It is most remarkable that Escher’s innocent-looking five-piece motif yields such a variety of patterns. While it is exciting to have a routine that successfully solves the topological problem of determining a proper array of color instructions and color switches for the big tile, there is still work to be done. The outstanding problem is how to get Mathematica to determine the smallest size of a big tile, for that would then make this project 100% automated. We have, in fact, dodged a central issue: Is it true that, for any motif, a big tile size always exists? At least we know it does for Escher’s main motif!
We hope that readers will investigate motifs of their own design. Our package requires that plane regions in a motif be given as polygons, but curves can be well approximated by polygons and surely many beautiful patterns are waiting to be discovered.