The Gingerbreadman Map is a two-dimensional piecewise linear map, defined by:

\begin{align}

x_{n+1} &= 1 – y_n + \lvert x_n \rvert \\

y_{n+1} &= x_n

\end{align}

The region in which the map is chaotic looks like a gingerbread man! In true festive spirit, one blogger has baked some cookies in the shape of the gingerbread man. Check out the blog post describing the cookies, and another one describing the method in more detail.

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!