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Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
The nature of chaos theory suggests that the predictability of any system is limited because it is impossible to know all of the minutiae of a system at the present time. In principle, the deterministic systems that chaos theory attempts to analyze can be predicted, but uncertainty in a forecast increases exponentially with elapsed time. [2]
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 term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
Butterfly effect image. The butterfly effect describes a phenomenon in chaos theory whereby a minor change in circumstances can cause a large change in outcome. The scientific concept is attributed to Edward Lorenz, a mathematician and meteorologist who used the metaphor to describe his research findings related to chaos theory and weather prediction, [1] [2] initially in a 1972 paper titled ...
By comparison, based on the concept of attractor coexistence within the generalized Lorenz model [26] and the original Lorenz model ([36] [37]), Shen and his co-authors [35] [38] proposed a revised view that “weather possesses both chaos and order with distinct predictability”. The revised view, which is a build-up of the conventional view ...
Chaos theory is sometimes pointed out as a contradiction to Laplace's demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. [9]
The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible [citation needed]. Computational irreducibility explains why many natural systems are hard to predict or simulate.