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Posted by Igor Livojevic on April 16, 1998 at 18:02:48:
In Reply to: Chaos Theory posted by Micaela Callahan on January 10, 1998 at 11:11:14:
Dear Ms Callahan
The main idea is that very little movements in basic system conditions lead to big changes in behaviour of the whole system. The theory actually started with Poincare, in his cricicism of Laplace's determinism, which implied that the behaviour of the system was actually determined by known factors. But, the theory, in a modern form, in which it is which is known today, started with meteorologist Lorenz, and is connected with the development of information technology as well. About ten years after his discovery, his achievements were accepted in maths and physics, and later in economics, biology etc. The theory is also known as the theory of non-linear, dynamic systems. You will probably be familiar with so called erfly effect-movements of wings of a erfly in one part of the world affects weather on the other side of the planet. It is not possible to know all basic conditions, but mathematical models use differential equations to express those basic, starting conditions,development of the system is done on the basis of them, and in every step we use iterations-the last formula from the last step becomes starting point of the next one. And now, we can see a curve, which represents system's behaviour. Also, now we have so called phase space, in which coordinates are variables. After certain time, curve goes into so called attractor, which is a part of phase system, in which the system stays forever, and chaotical attractors are called fractals-geometrical structures which consist of algorythms.
Best regards
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