Tinkerbell map

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Tinkerbell attractor with a=0.9, b=-0.6013, c=2, d=0.5.
Tinkerbell attractor with a=0.9, b=-0.6013, c=2, d=0.5.

The Tinkerbell map is a discrete-time dynamical system given by:

x_{n+1}=x_n^2-y_n^2+ax_n+by_n\,
y_{n+1}=2x_ny_n+cx_n+dy_n\,

Some commonly quoted values of a, b, c, and d are

  • a=0.3, b=0.6, c=2, d=0.27.
  • a=0.9, b=-0.6013, c=2, d=0.5.

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