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A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. 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.
Its Hausdorff dimension is estimated from above by the Lyapunov dimension (Kaplan-Yorke dimension) as 2.06 ± 0.01, [20] and the correlation dimension is estimated to be 2.05 ± 0.01. [21] The exact Lyapunov dimension formula of the global attractor can be found analytically under classical restrictions on the parameters: [ 22 ] [ 20 ] [ 23 ]
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 branch of mathematics ...
Had the butterfly not flapped its wings, the trajectory of the overall system could have been vastly different. As suggested in Lorenz's book entitled The Essence of Chaos, published in 1993, [6]: 8 "sensitive dependence can serve as an acceptable definition of chaos". In the same book, Lorenz defined the butterfly effect as: "The phenomenon ...
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 ...
Atmospheric thermodynamics is the study of heat-to-work transformations (and their reverse) that take place in the Earth's atmosphere and manifest as weather or climate. . Atmospheric thermodynamics use the laws of classical thermodynamics, to describe and explain such phenomena as the properties of moist air, the formation of clouds, atmospheric convection, boundary layer meteorology, and ...
She notes that, in general, people have a schema for how things should look in the world and filter their memories through that lens. Let's look at Mr. Monopoly, mascot of the famous board game.
Brown Willy effect (geography of Cornwall) (mesoscale meteorology) Bruce effect (reproduction) Bullwhip effect (distribution, retailing, and wholesaling) Butterfly effect (chaos theory) (physical phenomena) (stability theory) Bystander effect (crowd psychology) (social phenomena) Bystander effect (radiobiology) (radiobiology)