Welcome to the non-Euclidean tessellations movie page.
The term tessellate means 'fit together exactly a number of congruent tiles, leaving no spaces'. The term non-Euclidean refers to a kind of geometry that goes beyond what we were taught in high school math. This is a geometry where tiles have sides that are circular arcs, and they are congruent as long as their vertex angles correspond.
There's a good online introduction to these concepts in this article.
You can browse through a series of movies in the above widget (note that it has a full screen option in the lower right corner), or you can browse through an album.
Here's one of the movies broken down into a high resolution slide show.