Every rug design has a pattern, which is the foundation for the design. The pattern relies on three characteristics: unit, repetition, and a system of organization.

Symmetry is a fundamental organizing principle in nature and in culture. The analysis of symmetry allows for understanding the organization of a pattern, and provides a means for determining both invariance and change.

In all patterns, there are four basic symmetry operations that may be performed upon a region, design, or motif: translation, reflection, glide reflection, & rotation.

Surprisingly, symmetry often relies upon asymmetry. Asymmetry is both the absence of symmetry, and a fundamental basis for symmetry. A motif or design may be asymmetrical (the boteh motif), or it may be symmetrical (the dyrnak gul motif). It is the collaboration and repetition of these two design elements that form a pattern and define the design of the rug.

As we often see in Oriental carpets, it is the playfulness with symmetry that results in intriguing patterns. In nature as well as art, symmetry is imperfect.  It seems that the approximation of symmetry, rather than its precision is what teases the mind as well as the eye.