Symmetry and Pattern of Oriental Carpets

From site:  ORIENTAL CARPETS have long been appreciated for their beauty. That beauty is achieved through the choice of colors and designs, as well as by the manipulation of designs and colors to form pleasing patterns.

Patterns in Oriental carpets are never quite what you expect - a surprise here, a flourish there, a change of color, the flip or rotation of a design where you might not predict it. The more you look, the more variations you will find.

How can we explain this phenomenon? Is it the result of human choice, or human error?

The study of symmetry offers one approach to analyzing patterns in Oriental carpets. Through symmetry analysis we may identify areas of pattern that exhibit expected repetitions, and areas that vary from that expectation.