Octagon-Based Quasicrystalline Formations in Islamic Architecture

Abstract

The unexpected discovery of ancient Islamic ornaments with quasicrystalline symmetries has triggered significant discussion and a number of debates on the mathematical sophistication of Islamic geometry and its generating principles. Astonishingly, eight centuries before its description in Modern Science, ancient artists had constructed patterns with perfect quasicrystalline formations. Recent studies have provided enough evidence to suggest that ancient designers, by using the most primitive tools (a compass and a straight edge), were able to resolve the complicated long-range principles of quasicrystalline formations. Derived from these principles, a global multi-level structural model is presented that is able to describe the global long-range order of octagon-based quasicrystalline formations in Islamic Architecture. This new method can be used as a general guiding principle for constructing infinite patches of octagon-based quasicrystalline formations, including Ammann--Beenker tiling, without the need for local strategies (matching, scaling, etc.) or complicated mathematics.