Tricomplex dynamical systems generated by polynomials of even degree

Pierre-Olivier Parisé; Thomas Ransford; Dominic Rochon

doi:10.1142/s0218348x17500268

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arXiv · 1603.08548

Tricomplex dynamical systems generated by polynomials of even degree

Pierre-Olivier Parisé·Thomas Ransford·Dominic Rochon

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Abstract

In this article, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial $z^p+c$ where $z$ and $c$ are complex numbers and $p \geq 2$ is an even integer. Furthermore, we show that the same Multibrots defined on the hyperbolic numbers are always squares. Moreover, we give a generalized 3D version of the hyperbolic Multibrot set and prove that our generalization is an octahedron for a specific 3D slice of the tricomplex polynomial $\eta^p+c$ where $p \geq 2$ is an even integer.

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BibTeX RIS

Pierre-Olivier Parisé, Thomas Ransford, Dominic Rochon. 2016-03-23. Tricomplex dynamical systems generated by polynomials of even degree. https://doi.org/10.1142/s0218348x17500268

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