Baker’s Map

Animation of the Baker’s Map, obtained by iterating $$F(x,y) = \begin{cases} (2x, \frac{y}{2}) & 0 \leq x < \frac{1}{2}\
(2-2x, 1 - \frac{y}{2}) & \frac{1}{2} \leq x < 1 \end{cases}$$

on the unit square; it essentially flattens the square then folds it back onto itself.

The animation above shows the effect of applying this map repeatedly to 1000 random points in the square. Coded in Mathematica.