Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

Peter Lu and Paul Steinhardt's paper on decagonal and quasi-crystalline tilings in medieval Islamic architecture is a peer-reviewed physics and materials-science study published in Science, arguing from close geometric analysis of surviving girih tile patterns that some medieval architects achieved a form of quasi-crystalline tiling five centuries before the mathematics was formally described in the West. That is a strong empirical claim about pattern geometry, grounded in reproducible measurement of real building facades. Its limit is that it is a claim about geometric structure, not a claim about the design intentions or theoretical understanding of the historical craftsmen who built the patterns, a distinction the authors themselves are careful to draw and that some art historians have pressed further, questioning how much conscious mathematical insight the finding implies versus skilled empirical practice passed down through pattern books.