I love looking at fractals. The core characteristic of these calculations is that as you calculate (or zoom into a visual representation of the calculations) you see similar structures no matter how far you go. The video below shows just how extreme this can be.

Mandelbrot Fractal Set Trip To e214 HD from teamfresh on Vimeo.

If you are interested in a fuller explanation, below is part 1 of an explanation by Arthur C. Clark.