To understand a little about the importance of tessellations to Islamic Art I will quote Fatih Gelgi who wrote an article on
The Influence of Islamic Art on M.C. Escher. He said: Tessellations are one of the major components of Islamic art. Islamic artists mastered regular division of plane using, in particular, circles on triangular or square grids, because the circle – which has no beginning and no end and thus symbolizes infinity – was considered to be the most perfect geometric form. In mosques, where a wealth of these geometric patterns could be found, one could contemplate the infinite nature of God simply by looking at the walls or ceiling. http://www.fountainmagazine.com/Issue/detail/The-Influence-of-Islamic-Art-on-MC-Escher

I could go on forever about tessellations as they can be found in many, many cultures and are a basic element in learning about perspective. They are fascinating and before we become mesmerised by them I'll sign off for today.

If you have become interested in mathematical art and tessellations check out the work of RobertFathauer a contemporary American creating interesting works.