Arnold's Cat Map

Arnold's cat map is a chaotic transformation of the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat. Thought of as the quotient of the ordinary plane by the integer lattice, the map applies a simple linear transformation and then reduces the result modulo 1, folding everything that falls outside the unit square back inside it; it serves as a simple, pedagogical example of a hyperbolic toral automorphism.