In chaos theory, the butterfly effect is the sensitive dependency on initial conditions in which a small change at one place in 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 theoretical example of a hurricane's formation being contingent on whether or not a distant butterfly had flapped its wings several weeks earlier. Although the butterfly effect may appear to be an esoteric and unlikely behavior, it is exhibited by very simple systems. For example, a ball placed at the crest of a...