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arXiv · 1809.02020

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

Guillaume Brouillette·Dominic Rochon
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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.

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Guillaume Brouillette, Dominic Rochon. 2018-09-04. Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set. https://doi.org/10.1007/s00006-019-0956-1

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