77 citations · 233 across the 17 of their papers we have counts for
18 papers
On the Algebraic Foundation of the Mandelbulb
Vanessa Boily, Dominic Rochon
In this paper, we generalize the Mandelbrot set using quaternions and spherical coordinates. In particular, we use pure quaternions to define a spherical product. This product, whi…
Relationship between the Mandelbrot Algorithm and the Platonic Solids
André Vallières, Dominic Rochon
This paper focuses on the dynamics of the eight tridimensional principal slices of the tricomplex Mandelbrot set: the Tetrabrot, the Arrowheadbrot, the Mousebrot, the Turtlebrot, t…
Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets
Pierre-Olivier Parisé, Guillaume Brouillette, Dominic Rochon
In this article, we present a distance estimation formula that can be used to ray trace 3D slices of the filled-in Julia sets and the Multibrot sets generated by the tricomplex pol…
Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set
Guillaume Brouillette, Dominic Rochon
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 sli…
Tricomplex dynamical systems generated by polynomials of even degree
Pierre-Olivier Parisé, Thomas Ransford, Dominic Rochon
In this article, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial where and are complex numbers and is a…
Tricomplex dynamical systems generated by polynomials of odd degree
Pierre-Olivier Parisé, Dominic Rochon
In this article, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial where and are complex numbers and is an o…