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Let's not forget there is another large group of 3D type fractals out there which use sphere inversions. Here is an example that uses Mobius Transforms.

Both the Mobius inversions and the straight 3D inversions use the "Plane and Sphere Raytracing" formula in the Ultrafractal database (reb5.ucl). It in turn calls a raytrace library called RaytraceSphere in reb.ulb. Anyone who own UF 5 has access to the database and can see the code used. The tetrahedral sphere inversions and the Mobius inversions are plugins to RaytraceSphere.

i also have that book, it's such a joy

here are some sphere inversion fractals i rendered in 2005:

http://imgur.com/hQ7WG.jpg
http://imgur.com/3jzgU.jpg