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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.
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.
The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. [1] The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. [2] [3] The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.
The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is sensitive dependence on initial conditions). [4]
In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter [ 1 ] and is one of the early examples of modern ...
Higher-order catastrophes, such as the swallowtail and the butterfly, have also been observed. [17] Cusp catastrophe caustic, generated from a circle and parallel rays. A photograph of a cusp caustic produced by illuminating a flat surface with a laser beam through a droplet of water. This is a Pearcey function and stable under perturbations.
Lorenz was born in 1917 in West Hartford, Connecticut. [5] He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at the Massachusetts Institute of Technology, and his maternal grandfather, Lewis M. Norton, developed the first course in chemical engineering at MIT in 1888.
Theories in physics like the butterfly effect from chaos theory open up the possibility of a type of distributed parameter systems in causality. [citation needed] The butterfly effect theory proposes: "Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system."