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Stewart Dean's Guide to Artificial Life

Chaos Theory

Chaos theory is about explaining apparent disorder in a very ordered way. Chaos theory states that things are not really random, just complex. Many apparently random events can be represented by a simple computation which, when iterated, produce complex results. That is a formula which is constantly repeated can produce models of trees and weather system. The values from each stage are feed back into the next stage, also known as feed back. The result of iteration, formulas and feedback is a chaotic system. Most natural processes are chaotic systems as well as many man made ones. For example the sea is a chaotic system drive by a finite amount of inputs (wind, sun, tides, land masses, etc.). The result is a complex system which although possible to predict generally is hard to predict in detail. Any one who has, at one time or the other, played at dodging the wave at the beach will know that.

A man made example of a chaotic system is the financial markets of the world. These, from the outside, appear to be random and unpredictable, but, as we know, each financial decision is a conscious decision and is far from random. Each step of the way computations are used, along with previous knowledge to make these decisions. Yet, due to the sheer complexity of dependencies, the results can often appear to be far from rational.

Different algorithms produce different amounts of complexity when iterated. Also changes in a chaotic system can have different levels of impact. Each event has a constantly different amount of effect on the next step. The famous example is the butterfly effect, where it is claimed that the flapping of the wings of a butterfly can, given time, effect the direction of a hurricane on the other side of the planet. On the other side it may have no effect at all. It is this apparent lack of ease of prediction that creates what we call random effects. A chaotic system can only be predicted if all the inputs into the system are known and all the rules the system are know. If only the rules are known you can reproduce the behaviour of something but not the exact occurrence that has been produced before. For example you can grow a tree inside a computer (or at least a tree shape), but unless you know what the starting seed for the tree's growth was it will be very hard to reproduce that tree again, but it will still look like a tree, just not the same one.

An example of this is a general election. The reasons for why a person might vote for one party or the other are very complex. If we look at all those that vote, some reasons have more effect than others. Some events will make the local news that will effect hundreds of voters, some events happen only to one person and some will nearly effect all. All these influences will result in a person voting for one of, say, three parties. Each vote may seam to have very little effect on the whole result but a single vote could give one party the lead over the other. If this happens there is no way to really trace which vote it was, but one voter changing his mind could result in a coalition or a single party ruling the country. Mandlebrot Set Because each voter votes for a reason, general elections are not random, just unpredictable. This, to varying level of complexity, is true for all chaotic systems.

Chaos theory is about patterns. Because a chaotic system is about repeated steps often irregular patterns, or sometimes almost regular patterns are produces. One example of this is the Mandelbrot set. This is a pattern produced by a simple function that is infinite in detail but, quite clearly include many patterns that repeat themselves in constantly changing ways. Some patterns will reoccur at different intervals and stay relatively stable for some time. These are called attractors, sometimes called chaotic attractors or strange attractors.

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