Sturmian external angles of primitive components in the Mandelbrot set
Dynamical Systems
2024-09-13 v1
Abstract
In this work we introduce the broken line construction, which is a geometric and combinatorial algorithm that computes periodic Sturmian angles of a given period, yielding the locations of their landing parameters in the Mandelbrot set. An easy to implement method to compute the conjugated angle of a periodic Sturmian angle is also provided. Furthermore, if is a periodic Sturmian angle computed by the broken line construction, then we show the existence of a one-to-one correspondence between its binary expansion and its associated kneading sequence.
Cite
@article{arxiv.2409.07636,
title = {Sturmian external angles of primitive components in the Mandelbrot set},
author = {Benjamín A. Itzá-Ortiz and Mónica Moreno Rocha and Víctor Nopal-Coello},
journal= {arXiv preprint arXiv:2409.07636},
year = {2024}
}