Thank you for asking!
… Just fill the space with equal equilateral triangles. Only equilateral triangles. Everywhere.
In each triangle, draw exactly one edge in red, the two others in green. Since almost all edges are common to two triangles, it is a bit tricky. Just a bit.
Then, connect the middle of every red edge with the middles of the red edges of the neighboring triangles.
There are, except on the perimeter of the mesh, exactly 4 such neighboring triangles, and thus 4 segments connected to each red edge middle. These 4 segments may be seen as two lines crossing at that center, straight or making an angle.
Then delete the triangles…
… and the Lines become more visible.
Just make the angles a bit softer…
(I am using Bézier quadratic curves, but arcs of circles would be perfect too)
… and lines a bit fancier too.
One of my favorite patterns is to draw the line thick and dark at the beginning, and then redraw it repetitively thinner and thinner, and lighter and lighter.
Et voilà!
When this box is closed, click canvas for a new drawing.