Article · Wikipedia archive · Last revised Jun 16, 2026

Gingerbreadman map

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

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Gingerbreadman map for subset Q 2 , [ − 10..10 , − 10..10 ] {\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. source ↗

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

{ x n + 1 = 1 − y n + | x n | y n + 1 = x n {\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. source ↗
See also

See also

References

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.
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