====== Chaos Theory ======

{{tag>Unknowable}}

//Chaos Theory// is the concept that the behaviour of some complex dynamical systems (e.g. global weather patterns) can be extremely sensitive to tiny changes in initial conditions.

Any large-scale system which has a complex set of interacting feedback and feed-forward loops can become chaotic - thus making accurate and specific long-term predictions about the system unreliable, if not impossible.

In 1963, the publication of Edward Lorenz’s groundbreaking paper, [[http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2| 'Deterministic Nonperiodic Flow']]  in the //Journal of Atmospheric Science// hailed the beginning of a new field of mathematical study - with applications in meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, and philosophy.

And a now-famous talk, also by Edward Lorenz  (presented to the American Association for the Advancement of Science in Washington, D.C. in 1972) was entitled //'Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?'// It subsequently gave rise to the phrase [[https://en.wikipedia.org/wiki/Butterfly_effect|The Butterfly Effect]]

**Notes.**

1) The outcomes of a chaotic system are //not// truly  random - but they can degenerate into what appears to be randomness.

2) Although the flap of a butterfly's wings in Brazil could (in theory) set off a tornado in Texas, the chances of it doing so are astronomically small - thus, accurate predictions about which butterfly and when are essentially zero.

3) An (apparently) chaotic system can also 'spontaneously' fall into organised, or synchronised behaviour - so-called //Spontaneous Order// - examples are multiple connected-pendulum swings, firefly swarm light emissions, and group neuronal firing.


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Also see : [[content:mathematics:fractals]]

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