Cat Map (original) (raw)

Arnold's cat map is a simple discrete system that stretches and ``folds'' the trajectories in phase space, which is another typical feature of chaotic processes. The phase space for this simple system can be represented by a square, and the stretching and folding process is more apparent if we placed a picture of a cat in the square. One can then see the time evolution of the system by observing how the cat gets stretched, cut up, and then placed back into the square. From the figure below, we observe that typically, any two points that are initially very close together quickly become separated from each other after repeated applications of the map.

The above handiwork is courtesy of Leon "I really have nothing against cats" Poon