Source: Symmetry: Culture and Science


When one looks at an Oriental carpetin the context of Western art, one usually perceives a richness of colors andpatterns, and perhaps the contrast between central field and surroundingborders. A careful observer might notice the appearance of superimposed planepatterns in the central field and multiple linear patterns in the surroundingborders. Each of patterns, whether in the field or the borders, is composed ofvarious 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 repetitionare well-known today, but the mathematical aspects of pattern formation have beenglossed over in the study of Oriental carpets, or neglected in favor of eitheran 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 ofcolor and patterns in textiles and carpets of Morocco his paintings of the late19th and early 20th centuries, and Gaugin remarked that if one wantsto learn about color, one should look to carpets (Alexander 1993, p. 18).Before them, several Old Master painters, such as Lorenzo Lotto, Hans Holbeinthe Younger, Hans Memling, Carlo Crivelli, Giovanni Bellini, and DomenicoGhirlandaio, had observed color, form, and pattern, carefully portrayingaccurate renderings of carpets on tables in both genre scenes and still lifepaintings, 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 ofthese imported products in Europe and America was felt in the worlds of bothcollectors and scholars.


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About the Author


The authoris associated with The Textile Museum, Washington DC.