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Quasi-Periodicity in Medieval and Islamic architecture and ornament , Helmer Aslaksen2

Summary: Quasi-Periodicity in Medieval and Islamic architecture and ornament
Ser Zheng1
, Helmer Aslaksen2
SRP student, Raffles Junior College
Department of Mathematical Sciences, National University of Singapore
A recent article in Science by Lu and Steinhardt has caused a controversy over whether Medieval
Islamic tilings are examples of aperiodic and quasiperiodic tilings. The tilings have five- or ten-fold
symmetry, which cannot occur in traditional crystallography. Such tilings were only recently discovered in
the West. The goal of this project is to read several articles and write a summary of the various claims
regarding quasi-periodicity in Medieval Islamic tilings. We will focus on three properties: the method of
construction, its relation to Penrose tilings and whether the tiling is quasi-periodic. Such tilings appear on
buildings or on ornaments as decoration. Our main examples will be taken from the Gunbad-i Kabud tower
in Maragha, Iran (1197 C.E.) and the Darb-i-Imam shrine in Isfahan, Iran (1453 C.E.).
Most Medieval Islamic tilings are periodic. A periodic tiling is
one which possesses translational symmetry. It can be proven
that within a periodic tiling, only two-fold, three-fold, four-fold


Source: Aslaksen, Helmer - Department of Mathematics, National University of Singapore


Collections: Mathematics