The Short Tiles Category
Lars Eriksson

Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture
Pages 127–134
Regular Papers

Abstract

Islamic geometric patterns can often be decomposed into a set of modular equilateral tiles, each decorated with a small motif, which assemble to form patterns. As the floodgate for tiles with additional side lengths was opened in the previous Bridges paper (Adapter Tiles Evolves the Girih Tile Set) in which the Φ-category was defined, it is time to examine another non-equilateral category – the Short category, which include a new edge length. While many historical 5-fold patterns can be tiled in two ways, only one way has been used to replicate them. With the introduction of Short tiles, the other way is now possible. I argue that the Short category provides a better way to replicate some of the historical patterns. Together with categories not yet published, the Short tiles play a crucial role when creating patterns, especially historical patterns.

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