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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 of the effect, coined by Edward Lorenz, 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 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.
