A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -20.000 digits, -base 10- with 10.000 time steps [Une pseudo-marche aléatoire tridimensionnelle définie à l'aide de 'pi': 3.141592... -20.000 chiffres, -base 10- avec 10.000 pas de temps].
The first digits of 'pi' are giving birth to two sets 'Theta' and 'Phi' using the following way:
-------> Theta = 3 4 5 2 5 5 9 9 ...
| \ / \ / \ / \ / \ / \ / \ / \ /
pi = 3.141592653589793... --> 3141592653589793... | \ / \ / \ / \ / \ / \ / \ / \ /
| \ / \ / \ / \ / \ / \ / \ / \ /
-------> Phi = 1 1 9 6 3 8 7 3
Then 'Theta' and 'Phi' are renormalized inside [0,π] and [0,(9/10).(2.π)] respectively.
Then elementary tridimensional translations {DX,DY,DZ} are defined:
DX = DR.cos(Phi).sin(Theta)
DY = DR.sin(Phi).sin(Theta)
DZ = DR.cos(theta)
(DR being an arbitrary constant) and used as the successive steps of an "absolute" tridimensional random walk..
The coordinates {X,Y,Z} are renormalized as follows:
[-0.063,+0.546]x[+0.418,+0.911]x[-0.442,+0.248] --> [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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