Certain self-similar domino coverings support space-filling curve constructions akin to how the original Peano curve construction and its generalizations fill squares. But for domino coverings and motifs, there are interesting constraints and freedoms with which to play. Upon enumeration of coverings and relatively rare motifs, approximation paths for space-filling, space-underfilling, and space-overfilling curves support visually intriguing, self-negative tilings, some with lovely fractal interiors or whose finite self-crossing filigree patterns are reminiscent of Islamic designs.