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.

or for demos plus brilliant examples:

http://www.tessellations.org/mygallery16.htm (great examples)

For M.C. Escher’s tessellations see:
http://www.mcescher.com

Here’s my animated tessellation:

What is a tessellation?

Any regular pattern consists of identical areas, which repeat without overlaps or gaps. An obvious example would be tiles on a wall. However tiles are usually geometric shapes – rectangles or squares as a rule, though triangles or hexagons would be possible too. In a tessellation, the cells can have wiggly edges, but still fit together like jig-saw pieces.

If you try to make a pattern like that out of any old shape, you will either end up with gaps or overlaps:

To make cells that tessellate, you have to follow a recipe. There are a whole set of recipes, but to get an idea of how they work, take a look at just one.

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