Tilings: beautiful patterns in mathematics.

by Dr. Natalie M. Priebe
Department of Mathematical Sciences
Rensselaer Polytechnic Institute

We're going to look at mathematical objects called tilings. Tilings are coverings of two-dimensional space by tiles, just as the name suggests. There are many applications of tilings, for instance modeling atomic structures of crystals or cell growth in plants. However, we will primarily focus on their visual interest.

A special type of tiling called a self-similar tiling will be introduced, and we will experiment with creating this type of tiling. There are an infinite number variations possible, and many of them are truly fascinating to behold. As a final coup de grace, we will discover a special type of self-similar tiling which has a surprising visual effect when superimposed upon itself. Participants will be provided with copies of this sort of tiling so that they may play with them and discover the effect themselves.