Symmetry, Geometry and Symbols in Persian Patterns

Finally I have decided to fuscous on Symmetry, Geometry and Symbols in Persian Patterns (in the Islamic period). At the moment I am researching on patterns in different area such as tile, carpet, pottery etc. It seems they have a lot in common maybe because artisans were the same in different types of art or they use to share same philosophy and believes.
I have started my research by reading very interesting book, The Arabesque motif in Early Islamic Persian Art by Dr. Mohammad Khazaie. The book contains good information about root of some Islamic patterns in pre-Islamic period of Persian (Iranian) art as well as meaning of some patterns.
I am trying different ways to create these patterns. I started with very simple forms such as square and circle. To understand the structure of the pattern I decided to analyze some of the forms in very basic shapes.