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arXiv · 2409.07636

Sturmian external angles of primitive components in the Mandelbrot set

Benjamín A. Itzá-Ortiz·Mónica Moreno Rocha·Víctor Nopal-Coello
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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 $\theta$ 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.

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Benjamín A. Itzá-Ortiz, Mónica Moreno Rocha, Víctor Nopal-Coello. 2024-09-11. Sturmian external angles of primitive components in the Mandelbrot set. https://arxiv.org/abs/2409.07636

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