Arnold's cat map

In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name.

Thinking of the torus ${\displaystyle \mathbb {T} ^{2}}$ as the quotient space ${\displaystyle \mathbb {R} ^{2}/\mathbb {Z} ^{2}}$, Arnold's cat map is the transformation ${\displaystyle \Gamma :\mathbb {T} ^{2}\to \mathbb {T} ^{2}}$ given by the formula

...
Wikipedia