MandelbrotSetBoettcher

MandelbrotSetBoettcher[z]

gives an approximation of the Böttcher function of z, which maps the complement of the Mandelbrot set conformally to the complement of the closed unit disk.

Details and Options

  • The Mandelbrot set is the set of all complex numbers for which the sequence diverges to infinity when starting with .
  • The Böttcher function is given by and satisfies the conjugacy .
  • With the option MaxIterations->m, the sequence will be iterated at most m times to approximate .
  • The default setting is MaxIterations->100.
  • MandelbrotSetBoettcher can be evaluated to arbitrary numerical precision.
  • MandelbrotSetBoettcher automatically threads over lists.

Examples

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Basic Examples  (3)

Get the Böttcher coordinate of :

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Since is in the Mandelbrot set, the result is undefined:

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Make an asymptotic series approximation for the Böttcher function:

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Scope  (3)

Options  (1)

Applications  (3)

Neat Examples  (1)

See Also

MandelbrotSetDistance  MandelbrotSetPlot  MandelbrotSetMemberQ  JuliaSetBoettcher  JuliaSetPlot

Introduced in 2014
(10.0)