Unveiling Ancient Symmetry: Islamic Girih Tiles and the Mathematics of Aperiodicity

Isabelle C. Stratton

ABSTRACT

This essay explores the intersection of art and mathematics through the lens of Islamic architectural design, specifically focusing on the presence of quasiperiodic patterns. While seemingly random, these patterns possess order and structure without exact repetition, a concept that challenges traditional notions of symmetry.

The essay examines the role of girih tiles, a set of five geometric shapes documented in the 15th-century Topkapi Scroll, used by Islamic artisans to create intricate, non-repeating designs. These tilings, notably found in structures like the 15th-century Darb-i Imam Shrine, bear striking resemblance to Penrose tilings, mathematical constructs developed in the 1970s that exhibit five-fold rotational symmetry— a characteristic previously deemed impossible in crystallography.

The essay highlights the debate surrounding the intentionality of Islamic artisans in creating quasiperiodic patterns. While some scholars argue that these patterns were unintentional byproducts of the girih tile system, others propose that the artisans possessed a sophisticated understanding of geometric principles which prominently features in Penrose tilings.

The essay concludes by emphasizing the remarkable convergence of art and mathematics in Islamic architecture. Whether consciously intended or not, the presence of quasiperiodic patterns in these ancient structures showcases the depth of geometric knowledge possessed by Islamic artisans and their remarkable ability to translate complex mathematical concepts into visually stunning works of art.