Recipes for chaos

There are four possible ways to get chaos:
  1. Ignorance:this is labeled as "external influences". If you don't know what's happening than the result will be "surprising" and thus chaotic.
  2. Many simple systems interacting in space:you know well how the single system behaves but the overall result can be surprising and thus chaotic. The simplest case is cellular automata. In this case interaction in space is essential to have chaos .
  3. One single system developing in time:also here if the law is recursive than the result (after some time) can be surprising and thus chaotic. Time in this case is essential to get chaos.
  4. Use a quantum system like a radioactive material:the law is then intrinsically chaotic. There is no way to know when exactly a radiactive substance will decay.
In case 2 and 3 we speak of deterministic chaos i.e. chaos in presence of well known and simple laws. Note that a physical system may present in the same time all four kind of chaos! Fortunately in the cases 2,3,4 the chaos is not absolute since we can say a lot of things about the possible outcome of the experiment. For example in case 2 and 3 the result must lie in a well known range in phase space where we have the chaotic or strange attractor. In case 4 we know exactly what is the probability of each possible outcome.
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Maintained by Giuseppe last update 28 Apr 97