N-Dimensional Deterministic Fractal Sets
using Quaternions, Octonions and more
(MandelBulb, JuliaBulbs and beyond...)

Jean-François COLONNA
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CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France

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Abstract: Is it possible to extend the complexity of bidimensional fractal deterministic sets in tri-, four- and eight-dimensional spaces? What are "MandelBulb" and "JuliaBulb"s? Is it possible to "mix" deterministic and non deterministic fractal sets? Iterations are fundamental!

Keywords: Fractal Geometry, Deterministic Fractal Sets, MandelBulb, JuliaBulb, quaternionic numbers, pseudo-quaternionic numbers, octonionic numbers, pseudo-octonionic numbers.

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Preliminary remark: These fractal sets are dubbed deterministic for no random process is used mathematically speaking (contrary to non deterministic fractals). After all, their computations are non linear ones and then are subject to rounding-off errors that can produce random-like artifacts.

Copyright © Jean-François COLONNA, 2009-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2009-2023.