How to generate a fill curve with variable density not by cells?

Question

Algorithms

How to generate a curve that fills the canvas, taking into account the brightness of the original image, as in the example:

It is clear how this can be done with a Hilbert curve , but it is drawn in cells, consists of orthogonal segments. And in the picture there is a rather nice "organic" - how is it done?

Answer 1

TSP Art
Making TSP Art

Answer 2

Maybe there are points for the Hilbert curve, and then interpolated by a spline?