Deterministic and stochastic maps.

The left panels show an example map g⁽¹⁾ and g⁽²⁾, which is obtained from g⁽¹⁾ for a given value of τ. The right panel shows stochastic matrix corresponding to g⁽²⁾, with darker regions representing larger numbers. After 2τ has elapsed, the delta function distribution (arrow) is mapped to a Gaussian distribution (solid line) while the uniform distribution is mapped to a bimodal distribution (dashed line).