A sandpile simulator with documentation.
Complex adaptive systems arrange themselves around one or more critical factors (like in a sandpile, for example, where the pile will rearrange itself when you drop additional sand Grains onto it). The theory behind these systems is related to Chaos Theory, but the systems are "on the Edge Of Chaos", because they have the ability to adjust themselves (around the critical factors), unlike truly chaotic systems.
One interesting thing with CA-systems is that they can suddenly rearrange themselves rather violently. Like in a sandpile which has a grain added to it, which topples onto other grains, which in turn topple onto other grains, etc. You have an Avalanche effect.
Many phenomena in daily life are complex adaptive systems, like weather, traffic, Earthquakes, eco-systems, or the stock market. This is why the science behind CA-systems, which is relatively new, is very promising as it can probably help tell us a good deal about our world which we can't tell or simply don't know yet.