While fractals can make pretty pictures, they also started a new branch of mathematics which has helped us to understand the crazy world we live in.
It all began when some guy (think someone like Laurie but way geekier and not nearly as cool) was trying to model the weather. He had logged into his trusty campus computer, and had plugged in some equations for a really simple world. This planet was completely smooth like a big billiard ball. All it had were variables describing wind, sun and ocean.
Also being before the advent of computer screens the only output device he had was a dot matrix printer. This was quite limited in what it could output, so he just output the equivalent of the seabreeze graph on the paper. He'd start it going, and marvel at how the wind would go up, down, swing around, without a definite repeating pattern emerging. Other people at the campus would come around and gaze in awe at the strange patterns emerging from the printer. I guess people were easily amused in those days.
Anyway one day the computer stopped for some reason, so he plugged in the results that were printed out a page or two from the end of the printout and started the process going again. To his utter amazement the pattern started out the same as how the process had gone previously, but then rapidly diverged into a completely new system. This was the eureka moment, when the first glimmerings of chaos theory was born.
The mandelbrot set was invented by some french dude without even a computer to plug equations into. He just thought really hard about stuff, and invented the mandelbrot set. He even managed to draw some rough diagrams of what it might look like. That's pretty impressive...
If you're wondering how to make it yourself, firstly make a plane of numbers, with real numbers (-3 to 3 works well) going sideways, and imaginary numbers (again, -3i to 3i works well) going vertically.
Now pick a point anywhere on this plane. It will consist of two coordinates, and we'll call it c for the moment.
Now you have your starting point, repeat this equation 20 times:
z = z squared + c
(where z starts at 0 + 0i ).
If, after 20 iterations the number you're left with is a long way from the origin then paint that spot white, if it's still close to (0, 0i) then paint it black.
A really good book to sink your teeth into is called "Chaos", by James Gleick. Highly recommended for the geekier amongst us
