AVirtualMachineForExploringSpaceTimeAndBeyond : The K-smooth integers on a Tridimensional Hilbert Curve -iteration 1- (Les entiers K-friables sur une courbe de Hilbert tridimensionnelle -iteration 1-).

The K-smooth integers on a Tridimensional Hilbert Curve -iteration 1- [Les entiers K-friables sur une courbe de Hilbert tridimensionnelle -itération 1-].

Starting from the bottom front right corner of the [0,+1]x[0,+1]x[0,+1] cube, the spheres are numbered (N=2,..., 9) when following a tridimensional Hilbert curve -iteration 1-. The radius of the sphere displaying the number N is a decreasing function of the logarithm of the smoothness K of N (K being the largest prime factors of N).

Nota: the used color palette displays the parametric coordinate of the curve.

See some related pictures (including this one):