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.
Examplesopen 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:
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