Open AccessSome Facts and Conjectures about Mandelbrot Polynomials
Author(s) -
Neil J. Calkin,
Eunice Y. S. Chan,
Robert M. Corless
Publication year - 2021
Publication title -
maple transactions
Language(s) - English
Resource type - Journals
ISSN - 2564-3029
DOI - 10.5206/mt.v1i1.14037
Subject(s) - mandelbrot set , iterated function , mathematics , mathematical proof , pure mathematics , complex quadratic polynomial , combinatorics , discrete mathematics , mathematical analysis , fractal , geometry , polynomial
We show here some facts about the Mandelbrot iterates $z_k(c)$ where $z_0(c)=0$ and $z_{n+1}(c) = z_n^2(c) + c$, which are polynomials in $c$. Some of the facts have proofs, and some other ``"``facts" only have experimental evidence but no proof. We invite you to try your hand at filling in the gaps.