Tilings of the Plane

In the Spring of 2007, I took 6.891.

Justin Paluska, Luis Blackaller and I decided to see if we could design a Scheme system to generate tilings of the plane. In particular, the 17 crystallographic (wallpaper) groups.

As it turns out, the problem is hard. Undecidable, to be specific.

Together, we designed a system (in Scheme) to generate these groups, while emphasizing re-usability and extensibility.

A visualizer, tile generator, and tiler. All working together.

And it works. Below is the generated fundamental region for a p6 tiling from the kite.

More detail and sources can be found here.