Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture

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Colloquium Lecture: Harvard University Physics Department (Dec 07)
Interview: NPR's All Things Considered (Feb 2007)
Interview: BBC's The World Today (Feb 2007)
Interview: Deutschlandfunk's Forschung Aktuell [Germany] (Feb 07)
Interview: WHRB Harvard Radio (Feb 2007)
Gunbadi Kabud
Darbi Imam Tiles
Intimad AlDaula
Topkapi Scroll

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 (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.

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Peter J. Lu  |  Harvard University  |  Cambridge, MA 02138 USA |