Butterfly effect

The butterfly effect is a theorem of chaos theory that small variations in the initial conditions of a dynamical system can produce large variations in the results.

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.

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.