Student: I have played the so-called Chaos Game and experimented with the Simple Forest Fire. Both of these are somehow related to chaos. What is chaos??

Mentor: Chaos is the breakdown of predictability.

Student: So, the fact that when we played the chaos game we didn't know where we were moving next, and when we experimented with the fire simulation we couldn't predict exactly how many trees would burn for a given probability was chaos?

Mentor: Yes. Chaos can be present in many ways. It can be the unpredictability from randomness -- like not knowing what number will come up on your dice. It can be the breakdown in predictability caused by small changes in one piece of information producing a huge difference in the answer later. This latter idea was first stumbled upon by E. N. Lorenz in 1956 when he was trying to look at modeling the weather using mathematical equations. He found some good equations to work with (they now bear his name) and saw that if he made teeny tiny changes to the initial inputs for the weather, he got dramatically different, unpredictable results. Moreover, the further into the future he tried to predict, the worse it got!

Student: Weather forcasters seem to be able to predict the weather now at least for a little while into the future.

Mentor: That's because they've had over 40 years to find better equations. But they still don't have great predictions past two or three days.

Student: So if chaos is present, we can't do anything with our computer information? It is not good for predicting, so why do it?

Mentor: There are several reasons to look at chaos. Think about the Chaos game. The unpredictability on the small scale (where to move next) results in a predictable fractal shape! Chaos and Fractals are very closely linked. Chaotic things can end up with very interesting -- and predictable -- fractal patterns. The particular individual numbers are not predictable, but the overall pattern can be. With chaotic systems like weather, we just have to be careful about how far into the future we can predict.

Please direct questions and comments about this project to Addison-Wesley math@aw.com
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