Comments on tilings and quasicrystals

At the Geometry Center at the University of Minnesota you  
can connect to a computer program Quasitiler
which will create tilings to order.

There is a large literature on the subjects of tilings and 
quasicrystals, from mathematical and physical aspects. 

A popular introduction:

P.W. Stephens and A.I. Goldman
The structue of quasicrystals
Scientific American vol 264, April 1991, 24 - 31

Recent books on the mathematical aspects of this field:

Marjorie Senechal
Quasicrystals and geometry
Cambridge University Press 1996

Charles Radin
Miles of Tiles
American Mathematical Society 1999

A book on the physics:

Christian Janot
Quasicrystals: a primer, 2. ed
Oxford UP 1997

The original discovery of quasicrystals was published in:

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, 
Phys. Rev. Lett. 53 (1984), 1951-1953. 

Below, an example of a Penrose tiling.



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