Source: Symmetry: Culture and Science
When one looks at an Oriental carpet in the context of Western art, one usually perceives a richness of colors and patterns, and perhaps the contrast between central field and surrounding borders. A careful observer might notice the appearance of superimposed plane patterns in the central field and multiple linear patterns in the surrounding borders. Each of patterns, whether in the field or the borders, is composed of various design elements, which in combination are repeated according to the principles of symmetry, often with the addition of symmetry-breaking (Bier 1992, 1997, 1998, 2000a). The mathematical principles of pattern making according to symmetrical repetition are well-known today, but the mathematical aspects of pattern formation have been glossed over in the study of Oriental carpets, or neglected in favor of either an appreciation of color and form or a discussion of social and ethnic origins. This article seeks to address several mathematical aspects of Oriental carpets, which are both integral to their form and manifest in their visual make-up.
Matisse drew upon the richness of color and patterns in textiles and carpets of Morocco his paintings of the late 19th and early 20th centuries, and Gaugin remarked that if one wants to learn about color, one should look to carpets (Alexander 1993, p. 18). Before them, several Old Master painters, such as Lorenzo Lotto, Hans Holbein the Younger, Hans Memling, Carlo Crivelli, Giovanni Bellini, and Domenico Ghirlandaio, had observed color, form, and pattern, carefully portraying accurate renderings of carpets on tables in both genre scenes and still life paintings, beneath depictions of the Virgin Mary, and laid before the altar (Denny 2002, pp. 29-33; Mills 1975, 1983; Ydema1991). Apart from the visual impressions that luxurious carpets from the Orient made upon European painters, the impact of these imported products in Europe and America was felt in the worlds of both collectors and scholars.
About the Author
The author is associated with The Textile Museum, Washington DC.