All patterns, whether in nature or in art, exhibit systematic organization. Symmetry offers several possibilities for the organization of a pattern, each of which results in sets of corresponding points. In rug weaving, the symmetrical repetition of a design to form a pattern is effected by counting and repeating sequences of knots. There are many ways a weaver may choose to break the symmetry of a pattern. This article characterizes twelve methods, which group into four categories of transformation (color, shape, space, pattern). Mathematicians treat symmetry as an ideal. Symmetry-breaking requires an expectation of symmetry. For symmetry-breaking to exist, a pattern must first be stablished. The study of Oriental carpets may lead one to suppose that in art, as in nature, it is in the approximation of symmetry, rather than in its precision, that beauty is to be found and appreciated.
- Oriental carpets,
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