Strange Attractors

Strange attractors are the objects central to chaos theory and provide a link between dynamics and geometry and between feedback and fractals. They are a geometrical representation of of the history taken by the state of a chaotic system. The special properties of chaotic systems (that they never repeat exactly but follow similar paths and that they are highly sensitive to initial conditions) relates to the fractal properties of the strange attractor. A fractal object has self-similarity, or scale invariance. That is, it has similar detail on many scales. Fractal properties arise due to the repeated iteration, or feedback, of simple rules. In the Ueda system whose strange attractor is shown, this corresponds to a repeated folding and stretching of the state space, like pastry that has been repeatedly folded and rolled out. Repeated magnification of a portion of the attractor would reveal ever more similar detail.