| Popis: |
I nterlace patterns occur frequently in the ornaments of various cultures, especially in Islamic and Moorish art. By interlace pattern we mean a periodic pattern that appears to consist of interwoven strands (see Figs 1 and 2). (The exact meaning of the term 'periodic pattern' will be explained later.) The largest published collection of interlace patterns is that ofJ. Bourgoin [1]; more precisely, the majority of Bourgoin's diagrams can be interpreted as representing such patterns, and it appears that they were, in fact, created with interlace patterns as originals. Other examples can be found in works by d'Avennes, El Said and Parman, Wade, and Humbert [2-5]. A number of authors have relied on the Bourgoin drawings in their research; for example, they have been used by Makovicky and Makovicky in their analysis of the frequencies with which various classes of symmetry groups are represented in Islamic patterns [6]. This article has three main goals. First, we will observe that most of the interlace patterns shown by Bourgoin consist either of identical (congruent) strands or of two shapes of strands. This is unexpected because in many cases the strand patterns are very complicated-some of them are so intricately interwoven that a repeat is unlikely to have been visible in any actual ornament. The complications of an interlace pattern can be measured in several ways-for example, by the number of different shapes of strands or by the number of crossings in a repeat. Our second aim is to relate these measures to the symmetry properties of the pattern. The results that we obtain lead to our third goal: a plausible explanation of the frequent appearance of interlace patterns consisting of strands of a single shape or of just two different shapes in Islamic art. |
