"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 can 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 1952 Ray Bradbury short story A Sound of Thunder. In that story, a time traveller accidentally steps on a butterfly in the distant past, causing broad changes in the present. A common description of the effect says that a butterfly flapping its wings in Brazil can cause a tornado in Texas months later. A version from Car Talk is that "A butterfly flaps its wings in Africa, and the sink backs up in your garage."

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. Finite models that attempt to simulate these systems necessarily discard information about the system and the timing of events. These errors are magnified as each unit of time is simulated until the error bound on the result exceeds one hundred per cent.

Pop culture sightings

A "Quantum Weather Butterfly" appears in Terry Pratchett's novel Men at Arms. It has a fractal pattern on wings (Illustration in The Discworld Companion reveals it to be Mandelbrot set) and its survival depends on its ability to change weather by flapping its wings.

"Chaos Butterfly" is a recurring strip in Super-Fun-Pak Comics, part of Tom the Dancing Bug.

"Chaos Butterfly" is an item in the MMORPG Kingdom of Loathing.

In 2004, a movie starring Ashton Kutcher called The Butterfly Effect told of a college student who found a way to alter his past through repressed memories; each time he did, his life was dramatically altered in the present.

External links

• Butterfly Effect (Mathematical Recreations)
• From butterfly wings to single e-mail (Cornell University)
• The Chaos Hypertextbook. An introductory primer on chaos and fractals.
• The Butterfly Effect. New Line Cinema's feature film Butterfly Effect IMDB