Peter Saltzman
P.O. Box 9003, Berkeley, CA 94709 USA

A portion of the right half spandrel at the Darb-I Imam, Isfahan

For nearly 150 years, scholars have analyzed the symmetries of Islamic ornamental designs, constituting the most highly developed chapter in cultural symmetry studies. Yet these studies hardly exhaust the mathematically significant properties of Islamic designs. Over the past 30 years, mathematicians have given increasing attention to "quasi-periodic" geometric structures (such as the Penrose tilings) which exhibit infinite repetition of their bounded subparts and crystallographically forbidden symmetries, occupying an important niche between random and highly ordered, periodic structures. This paper provides a critical review of the literature and argues that the dualization of quasi-periodic tiling fragments from two designs from twelfth- and fifteenth-century Iran helps to inform their aesthetic complexity.

About the author
This email address is being protected from spambots. You need JavaScript enabled to view it. is a mathematician and lawyer living in Berkeley, California.

The correct citation for this paper is:
Peter Saltzman, "Quasi-Periodicity in Islamic Geometric Design", pp. 153-168 in Nexus VII: Architecture and Mathematics, ed. Kim Williams, Turin: Kim Williams Books, 2008.