A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section- [Un ensemble de Mandelbrot dans l'ensemble des pseudo-quaternions (un 'MandelBulb') -section tridimensionnelle-].




This Mandelbrot set was computed with a polynomial 'P' of the first degree and the following four functions:
                    P(q) = 1*q + q
                                  C
                                       8
                    fR(R ,R ) = (R *R )
                        1  2      1  2
                    fT(T ,T ) = 8*(T +T )
                        1  2        1  2
                    fP(P ,P ) = 8*(P +P )
                        1  2        1  2
                    fA(A ,A ) = 8*(A +A )
                        1  2        1  2



See some close-ups:

 
 
 



See some zooms in:




See a translation along the fourth axis:




See its pi rotation about the Y axis:




See some related pictures:




See some artistic views:




[for more information about pseudo-quaternionic numbers (en français/in french)]
[for more information about pseudo-octionic numbers (en français/in french)]

[for more information about N-Dimensional Deterministic Fractal Sets (in english/en anglais)]
[pour plus d'informations à propos des Ensembles Fractals Déterministes N-Dimensionnels (en français/in french)]


(CMAP28 WWW site: this page was created on 01/13/2010 and last updated on 04/01/2017 11:17:26 -CEST-)



[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related ArtAndScience picture gallery [Visitez la galerie d'images ArtAndScience associée]]
[Please visit the related DeterministicFractalGeometry picture gallery [Visitez la galerie d'images DeterministicFractalGeometry associée]]
[Go back to AVirtualSpaceTimeTravelMachine [Retour à AVirtualSpaceTimeTravelMachine]]
[The Y2K bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


Copyright (c) Jean-François Colonna, 2010-2017.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2017.