# Lorenz attractor

(redirected from*Lorenz equations*)

## Lorenz attractor

[′lȯr‚ens ə‚trak·tər] (physics)

The strange attractor for the solution of a system of three coupled, nonlinear, first-order differential equations that are encountered in the study of Rayleigh-Bénard convection; it is highly layered and has a fractal dimension of 2.06. Also know as Lorenz butterfly.

## Lorenz attractor

(mathematics)(After Edward Lorenz, its discoverer) A region
in the phase space of the solution to certain systems of
(non-linear) differential equations. Under certain
conditions, the motion of a particle described by such as
system will neither converge to a steady state nor diverge to
infinity, but will stay in a bounded but chaotically defined
region. By chaotic, we mean that the particle's location,
while definitely in the attractor, might as well be randomly
placed there. That is, the particle appears to move randomly,
and yet obeys a deeper order, since is never leaves the
attractor.

Lorenz modelled the location of a particle moving subject to atmospheric forces and obtained a certain system of ordinary differential equations. When he solved the system numerically, he found that his particle moved wildly and apparently randomly. After a while, though, he found that while the momentary behaviour of the particle was chaotic, the general pattern of an attractor appeared. In his case, the pattern was the butterfly shaped attractor now known as the Lorenz attractor.

Lorenz modelled the location of a particle moving subject to atmospheric forces and obtained a certain system of ordinary differential equations. When he solved the system numerically, he found that his particle moved wildly and apparently randomly. After a while, though, he found that while the momentary behaviour of the particle was chaotic, the general pattern of an attractor appeared. In his case, the pattern was the butterfly shaped attractor now known as the Lorenz attractor.

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