Quasicrystalline Medieval Islamic Architectural Tilings

The conventional view holds that girih (geometric star-and-polygon) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons, the girih tiles decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.


  1. Peter J. Lu, Paul J. Steinhardt, “Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture” Science. 315, 1106–1110 (2007). [pdf] [Supp. Info]

Print Media Coverage

  1. “Geometrische Schönheiten” Berliner Zeitung [Germany] (2007).
  2. “Das Geheimnis der islamischen Kachelmosaike” Bild der Wissenschaft [Germany] (2007).
  3. “Science imitates art?” The Boston Globe (2007).
  4. “New light on ancient patterns; Sophisticated Islamic geometric designs in Iran predate Western discovery by 500 years” Chicago Tribune (2007).
  5. “Matematiker avslöjade koden till islamska mönster” Dagens Nyheter [Sweden] (2007).
  6. “Moschee-Baumeister waren westlichen Mathematikern 500 Jahre voraus” Der Spiegel [Germany] (2007).
  7. “Matemática muito ’à frente’ explica mosaicos islâmicos” Diario de Noticias [Portugal] (2007).
  8. “Puzzle der Unendlichkeit” Die Zeit [Germany] (2007).
  9. “Top 100 Science Stories of 2007: 59. Medieval Mosque Shows Amazing Math Discovery” Discover (2008).
  10. “이슬람 문양 규칙성 찾았다\textellipsis “4, 5개 단위로 묶으면 패턴”” dongA [South Korea] (2007).
  11. “L’art des mosquées devance les maths” El Watan [Algeria] (2007).
  12. “Kvazikristalna geometrija” Feral Tribune [Croatia] (2007).
  13. “Islamische Kunst: Fliesen verblüffen Mathematiker” Focus [Germany] (2007).
  14. “Wzory zagubione na pół tysiąca lat” Gazeta Wyborcza [Poland] (2007).
  15. “Modern mathematicians are 500 years behind” The Globe and Mail [Canada] (2007).
  16. “Medieval Islamic artists made amazing maths breakthrough” Gulf News [United Arab Emirates] (2007).
  17. “Medieval Islamic architecture presages 20th century mathematics” Harvard Gazette (2007).
  18. “Islamic artists were 500 years ahead of Western scientists” The Independent [UK] (2007).
  19. “Los mosaicos árabes, geometrı́a de avanzada” La Nacion [Argentina] (2007).
  20. “Il segreto dell’architettura islamica medioevale ‘Usa formule matematiche del XX secolo’” La Repubblica [Italy] (2007).
  21. “Islamic tiles reveal sophisticated maths” Nature (2007).
  22. “Medieval Islamic tiling reveals mathematical savvy” New Scientist (2007).
  23. “In Medieval Architecture, Signs of Advanced Math” The New York Times (2007).
  24. “Mathematik und Kunst beim Plattenlegen” Neue Zürcher Zeitung [Switzerland] (2007).
  25. “Islamische Ornamente” Neue Zürcher Zeitung [Switzerland] (2007).
  26. “Designs from Islamic artists streets ahead of West” New Zealand Herald (2007).
  27. “Higher Math From Medieval Islam” Newsweek (2007).
  28. “Virtuoos vlechtwerk” NRC Handlesblad [The Netherlands] (2007).
  29. “Islamisk kunst forud for sin tid” Politiken [Denmark] (2007).
  30. “Cinq siècles d’avance !” Pour la Science [France] (2007).
  31. “The Tiles of Infinity” Saudi Aramco World (2009).
  32. “Ancient Islamic Penrose Tiles ” Science News (2007).
  33. “Islamic Artisans Constructed Exotic Nonrepeating Pattern 500 Years Before Mathematicians” Scientific American (2007).
  34. “Angewandte Mathematik: Das Geheimnis der Girih” Spektrum der Wissenschaft [Germany] (2007).
  35. “Quasikristalline islamische Muster” Spektrum der Wissenschaft [Germany] (2007).
  36. “Moderne Mathematik in islamischen Ornamenten” Spektrum der Wissenschaft [Germany] (2007).
  37. “Patterns of Islamic Genius Crystal Clear Centuries Ago” Sydney Morning Herald [Australia] (2007).
  38. “Medieval math feat” The Telegraph [Calcutta, India] (2007).
  39. “Islamic tilers may have led scientific field” The Daily Telegraph [UK] (2007).
  40. “Medieval Muslims made stunning maths breakthrough” The Times of India (2007).
  41. “Amazing maths of the mosaic makers” The Times [UK] (2007).
  42. “Medieval Muslims made stunning math breakthrough” Today’s Zaman [Turkey] (2007).
  43. “Muslim Tile Patterns Show Math Prowess” The Washington Post (2007).

Broadcast Media Coverage

  1. “Medieval Mosques Illuminated by Math” All Things Considered. National Public Radio (2007).
  2. “Advanced geometry of Islamic art” The World Today. British Broadcasting Corporation (2007).