An attractor in phase space, where the points never repeat themselves, and orbits never intersect, but they stay within the same region of phase space. Unlike limit cycles or point attractors, strange attractors are non-periodic, and generally have a fractal dimension. They are a picture of a non-linear, chaotic system. See: Attractor, Chaos, Limit Cycle, Point Attractor.

N-point attractor in which N equals infinity. Usually (perhaps always) self-similar in form.

Submitted By The Authors A Strange Attractor is the limit set of a chaotic trajectory. A Strange Attractor is an attractor that is topologically from a periodic orbit or a limit cycle. It can also be considered a fractal attractor.

an attractor for which the approach to its final point in phase space is chaotic

a dynamic and chaotic equilibrium that never exactly repeats itself but remains within calculable bounds

a fractal, an object that exhibits self-similarity on all scales

an attractor containing an infinite number of points and having the property that small changes in neighboring states give rise to large and apparently unpredictable changes in the evolution of the system

an attractor for which there is not an equilibrium point

an Attractor that displays sensitivity to initial conditions

an attractor with a self-similar or fractal nature

an indecomposable closed invariant set that "attracts" the points about it which contains a transversal homoclinic orbit

a pattern mysteriously formed and filled in by a line, generated by a non-linear equation, moving unpredictably from point to point, back and forth around itself

a term that describes the equilibrium towards which any chaotic system will descend

The orbital point in the mathematical mapping of a dynamic system that is neither fixed nor oscillating, but rather spirals inward.

An attractor whose variables never exactly repeat their values but always are found within a restricted range, a small area of state space.

The first strange attractor was discovered by Edward Lorentz in 1962 while developing models for weather forecasting. This discovery provided the foundation for the discipline we now call Chaos theory. The solution to a system of equations which converges to a single point is called a finite attractor. If the solution converges to a periodic orbit, it is a periodic attractor. If neither case is true and the solution is a fully determined curve that has no recursion and is a fractal, it is a strange attractor. More of an explanation will require some heavy duty math.

A representation, usually graphical and computer generated, of the states of a system over time where the system does not go chaotic but forms a kind of regular pattern that never exactly recurs.

A discrete time dynamical system is often called a map.

An attractor of a dynamical system that is usually fractal in dimension and is indicative of chaos.