A tridimensional pseudo-random walk defined by means of 'pi': 141592... -2.001 digits, -base 10- into 200303... -3.321 digits, -base 4- (Une pseudo-marche aleatoire tridimensionnelle definie a l'aide de 'pi': 141592... -2.001 chiffres, -base 10- en 200303... -3.321 chiffres, -base 4-) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

A tridimensional pseudo-random walk defined by means of 'pi': 141592... -2.001 digits, -base 10- into 200303... -3.321 digits, -base 4- [Une pseudo-marche aléatoire tridimensionnelle définie à l'aide de 'pi': 141592... -2.001 chiffres, -base 10- en 200303... -3.321 chiffres, -base 4-].

Each digit N -base 4- defines the current step of an "absolute" bidimensional random walk:

                    digit=0 ==> move(+1,0,0)
                    digit=1 ==> move(-1,0,0)
                    digit=2 ==> move(0,+1,0)
                    digit=3 ==> move(0,-1,0)

The first digit is at the center of the picture.

The luminance of the colors is an ascending function of the rank of the digits (from blue for the first ones to white for the last ones).

See some related pictures (possibly including this one):