### 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.