Random article ( of 1062 ) Latest updates

User Tools

Site Tools


content:mathematics:chaos_theory

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 Lorenz’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

unknowable

The word 'Fractal' was coined in 1975 by the mathematician Benoît 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".

Importance Rating


Show another (random) article

Suggestions for corrections and ideas for articles are welcomed : Get in touch!


Further resources :

Do NOT follow this link or you will be banned from the site!

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK MAY 2024