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 OptionsDetails 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.

ExamplesExamplesopen allclose all

Basic Examples  (3)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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Introduced in 2014
(10.0)