Eight Great Tessellations

Tessellation is really just a fancy word for tiling, but its formal definition is the repetition of geometrical shapes on a two- (or sometimes three-) dimensional plane - with no gaps or overlap - to form a mosaic pattern. Tessellated patterns have occurred in art from ancient times to the present and are also apparent in nature. Computer graphics experts tessellate polygons to make them suitable for rendering, and mathematicians have studied uniform tilings and regular division of the plane for centuries. Examples and applications of tessellation abound in our world. Here are eight notable examples.

1. The tessellation that started it all - the beehive. Those little guys love their hexagons…

2. M.C. Escher took tiling and kicked it up several notches, creating optical illusions using non-geometric patterns.

3. Tessellated pavement is an extremely rare natural occurrence. This example, found on the Tasman Peninsula, Tasmania, was formed when flat siltstone was cracked by changes in the Earth's crust. Through the natural process of erosion, the "pavement" has taken on a tiled appearance.

4. This one, created by Bruce Bilney, is a guilty pleasure entry. It's sort of neat (from an information perspective) that, with one glance, we can see a kangaroo as well as its country/continent of origin.

5. This bunny is a great example of using tiling for computer rendering. Starting from the tail and moving toward the head, it's clear that, as the surface is subjected to increasingly complex tessellation, the image becomes richer and more detailed.

6. These 14th century Moorish tiles at Alhambra originally inspired Escher's forays into tiling.

7. Nikolas Schiller is an interesting fellow - Wikipedia describes him as "a blogger, prominent digital map artist, vegetarian, and civil rights activist" - who morphs aerial photographs into kaleidoscopic or tiled art. He did the same with QR codes.

8. Geodesic domes comprised of nearly equilateral triangles are generally considered to be solid examples of (semi-regular) tessellations.

With practically unlimited applications, I've probably missed some; feel free to post your own!

(Image credits: AR Christensen | mcescher.com | RedBubble | tessellations.org | Martin Reimers | UC Riverside | TessellationsPlus | CPCache)