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Here are videos of the set rendered in real-time by "GigaVoxels", our sparse voxel octree rendering engine implemented with CUDA (more info here: http://artis.imag.fr/Membres/Cyril.Crassin/).
The fractal is computed on the GPU, not during the ray-casting as usually done, but as voxels stored into an Octree.
Voxels are produced on-the-fly and stored into a cache in video memory in order to be reused while they stay visible. The octree is also subdivided on-the-fly and the subdivision is triggered directly by the ray-casting kernel. That prevents to generate any occluded data.
I compute Ambient Occlusion very efficiently using filtered low resolution voxels and soft shadows are computed with secondary rays. Everything runs at around 20Hz.
More images and direct links to the videos there: http://www.icare3d.org/blog_techno/gpu/gigabroccoli_the_mandelbulb_into_gigavoxels.html

<a href="http://www.youtube.com/v/PFr-cEEb8y0&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/PFr-cEEb8y0&rel=1&fs=1&hd=1</a> <a href="http://www.youtube.com/v/xF4mTGyskr0&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/xF4mTGyskr0&rel=1&fs=1&hd=1</a>

wow, those are nice

If you're computing the iterative function in CUDA, I could offer a replacement "float" type (implemented as a class) that makes use of the dsfun math library, to emulate  double precision floats with two single precision floats.

very impressive indeed.  i too am curious about the blue "haze"...