The 'hyperbolic tangent' of a sphere [La 'tangente hyperbolique' d'une sphère ]

The 'hyperbolic tangent' of a sphere [La 'tangente hyperbolique' d'une sphère].




A tridimensional object is defined as a set of points P={X,Y,Z}. To each point P is associated the following octonion O={X,Y,Z,0,0,0,0,0}. Then each octonion O is submitted to the transformation: 
                    
                    O --> O' = tanh(O)


At last a new point P' is defined with {X',Y',Z'} being arbitrary linear combinations of the components of O'. The set of points P' defines a new tridimensional object...


See some related pictures using octonions (possibly including this one):

The 'exponential' of a sphere
exponential		The 'cosine' of a sphere
cosine		The 'sine' of a sphere
sine		The 'tangent' of a sphere
tangent		The 'hyperbolic cosine' of a sphere
hyperbolic cosine		The 'hyperbolic sine' of a sphere
hyperbolic sine		The 'hyperbolic tangent' of a sphere
hyperbolic tangent


See some related pictures using pseudo-octonions (possibly including this one):

The 'exponential' of a sphere
exponential		The 'cosine' of a sphere
cosine		The 'sine' of a sphere
sine		The 'tangent' of a sphere
tangent		The 'hyperbolic cosine' of a sphere
hyperbolic cosine		The 'hyperbolic sine' of a sphere
hyperbolic sine		The 'hyperbolic tangent' of a sphere
hyperbolic tangent


Nota: the radius and the colors of each particle visualizing a point P' vary according to its {X',Y',Z'} coordinates...


See a related picture:

A sphere -positive curvature-


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