click to view the MPEG movie (cliquez pour voir le film MPEG)

Sixteen pseudo-quaternionic Julia sets ('MandelBulb' like: 'JuliaBulb's) -tridimensional cross-sections- [Seize ensembles de Julia dans l'ensemble des pseudo-quaternions (comme un 'MandelBulb': des 'JuliaBulb's) -coupes tridimensionnelles-].




This Julia set is a tridimensional cross-section and was computed with a polynomial 'P' of the second degree and the following four functions:
                            2
                    P(q) = q  + {X ,Y ,0,0}
                                  A  A
                    
                    fR(R ,R ) = R *R
                        1  2     1  2
                    fT(T ,T ) = T +T
                        1  2     1  2
                    fP(P ,P ) = P +P
                        1  2     1  2
                    fA(A ,A ) = A +A
                        1  2     1  2
the point {XA,YA} following an Archimedes spiral located in the complex plane and with the origin of the coordinates as its center.


See some artistic views of these sets:

Artistic view of sixteen pseudo-quaternionic Julia sets ('MandelBulb' like: 'JuliaBulb's)-tridimensional cross-sections- Artistic view of sixteen pseudo-quaternionic Julia sets ('MandelBulb' like: 'JuliaBulb's)-tridimensional cross-sections-


See the sixteen points of view:

A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.036794,-0.638941,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.515054,-0.412698,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.671070,0.109841,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.378212,0.589030,0,0) -tridimensional cross-section-  
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.084747,0.553550,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.367328,0.448854,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.599332,0.028308,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.436137,-0.440664,0,0) -tridimensional cross-section-  
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.169701,-0.449001,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.229292,-0.444326,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.502970,-0.131991,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.451358,0.296439,0,0) -tridimensional cross-section-  
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.216121,0.336588,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.110797,0.405122,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.393069,0.197729,0,0) -tridimensional cross-section- A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.428590,-0.167064,0,0) -tridimensional cross-section-


[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)]


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