This was new to me. I didn't know that they had successfully rendered fractals in the third dimension. In this case the 'they' is Daniel White and Paul Nylander, who publish their work on the blog fractalforums.
For the savvy few, you can download the scripts at the excellent blog subblue. Apophysis also has scripts for Windows, if that's your OS.
Ron Eglash is the author of African Fractals, a book that examines the fractal patterns underpinning architecture, art and design in many parts of Africa. He does a fascinating TED talk that you should watch. Here is a great site stuffed with images of natural and man-made fractal designs, including a couple from Eglash's book.
The first two photos are from Skytopia
Mandelbulb zoom from subBlue on Vimeo.