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Fractal Frequently Asked Questions and Answers
Section - Strange attractors

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Q5: What is a strange attractor?  
A5: A strange attractor is the limit set of a chaotic trajectory. A strange  
attractor is an attractor that is topologically distinct from a periodic orbit  
or a limit cycle. A strange attractor can be considered a fractal attractor.  
An example of a strange attractor is the Henon attractor.  
  
Consider a volume in phase space defined by all the initial conditions a  
system may have. For a dissipative system, this volume will shrink as the  
system evolves in time (Liouville's Theorem). If the system is sensitive to  
initial conditions, the trajectories of the points defining initial 
conditions will move apart in some directions, closer in others, but 
there will be a net shrinkage in volume. Ultimately, all points will 
lie along a fine line of zero volume. This is the strange attractor.  All 
initial points in phase space which ultimately land on the attractor 
form a Basin of Attraction. A strange attractor results if a system is
sensitive to initial conditions and is not conservative.  
  
Note: While all chaotic attractors are strange, not all strange attractors 
are chaotic. Reference:  
  
1. Grebogi, et al., Strange Attractors that are not Chaotic, _Physica D_ 13  
(1984), pp. 261-268.  
  

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Last Update March 27 2014 @ 02:11 PM