The Lorenz attractor is the strange attractor that arises from the Lorenz system, a set of three ordinary differential equations first developed by the meteorologist Edward Lorenz in 1963 while modeling atmospheric convection. Solutions to the system are extremely sensitive to their initial conditions, so that two nearly identical starting states diverge into unpredictable long-term behavior despite the equations themselves being fully deterministic, a property that inspired the popular image of the butterfly effect. Plotted in three dimensions, trajectories trace out a bounded, non-repeating, butterfly-shaped surface, the Lorenz attractor itself, one of the first strange attractors studied in detail and a founding example of deterministic chaos.
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FAQs
Is the Lorenz attractor really a strange attractor?
Yes; Tucker proved it in 2002.
Yes, though this was settled only recently. Smale posed it as an open question in his list of challenging problems for mathematics, asking whether the Lorenz attractor is a strange attractor. Tucker answered it in the affirmative in 2002, with a proof that combines normal form theory and validated interval arithmetic.
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The Lorenz system is a set of three ordinary differential equations, first developed by the meteorologist Edward Lorenz while studying atmospheric convection.
- In Branch: Dynamical Systems
View the Source Edward Norton Lorenz (Wikipedia)
Principal Result Of: Edward Norton Lorenz, Chaos theoryQuote, Principal Result Of: Edward Norton Lorenz, Chaos theory
Lorenz's discovery, which gave its name to Lorenz attractors
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