There are a couple of ways to make them, but here is one. It requires 4 different tiles and there is a strange requirement that the area be divided up into a checkerboard arrangement of light and dark tiles. (I chose c for clockwise and a for anticlockwise.)
| odd | even | ||
| c | | | 0 |
| a | | | 1 |
| 0 | 1 |
Here is an area paved entirely with the two c tiles.
Click the buttons below to change them.
Call me crazy, but I bet this has something to do with superconductivity. Look at the lines. Now imagine that these depict the ways electrons can move in a material. Imagine that they can jump between lines, but that there is an energy cost in doing so. However if the lines all run in parallel like this (click ) then there is no cost -- superconductivity.