Baker's map

In dynamical systems theory, the baker's map is a map from the unit square into itself, which is chaotic. It is topologically equivalent to the horseshoe map.

Formal definition

The baker's map is the union of

<math>H_L : [0, 1/2] \times [0, 1] \to [0, 1] \times [0, 1/2] : (x, y) \mapsto (2x, y/2)<math>

and

<math>H_R : [1/2, 1] \times [0, 1] \to [0, 1] \times [1/2, 1] : (x, y) \mapsto (2x-1,(y+1)/2)<math>.

Using a few hundred mirrors, one can build an optical universal Turing machine in one's backyard, using a generalized Baker's map.