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19972026
most citedImbibition in Disordered Media

290 citations

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math.DS2022★ 3 cited

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…

math.DS2021★ 3 cited

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…

math.DS2018★ 2 cited

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…

math.DS2018★ 11 cited

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…

math.DS2013

The Inverse Iteration Method for Julia Sets in the 3-Dimensional Space

C. Matteau, D. Rochon

In this article, we introduce the adapted inverse iteration method to generate bicomplex Julia sets associated to the polynomial map . The result is based on a full characte…