Computer science professor Paul Bourke has an exhaustive amount of information about fractals on his website, but for my money the coolest part is his collection of naturally occurring fractal images from Google Earth. If I hadn’t looked them up, I’d suspect some of these were computer-generated — but no, they’re real rivers, lakes, and mountain ranges branching into mathematically and aesthetically beautiful patterns, like a freaking Piers Anthony novel or something. (Fractal Mode? Anyone else? No? It’s pretty bad.)
Bourke has way more fractals on his site, along with data files so you can find them on Google Earth. These are some of my favorites (click to embiggen), but frankly they’re all staggering. Did you have any idea you lived inside a Mandelbrot set? Well, now you do.