About chaotic attractors

There are two main types of dynamical system, those with continuous time (often called flows), and those with discrete time (called iterations). This gallery is devoted to the latter. In this case, a map is defined from a state space into itself and iterated. Choosing an initial point in the sate space and marking its location after each iteration of the map defines a trajectory.

In general, a trajectory will wander about in the state space and eventualy settle down to a subset called its attractor. All the initial points converging to an attractor comprise the basim of that attractor. There may be many distinct basins in the state space, each containing a single attractor. These basins are separated by boundaries called separatrices. The main features of a dynamical system are its attractors, their basins, and the boundaries of its basins, or separatrices. The image of the state space divided into attractors, basins, and separatrices is called the portrait of the system.

Attractors are divided into three types.

  • static attractors, containing a single point,
  • periodic attractors, containing a finite number of points, and
  • chaotic attractors, containing an infinite number of points.
This gallery is devoted to chaotic attractors of iterations, in which the state space is two- or three-dimensional euclidean space.

Revised 01 October 2015 by Ralph Abraham, <abraham@vismath.org>