JuliaSetBoettcher

JuliaSetBoettcher[c,z]

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

Details and Options

  • The Julia set of a function f is the closure of the set of all repelling fixed points of f.
  • The Böttcher function is given by .
  • With the option MaxIterations->m, the sequence will be iterated at most m times to approximate .
  • The default setting is MaxIterations->100.

Examples

open allclose all

Basic Examples  (2)

Get the Böttcher coordinate of for the Julia set given by :

In[1]:=
Click for copyable input
Out[1]=

Since is in the Julia set given by , the result is undefined:

In[1]:=
Click for copyable input
Out[1]=

Scope  (2)

Generalizations & Extensions  (1)

Neat Examples  (3)

See Also

MandelbrotSetBoettcher  JuliaSetPlot  MandelbrotSetPlot

Introduced in 2014
(10.0)