Mathematicians have given this some thought. The relevant keyword seems to be "Truchet tilings", though there's a curved variation that's more widely known. H

Mathematicians have given this some thought. The relevant keyword seems to be "Truchet tilings", though there's a curved variation that's more widely known. Here's a very accessible overview with some lovely generalizations of this pattern: http://mypages.iit.edu/~krawczyk/rjkisama11.pdf http://mypages.iit.edu/~krawczyk/rjkisama11.pdf