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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.
Lorenz equations used to generate plots for the y variable. The initial conditions for x and z were kept the same but those for y were changed between 1.001, 1.0001 and 1.00001. The values for , and were 45.91, 16 and 4 respectively. As can be seen from the graph, even the slightest difference in initial values causes significant changes after ...
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 ...
Organizers of the ‘F1 in Schools’ competition say the Netflix ‘Drive to Survive’ effect is reaching the classroom with a record number of teams entered in this year’s finals in Singapore ...
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 ...
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 second-largest U.S. producer is partnering with investment firm Engine No. 1 and electric services company GE Vernova on the project. Chevron's announcement comes a day after Chinese startup ...