Repetitive interlace patterns are one of the hallmarks of Islamic and Moorish art. Through the study of various collections of such patterns, it is easy to verify that, despite the considerable complexity of the designs, most of the interlaces are formed by strands of a small number of shapes—often just a single shape stretching over many repeats of the design. This observation is described and documented by the authors, who present a simple explanation for this phenomenon.
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Grünbaum et al. (1992) studied this question.
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