# 5: What is a strange attractor?

## Description

This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by
others.

# 5: What is a strange attractor?

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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