Difference between revisions of "Strange Attractors"

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[[Image:Strange Attractor.jpg|thumb|300px|right|A visualization of the Poisson Saturne attractor, an example of a strange 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.
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[[Image:Strange Attractor.jpg|thumb|300px|right|A visualization of the Poisson Saturne attractor, an example of a strange attractor.]]
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==Basic Description==
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A '''strange attractor''' is an infinite-point [[Field:Dynamic Systems#Jump3|attractor]] with [[Fractal Dimension|non-integer dimension]].   Strange attractors are a type of [[Field:Fractals|fractal]], exhibiting self-similarity on all scales. Although strange attractors consist of an infinite number of points, they do not fill [[Field:Dynamic Systems#Jump2|state space]].  Instead strange attractors are contained within a bounded region of state space and are often highly structured.
  
Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], Rössler attractor, [[Lorenz Attractor]], Tamari attractor.
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==More Details==
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If you examined the evolution of a system characterized by a strange attractor, you would notice some interesting things. As with any attractor, the trajectory of the system would migrate towards the strange attractor region of state space and return there if displaced.  But a trajectory following a strange attractor would never repeat itself, no matter how long you watched. The system would never take on the exact same state twice.
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Furthermore, if you started the system at two similar states and watched the resulting evolution, you would see the two trajectories diverge from each other expoentially.  Even if the starting points are ''almost'' identical, given a little time the resulting outcomes would look totally different from each other.
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==Examples of Strange Attractors==
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Examples of strange attractors include the [[Henon Attractor| Hénon attractor]], [[Rössler attractor]], and [[Lorenz Attractor]].

Revision as of 15:59, 5 June 2012

A visualization of the Poisson Saturne attractor, an example of a strange attractor.

Basic Description

A strange attractor is an infinite-point attractor with non-integer dimension. Strange attractors are a type of fractal, exhibiting self-similarity on all scales. Although strange attractors consist of an infinite number of points, they do not fill state space. Instead strange attractors are contained within a bounded region of state space and are often highly structured.

More Details

If you examined the evolution of a system characterized by a strange attractor, you would notice some interesting things. As with any attractor, the trajectory of the system would migrate towards the strange attractor region of state space and return there if displaced. But a trajectory following a strange attractor would never repeat itself, no matter how long you watched. The system would never take on the exact same state twice.

Furthermore, if you started the system at two similar states and watched the resulting evolution, you would see the two trajectories diverge from each other expoentially. Even if the starting points are almost identical, given a little time the resulting outcomes would look totally different from each other.

Examples of Strange Attractors

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