A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps [Une pseudo-marche aléatoire tridimensionnelle définie à l'aide de 'pi': 3.141592... -90.000 chiffres, -base 10- avec 30.000 pas de temps].




The first digits of 'pi' are giving birth to three sets 'DX', 'DY' and 'DZ' using the following way: 
                                                                           -------> DX = 3               1               2               3               9               3                ...
                                                                          |               \             / \             / \             / \             / \             / \             /
                                                                          |                \           /   \           /   \           /   \           /   \           /   \           /
                                                                          |                 \         /     \         /     \         /     \         /     \         /     \         /
                    pi = 3.14159265358979323... --> 314159265358979323... |-------> DY =     1       /       5       /       6       /       5       /       7       /       2       /
                                                                          |                   \     /         \     /         \     /         \     /         \     /         \     /
                                                                          |                    \   /           \   /           \   /           \   /           \   /           \   /
                                                                          |                     \ /             \ /             \ /             \ /             \ /             \ /
                                                                           -------> DZ =         4               9               5               8               9               3
Then 'DX', 'DY' and 'DZ' are renormalized inside [-DR,+DR] (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: 
                    [-0.025,+0.695]x[+0.138,+0.827]x[-0.170,+0.482] -->[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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