Penrose Tiles
The Art and Science of Tiling

The tile pattern above contains just two shapes: kites and darts. They were discoverd in 1974 by the British mathematical physicist Roger Penrose. In 1984, he demonstrated that, when fit together according to certain simple rules, they will cover an infinite plane in an uncountable infinite number of arrangements.

As the kite and dart pattern expands to fill the plane, it displays certain local symmetries, but no specific patch is ever repeated; that is, the system is aperiodic. By contrast, the surrounding rectangular tile pattern may also extend infinitely, but does repeat itself; any patch matches all others. Every Penrose kite and dart tiling of a plane contains the cartwheel patch displayed here, but just once. Understanding its composition is essential to understanding all Penrose tilings.

The installation of our tiles grew out of discussions between Elisabeth Steele '96 and Professor Brian Loe following the 1992 Pre-Freshman Math and Science Program sponsored by the Office of Multicultural Affairs. It was made possible in part by gifts from members of the Department of Mathematics and Computer Science and friends of the College. It is used with the permission of Roger Penrose.



For more information on Penrose and his tilings visit these sites:

The Dr. Matrix Weird Web World of Science (a good intro to periodic tilings)
Penrose Tilings and the Golden Mean
Roger Penrose at Penn State
Penrose Tiles at the Geometry Junkyard
Roger Penrose biography from World of Escher
More on Penrose Tiles


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Michael N. Tie mtie@carleton.edu
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