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 arbitrary colors used are displaying the rank of each digit (from white for the first ones -{3,1,4,1,5,...}- to dark blue for the last ones.)


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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