Persian Variations

Abstract

The concept of variation is essential in geometric design. It is surprising that patterns very different may be variations of the same model. We define two families of pentagonal patterns with three kind of variations, and give some suggestions how to analyse these patterns and create in this style. We then search for self-similarity systems in a strict sense. Although from a systematic search, the two solutions proposed here can also generate some traditional 2-level patterns. In searching for subdivisions of the tiles into rhombuses, we found two solutions. Both can be compatible with the Binary Tiling (not with the Penrose Tiling). Then, using the concept of X-Tiles defined in a previous paper (Castera et al., http://castera.net/entrelacs/public/articles/Flying_Patterns.pdf , 2011), we find new relationship between the two families of pentagonal patterns. In the last chapter we show and comment some examples taken from traditional architecture in Iran, and infer a self-similar system for pattern with interlaces from a 2-level tiling in Isfahan. This paper reflect the point of view of a pattern designer.