A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -100.000 digits, -base 10- with 50.000 time steps [Une pseudo-marche aléatoire tridimensionnelle définie à l'aide de 'pi': 3.141592... -100.000 chiffres, -base 10- avec 50.000 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:
```                    +[+0.218,+0.693]x[+0.292,+0.937]x[-0.431,+0.124]
```

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 06/06/2024 and last updated on 09/05/2024 14:17:22 -CEST-)

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