A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -20.000 digits, -base 10- with 10.000 time steps [Une pseudo-marche aléatoire tridimensionnelle définie à l'aide de 'pi': 3.141592... -20.000 chiffres, -base 10- avec 10.000 pas de temps].




The first digits of 'pi' are giving birth to two sets 'Theta' and 'Phi' using the following way: 
                                                                       -------> Theta = 3       4       5       2       5       5       9       9        ...
                                                                      |                  \     / \     / \     / \     / \     / \     / \     / \     /
                    pi = 3.141592653589793... --> 3141592653589793... |                   \   /   \   /   \   /   \   /   \   /   \   /   \   /   \   /
                                                                      |                    \ /     \ /     \ /     \ /     \ /     \ /     \ /     \ /
                                                                       -------> Phi   =     1       1       9       6       3       8       7       3
Then 'Theta' and 'Phi' are renormalized inside [0,π] and [0,(9/10).(2.π)] respectively.

Then elementary tridimensional translations {DX,DY,DZ} are defined: 
                    DX = DR.cos(Phi).sin(Theta)
                    DY = DR.sin(Phi).sin(Theta)
                    DZ = DR.cos(theta)
(DR being an arbitrary constant) and used as the successive steps of an "absolute" tridimensional random walk..


The coordinates {X,Y,Z} are renormalized as follows: 
                    [-0.063,+0.546]x[+0.418,+0.911]x[-0.442,+0.248] --> [0.1,0.9]x[0.1,0.9]x[0.1,0.9]



See some related pictures (possibly including this one):

 


 
 
 
 


 
 
 



[See the 100.000 first digits -base 10- of 'pi'.]


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