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

  • Guillaume Brouillette
  • Dominic RochonEmail author
Article
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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.

Keywords

Multicomplex dynamics Multibrot Generalized Mandelbrot sets Metatronbrot 3D Fractals Tricomplex space 

Mathematics Subject Classification

37F50 32A30 30G35 00A69 

Notes

Acknowledgements

DR is grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. GB would like to thank the FRQNT and the ISM for the awards of graduate research grants. The authors are grateful to Louis Hamel and Étienne Beaulac, from UQTR, for their useful work on the MetatronBrot Explorer in Java.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Département de mathématiques et d’informatiqueUniversité du Québec à Trois-RivièresTrois-RivièresCanada

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