Here we have a derivation of the popular Koch fractal. But I added some randomness to make things a bit more interesting.

Vera Molnar once said, that she found the most interesting and aesthetically pleasing results when she added 1% randomness to a given structure.
Here the average probability that something happens that does not follow the rules of the Koch curve is 2.8%.
– maybe that´s too much?

2007
Java applet
built with Processing

run the applet
(You may want to download an up-to-date version of Java and run it on a reasonably fast machine. Might take a while to actually start.)