A tridimensional pseudo-random walk -spherical 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 sphériques- 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 'RHO', 'THETA' and 'PHI' using the arbitrary following way: 

                                                                           -------> RHO   = 1               4               7               0               3               6                ...
                                                                          |                  \             / \             / \             / \             / \             / \             /
                                                                          |                   \           /   \           /   \           /   \           /   \           /   \           /
                                                                          |                    \         /     \         /     \         /     \         /     \         /     \         /
                    0.12345678901234567890... --> 12345678901234567890... |-------> THETA =     2       /       5       /       8       /       1       /       4       /       7       /
                                                                          |                      \     /         \     /         \     /         \     /         \     /         \     /
                                                                          |                       \   /           \   /           \   /           \   /           \   /           \   /
                                                                          |                        \ /             \ /             \ /             \ /             \ /             \ /
                                                                           -------> PHI   =         3               6               9               2               5               8

Then 'RHO', 'THETA' and 'PHI' are renormalized inside [0.01,0.10], [0,π] and [0,20π/11] respectively and used in order to define the successive steps {RHO.cos(PHI).sin(THETA),RHO.sin(PHI).sin(THETA),RHO.cos(THETA)} of an "absolute" tridimensional random walk -spherical 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...)
 
pi-e
(0.4233108251...) 		 
pi+e
(5.8598744820...) 		 
pi
(0.1 2 3 4 5 6 7 8 9 10 11 12...)






Each decimal is displayed with a sphere whose radius is a decreasing linear function of its rank and the arbitrary colors used are also displaying the rank (from white for the first ones to dark blue for the last ones).


(CMAP28 WWW site: this page was created on 10/19/2024 and last updated on 10/31/2024 13:50:03 -CET-)



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