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

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

Starting from the bottom left corner of the [0,+1]x[0,+1] square, the spheres are numbered (N=2,..., 5) when following a bidimensional 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):