I would think horizontal and vertical line segments (or, by extension, straight line segments with two different orientations; take the map with only horizontal

I would think horizontal and vertical line segments (or, by extension, straight line segments with two different orientations; take the map with only horizontal and vertical line segments and apply a shear mapping (https://en.wikipedia.org/wiki/Shear_mapping https://en.wikipedia.org/wiki/Shear_mapping) and a rotation) are sufficient. That’s basically what this is, if you draw it on a pixel grid.