Some Facts and Conjectures about Mandelbrot Polynomials
DOI:
https://doi.org/10.5206/mt.v1i1.14037Keywords:
Mandelbrot polynomials, asymptotic behaviour, Mandelbrot generating function, Online Encyclopedia of Integer SequencesAbstract
We show here some facts about the Mandelbrot iterates zₖ(c) where z₀(c)=0 and zₙ₊₁(c) = zₙ²(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.
Edited, and a new version of the paper uploaded: Peter Luschny caught an error, now corrected in Version 5: we had an incorrect OEIS sequence listed. We also took the opportunity to use unicodeit.net to remove the LaTeX from this abstract.
Versions 1--4 were just administrative changes, while we were learning OJS.
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Copyright (c) 2021 Neil J. Calkin, Dr. Eunice Y. S. Chan, Robert M. Corless
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.