Difference between revisions of "Strange Attractors"

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(New page: An '''attractor''' is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Ge...)
 
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An '''attractor''' is a set to which a 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]]An '''attractor''' is a set to which a 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.
  
An attractor is informally described as '''strange''' if it has non-integer '''[[Fractal Dimension| dimension]]''' or if the dynamics on it are '''[[Chaos Theory| chaotic]]'''. 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 differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.
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[[Image:Henon1.jpg|200px|left|thumb|Henon Attractor]]An attractor is informally described as '''strange''' if it has non-integer '''[[Fractal Dimension| dimension]]''' or if the dynamics on it are '''[[Chaos Theory| chaotic]]'''.
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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].
 
'''Note: Must be edited... This is directly taken from [http://en.wikipedia.org/wiki/Attractor wikipedia].

Revision as of 14:02, 30 May 2009

The Lorenz Attractor

An attractor is a set to which a 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.

Henon Attractor

An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic.

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 differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.

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

Note: Must be edited... This is directly taken from wikipedia.