah: It calculates RGB colors for voxels in a volume, then samples along lines through it (back to front) to create pixels. So far I have used something like alpha = RGB dot (0.2).xyz (dark voxels transparent, light ones more opaque) for transparency.

Schlega: I have tried the ones called original and positive z component methods from http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/. I havent done that much testing with them though so its very possible that one can get better results with them.