AVirtualMachineForExploringSpaceTimeAndBeyond : A bidimensional pseudo-random walk defined by means of 'pi' : 3.141592... -10.000 digits, -base 10- into 021003... -16.607 digits, -base 4- (Une pseudo-marche aleatoire bidimensionnelle definie a l'aide de 'pi' : 3.141592... -10.000 chiffres, -base 10- en 021003... -16.607 chiffres, -base 4-).

A bidimensional pseudo-random walk defined by means of 'pi': 3.141592... -10.000 digits, -base 10- into 021003... -16.607 digits, -base 4- [Une pseudo-marche aléatoire bidimensionnelle définie à l'aide de 'pi': 3.141592... -10.000 chiffres, -base 10- en 021003... -16.607 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):