A class of automorphisms of the unit square called generalized baker'stransformations (gbt) is defined in such a way that every stationary stochastic process may be represented as the movement of a simple partition of the square under a gbt. This extends the classical example of the representation of independent processes by the well-known baker's transformation.
Every ergodic, positive-entropy automorphism is measurably isomorphic to some gbt (again generalizing the classical result about Bernoulli shifts), and we show that a large class of gbt's satisfying certain continuity restrictions are actually measurably isomorphic to Bernoulli shifts.