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'.]


(CMAP28 WWW site: this page was created on 06/08/2024 and last updated on 09/05/2024 14:17:33 -CEST-)



[See the generator of this picture [Voir le générateur de cette image]]

[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related Pi picture gallery [Visitez la galerie d'images Pi associée]]

[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]

[The Y2K Bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


Copyright © Jean-François COLONNA, 2024-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2024-2024.