TRICOMPLEX DYNAMICAL SYSTEMS GENERATED BY POLYNOMIALS OF ODD DEGREE

Abstract

In this paper, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial [Formula: see text] where [Formula: see text] and [Formula: see text] are complex numbers and [Formula: see text] 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 [Formula: see text] where [Formula: see text] is an odd integer.