Gingerbreadman map

Gingerbreadman map for subset $Q^2, [-10..10,-10..10]$: the color of each point is related to the relative orbit period. To view the gingerbread man, you must rotate the image 135 degrees clockwise.

In dynamical systems theory, the Gingerbreadman map is a chaotic two-dimensional map. It is given by the piecewise linear transformation:^[1]

$\begin{cases} x_{n+1} = 1 - y_n + |x_n|\\ y_{n+1} = x_n \end{cases}$

See also

• List of chaotic maps

References

1. Devaney, Robert L. (1988), "Fractal patterns arising in chaotic dynamical systems", in Peitgen, Heinz-Otto; Saupe, Dietmar, The Science of Fractal Images, Springer-Verlag, pp. 137–168, doi:10.1007/978-1-4612-3784-6_3. See in particular Fig. 3.3.

External links

• Weisstein, Eric W., "Gingerbreadman Map", MathWorld.