A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...) -base 10- with 33.333 time steps [Une pseudo-marche aléatoire tridimensionnelle -coordonnées cartésiennes- définie à l'aide des 99.999 premières décimales de 'pi' (141592...) -base 10- avec 33.333 pas de temps].




The first decimals of an arbitrary real number (0.12345678901234567890... for example) are giving birth to three sets 'DX', 'DY' and 'DZ' using the arbitrary following way: 

                                                                           -------> DX = 1               4               7               0               3               6                ...
                                                                          |               \             / \             / \             / \             / \             / \             /
                                                                          |                \           /   \           /   \           /   \           /   \           /   \           /
                                                                          |                 \         /     \         /     \         /     \         /     \         /     \         /
                    0.12345678901234567890... --> 12345678901234567890... |-------> DY =     2       /       5       /       8       /       1       /       4       /       7       /
                                                                          |                   \     /         \     /         \     /         \     /         \     /         \     /
                                                                          |                    \   /           \   /           \   /           \   /           \   /           \   /
                                                                          |                     \ /             \ /             \ /             \ /             \ /             \ /
                                                                           -------> DZ =         3               6               9               2               5               8

Then 'DX', 'DY' and 'DZ' are renormalized inside [-DR,+DR] (DR being an arbitrary constant) and used in order to define the successive steps {DX,DY,DZ} of an "absolute" tridimensional random walk -cartesian coordinates-.



See some related pictures (including this one):


 
An arbitrary random number
(0.1904968414...) 		 
The square root of 2
(1.4142135623...) 		 
The golden ratio
(1.6180339887...) 		 
e
(2.7182818284...) 		 
pi
(3.1415926535...)



The arbitrary colors used are displaying the rank of each decimal (from white for the first ones to dark blue for the last ones.)


(CMAP28 WWW site: this page was created on 10/06/2024 and last updated on 10/31/2024 13:49:48 -CET-)



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