What is "butterfly effect"

n. The technical notion of sensitive dependence on initial conditions in chaos theory.

n. the phenomenon whereby a small change at one place in a complex system can have large effects elsewhere, e.g., a butterfly flapping its wings in Rio de Janeiro might change the weather in Chicago

The butterfly effect is the concept that small causes can have large effects. Initially, it was used with weather prediction but later the term became a metaphor used in and out of science.

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The name, coined by Edward Lorenz for the effect which had been known long before, is derived from the metaphorical example of the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

The idea, that small causes may have large effects in general and in weather specifically, was used from Henri Poincaré to Norbert Wiener. Edward Lorenz's work placed the concept of instability of the atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.

The butterfly effect is exhibited by very simple systems. For example, the randomness of the outcomes of throwing dice depends on this characteristic to amplify small differences in initial conditions—the precise direction, thrust, and orientation of the throw—into significantly different dice paths and outcomes, which makes it virtually impossible to throw dice exactly the same way twice.

The butterfly effect is a metaphor for sensitive dependence on initial conditions in chaos theory.

It may also refer to:

is the 6th major single by the Japanese girl idol group Shiritsu Ebisu Chugaku. It was released in Japan on June 4, 2014 on the label Defstar Records. The song was used as the opening theme for the 2014 anime series Nanana's Buried Treasure.

Butterfly Effect is the debut solo studio album by American singer-songwriter Ashley Roberts. It was released through Metropolis London on September 1, 2014. There are two singles released from the album: " Clockwork", on May 25, and " Woman Up" on August 25. It was produced by eight producers including Frankmusik.