Anarchy: good luck with that!
Some people have a hard time grasping that disorder can yield order, or that an impossibly stupid approach can yield beautiful results. Those people have clearly never heard of the Chaos Game. I bet you knew my earlier talk of fractals would get us here eventually.
Note: my code attempts to use the canvas element to draw the dots. For browsers that don't support that, the code uses 1 pixel div elements. Having thousands of elements in the document for longer plots can potentially suck up a lot of resources. If you're going to let it run for longer than around 30 seconds, you're probably best served by using a browser with canvas support.
Update: the code has been modified since original publication as explained here