Function Repository Resource:

CatMap

Apply a cat map to an image

Contributed by: Enrique Zeleny

ResourceFunction["CatMap"][image,n]

gives n steps of the cat map on the points of image.

Details and Options

Arnold's cat map is a simple, discrete system that stretches and folds points (x, y) to (x+y, x+2y) mod 1 in phase space.

Typically, any two points that initially are very close together quickly become separated from each other after repeated applications of the map. The picture first shears apart and later looks random or, in some steps, shows a ghost-like, repeated image of the original. Finally, the points return to their original positions.