I love tessellations. Here’s quite a complicated example, with a transformation running across it, and an added graphic twist.
Want to try your own tessellations? There are software short-cuts you can use but to really get the hang of them, do them by hand, with a graphics package on a computer. (I use the graphics facility in a full version of Photoshop, but any capable graphics package should do the business. You will need to be fairly handy with it before you start doing tessellations, however). Or you can also really do them by hand, with tracing paper and pencil.
For an extended tutorial, see my tessellation tutorial, or visit another page with outstanding “how-to-do-it” demos.
Note added in March 2011! If you are new to tessellations, first watch my later post with an animated demo of how tessellations work.
or for demos plus brilliant examples:
http://www.tessellations.org/mygallery16.htm (great examples)
For M.C. Escher’s tessellations see:
Here’s my animated tessellation: