Butterfly effect
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- For other uses, see Butterfly effect (disambiguation).
The Butterfly Effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. The idea is that small variations in the initial conditions of a dynamical system produce large variations in the long term behavior of the system.
Edward Lorenz first analyzed the effect in a 1963 paper for the New York Academy of Sciences. According to the paper, "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings would be enough to alter the course of the weather forever." Later speeches and papers by Lorenz used the more poetic butterfly, possibly inspired by the diagram generated by the Lorenz attractor, which looks like a butterfly; other theories propose that the phrase's basis is to be found in fiction (Ray Bradbury's A Sound of Thunder-1952), but there is no proof available that Lorenz was swayed by literary precedent.
The practical consequence of the butterfly effect is that complex systems such as the weather or the stock market are difficult to predict over any useful time range. This is because any finite model that attempts to simulate a system must necessarily truncate some information about the initial conditions—for example, when simulating the weather, one would not be able to include the wind coming from every butterfly's wings. In a chaotic system, these errors are magnified as each unit of time is simulated until the bound on the percent error of the result exceeds one hundred percent. Thus the predictions of the simulation are useless after a certain finite amount of time.
See also
- Chaos theory
- The Butterfly Effect - A movie starring Ashton Kutcher and Amy Smart.
External links
- Butterfly Effect (http://www.fortunecity.com/emachines/e11/86/beffect.html) (Mathematical Recreations)
- From butterfly wings to single e-mail (http://www.news.cornell.edu/releases/Feb04/AAAS.Kleinberg.ws.html) (Cornell University)
- The Chaos Hypertextbook (http://hypertextbook.com/chaos/). An introductory primer on chaos and fractals.
- The Butterfly Effect (http://www.butterflyeffectmovie.com/). New Line Cinema's feature film Butterfly Effect IMDB (http://www.imdb.com/title/tt0289879/)de:Schmetterlingseffekt
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