I dunno how many of you guys have heard of "imaginary numbers" or "fractals"... anyway, the most famous fractal (which I'm sure you've seen somewhere) is basically a picture of a certain set of imaginary numbers called the Mandelbrot set.

The set itself contains every complex (imaginary) number 'z' that doesn't cause the following sequence to blow up to infinity:

z(0) = z, z(n+1) = z(n)*z(n) + z, n = 1,2,3,4,....

Instead of doing my homework today, I wrote a computer program to "draw" the Mandelbrot set... these were some of the coolest images it produced:

It's amazing how such a simple formula can produce this beautiful result. You can make your viewing window as small as you want (and I did, though I have to do some fine-tuning before I can take good pictures) and you will always see the same incredible level of complexity, and you'll be seeing parts of the set that nobody has probably looked at before simply because it has that infinite complexity.

Anyone else ever play around with this stuff? The math isn't actually that complicated...