Gingerbreadman map

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

Gingerbreadman map for subset ${\displaystyle Q^{2},[-10..10,-10..10]}$: 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.

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

A crude Gingerbreadman map made using the turtle library in python.

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 (eds.), 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.