University of Arkansas, Fayetteville


Imagine a never-ending checkerboard, red and black squares alternating forever in every direction. Now close your eyes, wait for a second, and open them again. There is still the checkerboard, but is it different? Has somebody moved the checkerboard over two squares? Four squares? One million squares? It still looks the same. This is the nature of periodic tilings. Wang tiles are squares, much like the red and black ones used on a checkerboard, except Wang tiles have colors on their edges instead of on the whole square. Also, Wang tiles can only be put edge-to-edge with each other where these colors are the same. So what's so special about Wang tiles? If you cover the infinite plane with certain sets of Wang tiles, close your eyes, and open them again, you will always be able to tell if it has changed. In these sorts of tilings, there is always something that does not quite overlap when moved any amount in any direction. This is the nature of aperiodic tilings. The smallest known such set of Wang tiles has thirteen tiles. This paper computationally explores sets of six, seven, and eight Wang tiles, looking for the same aperiodic structure.