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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
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.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
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 ...
In order to ease this problem, Mackey, M.C. & Glass, L. (1977) proposed changing the production rate to a function (()) of the concentration at an earlier point in time, in hope that this would better reflect the fact that there is a significant delay before the bone marrow produces and releases mature cells in the blood, after detecting low ...
[23] [24] Visual patterns in nature find explanations in chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns. For example, L-systems form convincing models of different patterns of tree growth. [19] The laws of physics apply the abstractions of mathematics to the real world, often as if it were perfect.
For example, even the small flap of a butterfly's wings could set the earth's atmosphere on a vastly different trajectory, in which for example a hurricane occurs where it otherwise would have not (see Saddle points). The shape of the Lorenz attractor itself, when plotted in phase space, may also be seen to resemble a butterfly.
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 ...