Tricomplex dynamical systems generated by polynomials of even degree

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 $p\ge 2$ 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 $p\ge 2$ is an even integer.

arXiv admin note: substantial text overlap with arXiv:1511.02249

Cited by in corpus (4)

• Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set
• Relationship between the Mandelbrot Algorithm and the Platonic Solids
• Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets
• Cross-sections of multibrot sets