arXiv Open Access 2024

Sturmian external angles of primitive components in the Mandelbrot set

Benjamín A. Itzá-Ortiz Mónica Moreno Rocha Víctor Nopal-Coello

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Abstrak

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 $θ$ 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.

Topik & Kata Kunci

math.DS

Penulis (3)

Benjamín A. Itzá-Ortiz

Mónica Moreno Rocha

Víctor Nopal-Coello

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APA MLA BibTeX

Itzá-Ortiz, B.A., Rocha, M.M., Nopal-Coello, V. (2024). Sturmian external angles of primitive components in the Mandelbrot set. https://arxiv.org/abs/2409.07636

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓