SURPRISINGLY, symmetry often relies upon asymmetry.
WHAT IS ASYMMETRY? Asymmetry is both the absence of symmetry, and a fundamental basis for symmetry. Symmetry analysis may result in the identification of a fundamental region that is the smallest element required to explain the repetition that forms a pattern. The fundamental region is asymmetrical.
A motif or design may be asymmetrical (as for example, the boteh), or it may be symmetrical (as for example, the dyrnak gul). The fundamental region, repeated to form a pattern, consists of a motif or design, or portion thereof, and the surrounding area that defines the unit of repeat.
an asymmetrical motif
a symmetrical motif
WHAT DO VIRUSES, ELECTROMAGNETISM, ORIENTAL CARPETS, and music all have in common? They rely upon symmetry and symmetry-breaking for their strength and vitality.
WHAT IS SYMMETRY-BREAKING? Symmetry-breaking exists where a symmetry is expected, but that expectation is not met. As we often see in Oriental carpets, it is a playfulness with symmetry that results in intriguing patterns.
In nature, symmetry is imperfect, although mathematicians may treat it as an ideal. In art, too, it seems that the approximation of symmetry, rather than its precision, teases the mind as it pleases the eye.
[About Symmetry and Pattern]