Some of the new 3d objects that have been rendered in the last few years are some of the most beautiful mathematical objects I've ever seen. Almost a Technological Baroque Architecture. I think it will be a grand day when Architects start being inspired by this and actual spaces start to take on this look...something that may only be possible with additive manufacturing.
edit: the demoscene has been experimenting with objects like this for the last few years in terms of real-time navigable demonstrations with some stunning results in 4Kb.
Loved the discussion of distance estimator formulae. As I recall them, to derive one of the results in The Science of Fractal Images you'd need to use Koebe's 1/4th theorem applied to the potential function (or a related function which is analytic) and thus you'd solve the factor problem. It's a little hazy, since I did this 6 years ago, since then I've only worked with entire transcendental functions where potentials are harder to come by. A useful approach then is to use a bifurcation loci approximation result (like this thing I worked on for a while: http://www.maia.ub.es/~ruben/docs/20110531Centres.pdf
The paper with the result kind of entered a limbo while I finished my PhD... and is still there (after all it is just like 8 pages long)
PS: Why orange? Just to avoid using the "standard blue" used in most Beamer slides :D It doesn't look as offensive in a projector as in a screen, too.
These are stunning images, what I find fascinating is the similarity between these images and ones found in nature. For example http://blog.hvidtfeldts.net/media/mbulb3.jpg looks to me a lot like a virus to me. For a long time fractals have been used to create computer generated landscapes that look real but this takes that technique to a new level.
http://www.gizmag.com/swiss-architects-3dprint-a-room/29299/
edit: the demoscene has been experimenting with objects like this for the last few years in terms of real-time navigable demonstrations with some stunning results in 4Kb.
http://www.youtube.com/watch?v=UjgRGDhgehA
http://www.youtube.com/watch?v=pkD0AzYcJIQ