Difference between revisions of "Strange Attractors"

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[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]An '''attractor''' is a set to which a '''[[Dynamical Systems| dynamical system]]''' evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
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[[Image:Lorenz-attractor-render-1-small.jpg|200px|right|thumb|The Lorenz Attractor]]A '''strange attractor''' is an infinite-point [[Field:Dynamic Systems#Jump3|attractor]] with [[Fractal Dimension|non-integer dimension]]. The trajectory of a system characterized by a strange attractor never repeats itself, but still stays within a bounded region of [[Field:Dynamic Systems#Jump2|state space]]. Strange attractors are a type of [[Field:Fractals|fractal]], exhibiting self-similarity on all scales.
 
 
 
 
An attractor is informally described as '''strange''' if it has non-integer '''[[Fractal Dimension| dimension]]''' or if the dynamics on it are '''[[Chaos| chaotic]]'''.
 
 
 
[[Image:Henon1.jpg|200px|left|thumb|The Hénon Attractor]]
 
 
 
The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often '''[[Differentiability| differentiable]]''' in a few directions, but some are like a Cantor dust, and therefore not differentiable.
 
 
 
  
 
Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], Rössler attractor, [[Lorenz Attractor]], Tamari attractor.
 
Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], Rössler attractor, [[Lorenz Attractor]], Tamari attractor.
 
'''Note: Must be edited... This is directly taken from [http://en.wikipedia.org/wiki/Attractor wikipedia].
 

Revision as of 14:11, 5 June 2012

The Lorenz Attractor

A strange attractor is an infinite-point attractor with non-integer dimension. The trajectory of a system characterized by a strange attractor never repeats itself, but still stays within a bounded region of state space. Strange attractors are a type of fractal, exhibiting self-similarity on all scales.

Examples of strange attractors include the Hénon attractor, Rössler attractor, Lorenz Attractor, Tamari attractor.