JuliaSetBoettcher[c,z]
gives the Böttcher coordinate of z with respect to the quadratic Julia set Jc.


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 all close allBasic Examples (2)
Scope (2)
JuliaSetBoettcher threads itself element-wise over lists:
JuliaSetBoettcher works on all kinds of numbers:
Generalizations & Extensions (1)
Related Guides
History
Text
Wolfram Research (2014), JuliaSetBoettcher, Wolfram Language function, https://reference.wolfram.com/language/ref/JuliaSetBoettcher.html.
CMS
Wolfram Language. 2014. "JuliaSetBoettcher." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JuliaSetBoettcher.html.
APA
Wolfram Language. (2014). JuliaSetBoettcher. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JuliaSetBoettcher.html
BibTeX
@misc{reference.wolfram_2025_juliasetboettcher, author="Wolfram Research", title="{JuliaSetBoettcher}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/JuliaSetBoettcher.html}", note=[Accessed: 09-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_juliasetboettcher, organization={Wolfram Research}, title={JuliaSetBoettcher}, year={2014}, url={https://reference.wolfram.com/language/ref/JuliaSetBoettcher.html}, note=[Accessed: 09-August-2025]}