JuliaSetBoettcher

JuliaSetBoettcher[c,z]

gives the Böttcher coordinate of z with respect to the quadratic Julia set Jc.

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 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.

Examples

open allclose all

Basic Examples  (2)

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

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

Scope  (2)

JuliaSetBoettcher threads itself element-wise over lists:

JuliaSetBoettcher works on all kinds of numbers:

Generalizations & Extensions  (1)

Find a series approximation for the Böttcher function for the Julia set for :

Neat Examples  (3)

Use the absolute value to display "equipotential lines" for a Cantor-like Julia set:

Use the argument to display "field lines" for a connected Julia set:

Use the argument to display the "external rays" with angle :

Introduced in 2014
 (10.0)