A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'phi' -the golden ratio- (618033...) -base 10- with 33.333 time steps [Une pseudo-marche aléatoire tridimensionnelle -coordonnées cartésiennes- définie à l'aide des 99.999 premières décimales de phi -le nombre d'or- (618033...) -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 10/09/2024 09:45:19 -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 NumberTheory picture gallery [Visitez la galerie d'images NumberTheory 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.