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The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other. Experimental demonstration of the butterfly effect with six ...
Chaos theory 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. [1]
Lorenz system. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
Butterfly effect in popular culture. 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 ...
Sabattier effect (solarization) (photographic processes) (science of photography) Sachs–Wolfe effect (astronomy) (physical cosmology) Sagnac effect (optics) (relativity) Sailing Ship Effect (business) (economics) Samba effect (Brazil) (economy of Brazil) (history of Brazil) Sandbox effect (Internet technology) (search engine optimization)
Edward Norton Lorenz. Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology. [1][2] He is best known as the founder of modern chaos theory, a ...
In mathematics, a dynamical system is chaotic if it is (highly) sensitive to initial conditions (the so-called "butterfly effect" [61]), which requires the mathematical properties of topological mixing and dense periodic orbits. [62] Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature.
Causality is the relationship between causes and effects. [1][2] While causality is also a topic studied from the perspectives of philosophy and physics, it is operationalized so that causes of an event must be in the past light cone of the event and ultimately reducible to fundamental interactions. Similarly, a cause cannot have an effect ...