Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set

Abstract

This article focuses on the dynamics of the different tridimensional principal slices of the multicomplex Multibrot sets. First, we define an equivalence relation between those slices. Then, we characterize them in order to establish similarities between their behaviors. Finally, we see that any multicomplex tridimensional principal slice is equivalent to a tricomplex slice up to an affine transformation. This implies that, in the context of tridimensional principal slices, Multibrot sets do not need to be generalized beyond the tricomplex space.

References in corpus (1)

• Tricomplex dynamical systems generated by polynomials of even degree

Cited by in corpus (5)

• On the Algebraic Foundation of the Mandelbulb
• Relationship between the Mandelbrot Algorithm and the Platonic Solids
• Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets
• Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras
• On Commutative Analogues of Clifford Algebras and Their Decompositions