Above you see two graphs representing two independent populations. The equation determing those species development is as easy as you can imagine (the population sizes are normalized to values between 0.0 and 1.0): fertility*oldSize*(1.0-oldSize) When you try some runs with low values for the fertility (<3.4) you will realize that the graphs tend to some equlibrium state (they no longer change) or that they always jump up and down. But when you try higher fertility rates you will realize that already small differences in the initial population sizes accumulate and give the graphs a very different development. This is chaotic behaviour. For more information I refer to: Sigmund, Karl: Games of Life, Wien 1993 If you don't see the graphs Java VM is disabled or not even installed. Click here to download Java VM now