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




This Mandelbrot set is a tridimensional cross-section and was computed with a polynomial 'P' of the first degree ('C' denoting the current octonionic point) and the following eight functions:
                    
                    P(o) = 1*o + C
                    
                                       8
                    fR(R ,R ) = (R *R )
                        1  2      1  2
                    
                    fA1(A1 ,A1 ) = 8*(A1 +A1 )
                          1   2         1   2
                    
                    fA2(A2 ,A2 ) = 8*(A2 +A2 )
                          1   2         1   2
                    
                    fA3(A3 ,A3 ) = 8*(A3 +A3 )
                          1   2         1   2
                    
                    fA4(A4 ,A4 ) = 1*(A4 +A4 )
                          1   2         1   2
                    
                    fA5(A5 ,A5 ) = 1*(A5 +A5 )
                          1   2         1   2
                    
                    fA6(A6 ,A6 ) = 1*(A6 +A6 )
                          1   2         1   2
                    
                    fA7(A7 ,A7 ) = 1*(A7 +A7 )
                          1   2         1   2



See another cross-section:




See the zoom in on the pseudo-octonionic Mandelbrot set:




See some close-ups including possibly this one:




See some conformal transformations in the pseudo-octonionic space:

 
 
 



[for more information about pseudo-octonionic numbers (in english/en anglais)]
[pour plus d'informations à propos des pseudo-octonions (en français/in french)]


(CMAP28 WWW site: this page was created on 10/23/2014 and last updated on 04/26/2015 11:59:51 -CEST-)



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