While I'm trained as an experimental scientist/engineer, and have a visceral rejection of pure mathematics, every now and again something worthwhile (in my narrow view of math) appears. Actually as I've touched on before I don't think I have the capacity to have a visceral reaction to anything as my logical side generally overwhelms more low level reactions, but I digress.
While cruising /. I stumbled upon this interesting bit on the search for a 3D Mandelbrot set. A 2D Mandelbrot set leads to pretty stunning images that have a fractal nature, and the 3D "equivalent" is pretty mind blowing. the overarching basic concept of a fractal is that is comprised of smaller building blocks that are of the same form, this is self-similarity. This patterning holds at any scale so as you "zoom in" the structure is maintained. A classic example is the Sierpinski triangle.
The Mandelbrot set is a more complex fractal, and someone has tried to create a 3D analog. This is what it looks like:
While this is a pretty interesting looking "thing", it gets better as you zoom in:
Checkout the rest of the site to see some other really cool images that are found by zooming in on different parts of the rendering.