Penrose patterns, physics and tile polygons

Isfahan/ Charbagh Theological Shool/ Ceiling, originally uploaded by HORIZON.

Science 23 February 2007:Vol. 315. no. 5815, pp. 1106 – 1110DOI: 10.1126/science.1135491
Reports
Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture
Peter J. Lu1* and Paul J. Steinhardt2
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 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 Department of Physics, Harvard University, Cambridge, MA 02138, USA.2 Department of Physics and Princeton Center for Theoretical Physics, Princeton University, Princeton, NJ 08544, USA.* To whom correspondence should be addressed. E-mail: plu@fas.harvard.edu

Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture — Lu and Steinhardt 315 (5815): 1106 — Science

 

Penrose Tiling c. 2001, originally uploaded by dmswart.

citroen-flag, originally uploaded by yeled.

 

Penrose Tiled, originally uploaded by Kevan.

Penrose tiles for Mr Webb, originally uploaded by Tom Coates.

 

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