Strange Attractors

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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 dimension or if the dynamics on it are chaotic.

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 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.