Tricomplex dynamical systems generated by polynomials of odd degree

Pierre-Olivier Parisé; Dominic Rochon

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arXiv · 1511.02249

Tricomplex dynamical systems generated by polynomials of odd degree

Pierre-Olivier Parisé·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 $p > 2$ is an odd 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 dynamical system generated by the tricomplex polynomial $\eta^p+c$ where $p > 2$ is an odd integer.

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Pierre-Olivier Parisé, Dominic Rochon. 2015-11-05. Tricomplex dynamical systems generated by polynomials of odd degree. https://arxiv.org/abs/1511.02249

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