What are Tessellations ?

The word 'tessera' in latin means a small stone cube. They were used to make up 'tessellata' - the mosaic pictures forming floors and tilings in Roman buildings

Notice, in the example at right, that the artists used many small square tiles to create one big picture of a bull.

Nowadays, the term "tessellation" has expanded to have at least four meanings.

Now it has the original meaning, of big pictures made from small square tiles, but it also means tile-sized uniformly shaped pictures or big pictures made from tiles that aren't just square-shaped.

Tessellation can also mean simply filling a large surface, without gaps or overlaps, using non-square tiles. In nature, we see this kind of tessellation in cracked mud, turtle shells, and other places. In man-made areas, we see it in architecture, for example...from brick walls and bathroom floors to decorated magnificent, beautiful buildings like the Alhambra in Spain.

In the world of three-dimensional CGI (Computer Graphic Imagery), tessellation refers to the "wire frame" shape created from small interconnected nonidentical polygon shapes-- not just squares. These give us the shape-- but not the coloring-- of Jurassic Park's dinosaurs, video game monsters and heroes, and other invented animals and objects.

Tessellation now also means tile-sized pictures made from single tiles that repeat to fill a 2D or 3D space completely without gaps or overlaps. Most people call these "M. C. Escher-style tessellations". In these tessellations, the tiles aren't square. The individual tiles are the shape of animals, people, and things. Nowadays, when we say "this is an animal tessellation", we don't see lots of little tiles making a big picture of an animal. Instead, each little tile is a little picture of an animal. The tiles cover a surface -- usually a 2D (i.e., flat) plane -- in a symmetrical way without overlapping or leaving gaps. You can see examples in the many art galleries here at Tessellations.org.

roman mosaic of a bull
A Roman floor mozaic:
Big picture, small square tiles.

tessellation of foxes
A tessellation:
Big picture-shaped "tiles".