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}}

References

↑ 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.

Chaos theory
Chaos theory	Anosov diffeomorphism Bifurcation theory Butterfly effect Chaos theory in organizational development Complexity Control of chaos Dynamical system Edge of chaos Fractal Predictability Quantum chaos Santa Fe Institute Synchronization of chaos Unintended consequences
Chaotic maps (list)	Arnold tongue Arnold's cat map Baker's map Complex quadratic map Complex squaring map Coupled map lattice Double pendulum Double scroll attractor Duffing equation Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Kaplan–Yorke map Logistic map Lorenz system Multiscroll attractor Rabinovich–Fabrikant equations Rössler attractor Standard map Swinging Atwood's machine Tent map Tinkerbell map Van der Pol oscillator Zaslavskii map
Chaos systems	Bouncing ball dynamics Chua's circuit Economic bubble FPUT problem Tilt-A-Whirl
Chaos theorists	Michael Berry Mary Cartwright Leon O. Chua Mitchell Feigenbaum Celso Grebogi Martin Gutzwiller Brosl Hasslacher Michel Hénon Svetlana Jitomirskaya Sofia Kovalevskaya Bryna Kra Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Hee Oh Edward Ott Henri Poincaré Mary Rees Otto Rössler David Ruelle Caroline Series Oleksandr Mykolayovych Sharkovsky Nina Snaith Floris Takens Audrey Terras Mary Tsingou Amie Wilkinson James A. Yorke Lai-Sang Young

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