Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section- [Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme (4xO+1)/(1xO-1) dans l'ensemble des Octonions -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 the related close-up on the pseudo-octonionic Mandelbrot set:




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