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There is no real interaction, it just runs. The Conway rule changes the edges to random values every frame, the other two rules just set the edges to a random value at the start. I looked at other "life-like" rules but most of them seem to result in the whole screen just filling pretty quickly.

HTML5 Canvas obviously, the javascript is a bit sloppy since I pretty much just sat down and banged it out at 3am last night. I didn't minify it, so you can take a look at it pretty easily but don't expect something pretty.