Tessellating Patterns

Tessellation

A tessellating pattern can cover an infinite surface with one or more geometric shapes with no gaps between them. The patterns can be regular (one shape only) or semi-regular (more than one shape). We see lots of tessellating patterns in everyday life, they're all around us. Even our tiled walls and floors are simple regular tessellating patterns.

Today's challenge topic is 'Pattern' so I made one by tessellating some pencils. The edges of the pencils are a bit rounded (presumably to make them easier to hold) so the edges don't quite meet and there are gaps between them. If they were regular hexagons there would be no gaps. Nevertheless I liked the effect.

MC Escher made the best tessellating patterns although he didn't use geometric shapes and was trying to make art rather than mathematics. Have a look at some of his patterns. Click on symmetry after pressing this link.