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






Jean-François COLONNA
[Contact me]

www.lactamme.polytechnique.fr

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

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K Bug [Le bug de l'an 2000]]
[Real Numbers don't exist in Computers and Floating Point Computations aren't safe. [Les Nombres Réels n'existent dans les Ordinateurs et les Calculs Flottants ne sont pas sûrs.]]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 12/24/2009 and last updated on 11/14/2023 17:55:58 -CET-)



[en français/in french]


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.



Contents of this page:



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.