Lorenz attractor


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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.
References in periodicals archive ?
Unlike the Lorenz attractor that swiftly exhibits beautiful butterfly wings after a few hundred iterations (Palmer 1993), one further notices in Fig.
Examples of such strange attractors include the famous Lorenz attractor illustrated in Figure 6(d) [30], Henon attractor, and logistic map attractor.
With these examples, what is clear is that any extended object demarcated by a set of points of the phase space, configured in any form whatsoever, will be transformed into the wings of the Lorenz attractor.
The Lorenz Attractor was created with MapleSim's Signal Blocks and is used to simulate chaotic systems such as climate and weather.
Visualizations of the Mandelbrot Set, the Lorenz Attractor and the Feigenbaum function in the complex plane are stunning and rival many renditions of what are considered more conventional art forms.
The graph that produces the Lorenz attractor can be seen at the Bourke (1997) site and is shown in Figure 5 below.
Most students are interested in music (and computers) and may be motivated to learn mathematics by studying, for example, the Lorenz attractor and the techno music it produces when mapped to sonic parameters.
233-36) Sometimes this has been called the Lorenz attractor.
It's called the Lorenz attractor, named for meteorologist Edward N.
This phenomenon may be observed by studying the Lorenz attractor.
proposed a new chaotic system: the system connects the Lorenz attractor and Chen attractor; Lu system is a special case; hence, it is called the unified chaotic system [24].
In the original papers, it is said that the value 8/3 for the parameter b is used by scholars in many disciplines who use Lorenz attractors (Losada and Heaphy, 2004).