The search for quasi-periodicity in Islamic 5-fold ornament
The author describes a tiling-based method for constructing Islamic geometric designs, examines some 5-fold ornaments that exhibit features comparable with quasi-periodic tilings, and uses the underlying geometry to highlight similarities and differences. In the case of a crystalline material the presence of sharp spots in a diffraction pattern is an evidence of long-range order. In the study of the decorative arts, however, the term `quasi-periodic' is used somewhat informally, namely, it concerns a homogeneity of the distribution of local configurations. A wide range of traditional patterns show a design superimposed on an edge-to-edge tiling containing regular convex polygons. Some large Islamic ornaments found on buildings show designs of different scales superimposed on one another. The viewers experience a succession of patterns as they approach. The author arrives at the following conclusions: it is possible to construct quasi-periodic tilings from the set of prototiles used by Islamic artists, they did use subdivision to produce hierarchical designs, there is no evidence that the Islamic artists iterated the subdivision process and the matching rules.
scientific article; zbMATH DE number 5506572