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The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. This is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.

The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or, for that matter, prevent a tornado from appearing). The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.

Recurrence, the approximate return of a system towards its initial conditions, together with the sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range—approximately a week, in the case of weather.
Image Details:
These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ only by 10-5 in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t=30.

History
Sensitive dependence on initial conditions was first described in the literature by Hadamard and popularized by Duhem’s 1906 book. The term butterfly effect is related to the work of Lorenz, who in a 1963 paper for the New York Academy of Sciences noted that “One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings could change the course of weather forever.” Later speeches and papers by Lorenz used the more poetic butterfly. According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the AAAS in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? as a title.

Popular media
The concept of the Butterfly effect is sometimes used in popular media dealing with the idea of time travel, usually inaccurately. In the 1952 short story by Ray Bradbury, “A Sound of Thunder”, the killing of a butterfly during the time of dinosaurs causes the future to change in subtle but meaningful ways: e.g., the spelling of English, and the outcome of a political election. According to the actual theory, however, the mere presence of the time travelers in the past would be enough to change short-term events (such as the weather), and would also have an unpredictable impact on the distant future.

In a Simpsons episode about Homer going back to the time of dinosaurs with a time machine (a la Bradbury’s story), Homer commits intentional and unintentional violence in the past, violence which drastically changes the future (i.e., Homer’s present).

In many cases, minor and seemingly inconsequential actions in the past are extrapolated over time and can have radical effects on the present time of the main characters. In the movie The Butterfly Effect, Evan Treborn (Ashton Kutcher), when reading from his adolescent journals, is able to essentially “redo” parts of his past. As he continues to do this, he realizes that even though his intentions are good, the actions he takes always have unintended consequences. However, this movie does not seriously explore the implications of the butterfly effect; only the lives of the principal characters seem to change from one scenario to another. The greater world around them is mostly unaffected.

Another movie which explores the butterfly effect (though not advertised as such) is Sliding Doors. The movie observes two parallel life paths of a woman named Helen, played by Gwyneth Paltrow. These two paths diverge when Helen attempts to catch a commuter train. In one life path she catches the train, and in another she is delayed for just a few seconds and barely misses the train. This results in two dramatically different sets of events.

The Butterfly effect was also invoked by fictional mathematician Ian Malcolm in both the novel and film versions of Jurassic Park. He used it to explain the inherent instability of (among other things) an amusement park with dinosaurs as the attraction - although this interpretation can also be taken to mean that zoo animals will always escape and kill their captors.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Butterfly effect”.