# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Chaos Theory

*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 Lorenzâ€™s groundbreaking paper, '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 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.

Also see : Fractalsplugin-autotooltip__plain plugin-autotooltip_bigFractals

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The word 'Fractal' was coined in 1975 by the mathematician BenoÃ®t Mandelbrot - but the study of self-repeating mathematical systems dates back several centuries.

Mandelbrot provided a definition of a fractal as : "A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole".

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