Totally Tessellated: Welcome

We hope you enjoyed the splash page. All of the images on the splash page have connections to the topic of tessellations and can be found somewhere on this site. Hopefully, your interest in the world of tessellations has been excited!

A sample tessellation created by famous Dutch artist M. C. Escher

All M. C. Escher works (c) Cordon Art B.V.-Baarn-the Netherlands. Used with permission.

In short, a tessellation is any repeating pattern of interlocking shapes. Tessellations are also sometimes known as tilings, but the word "tilings" usually refers to patterns of polygons (i.e., shapes with straight boundaries), which is a more restrictive category of repeating patterns.

The definition sounds fairly simple, but the ideas involved in designing and understanding tessellations can grow very complex and interesting.

This site will give you a comprehensive introduction to tessellations. It will explain the basic mathematics underlying tessellations, as well as allow you to browse through many examples of tessellations in real life. M. C. Escher and his well-known tessellations are also covered in this site.

Tessellations are quite graphic-oriented, and the many images and animations throughout the site are crucial. Thus, you need a color monitor capable of displaying at least 256 colors and a web browser capable of displaying animated GIFs to make the most of this site. Such requirements are not steep, and the vast majority of users should be able to use this site without any problems.

A note about animations: animations are substantially larger in file size and download time than normal images. Please allow pages to complete load before clicking on links in order to make sure that animations are loaded fully. You may scroll and read text, however, at any time. If an animation seems to be broken, click the Reload button in your browser and let the page load completely.

Simply browsing this site is not enough if you want to really understand why tessellations work and how to create your tessellations. Make use of the many hands-on activities and templates provided in this site for your personal exploration of tessellations. For these, you will need access to a printer.