This is a variation on the a mathematical Random Walk. Essentially what this thing does is plot a curve using the Actionscript Drawing API. Then it randomly picks another point to draw a curve to. Just for fun it randomly picks from a range of colors and opacities just for added visual appeal.
I only put a few hours of work/play into this so there are some rough edges here and there. The main thing is that there is some odd behavior when you hit the “Start Over” button so you might want to use refresh instead. And this SWF can put a pretty serious dent on your CPU cycles so I wouldn’t leave it running for too long. The code is all included in the download if you would like to play with this yourself.

Watch the Walk

Download

Here’s the main bit of code that makes everything happen.