JuliaSetBoettcher

JuliaSetBoettcher[c,z]

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

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 :

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