Attractor

In dynamical systems, an attractor is a set of states toward which a system tends to evolve for a wide variety of starting conditions, so that values close enough to the attractor remain close even if slightly disturbed. In a finite-dimensional system the evolving variable can be represented as an n-dimensional vector, and the attractor occupies a region of that n-dimensional space; if the variable is two- or three-dimensional the attractor can be pictured geometrically, and it may take the form of a point, a finite set of points, a curve, a manifold, or a complicated fractal-structured set known as a strange attractor. A trajectory within the attractor need not satisfy any special constraint beyond remaining on the attractor going forward in time, and may be periodic or chaotic; a periodic or chaotic set of points whose neighboring flow moves away from it, rather than toward it, is called a repeller instead of an attractor.