  We describe families of plane-filling curves on any edge-to-edge tiling of
the plane with regular polygons and finitely many classes of edges. It is shown
how to partition the minimal number of edge classes from the group G of
symmetries of the tiling into refined colorings of the tiling, corresponding to
finite subgroups of G. All of these colorings correspond to families of
plane-filling curves which we call curve-sets. Our exposition is driven by
illustrated examples.
