Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

@article{Lu2007DecagonalAQ,
  title={Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture},
  author={Peter J. Lu and Paul J. Steinhardt},
  journal={Science},
  year={2007},
  volume={315},
  pages={1106 - 1110}
}
The conventional view holds that girih (geometric star-and-polygon, or strapwork) 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… Expand
Response to Comment on "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture"
TLDR
Historically accurate reconstructions show that Darb-i Imam is unique, the only known example that does not repeat periodically and that displays a self-similar transformation enabling its continuation ad infinitum to a perfect quasi-crystalline pattern. Expand
Comment on "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture"
TLDR
It is demonstrated that the Darb-i Imam pattern is periodic and that the quasi-crystalline discs superimposed on its lattice are derivatives of the Maragha pattern. Expand
Quasi-Periodicity in Medieval and Islamic architecture and ornament
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-foldExpand
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Quasi-Periodicity in Islamic Geometric Design
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 hardlyExpand
Medieval Islamic Architecture, Quasicrystals, and Penrose and Girih Tiles: Questions from the Classroom
Tiling Theory studies how one might cover the plane with various shapes. Medieval Islamic artisans developed intricate geometric tilings to decorate their mosques, mausoleums, and shrines. Some ofExpand
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The tympanum of the entrance of the Zaouia Moulay Idriss II in Fez contains the only known example of a dodecagonal cartwheel quasiperiodic pattern in Islamic art, dating possibly from the MerinidExpand
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