펜로즈 타일 붙이기

A Penrose tiling is an aperiodic tiling of the plane discovered by Roger Penrose in 1973.[1] Being aperiodic, it has no translational symmetry — it never repeats itself exactly, but nevertheless it has a fivefold rotational symmetry.

The Penrose tiling is also a prime example of a quasicrystal as it produces a sharply outlined diffractogram. There are two popular variants of the Penrose tiling which use different sets of tiles. Robert Ammann independently discovered the tiling. A similarity with some decorative patterns used in the Middle East has been frequently noted [2] [3] and in February 2007 a paper by Steinhardt and Lu offered evidence that a Penrose tiling underlies some examples of medieval Islamic art.[4] Roger Penrose acknowledges inspiration from the work of Johannes Kepler.

In 1982 Dan Shechtman reported that a sample of aluminium-manganese alloy produced a sharp diffractogram with fivefold symmetry. At that time it was assumed that such symmetry is incompatible with the ability to diffract. The combination of these two features is possible only in an aperiodic structure. The full three-dimensional arrangement, which exhibits icosahedral symmetry, had been worked out by Robert Ammann. The atoms in the planes corresponding to the unusual symmetry are arranged in the pattern of a Penrose tiling.

De Bruijn has shown that it was possible to obtain the Penrose tiling as a projection from a five-dimensional cubic lattice, which explains its crystal-like ability to diffract. The Penrose Tiling has become the most studied — and most popular — quasicrystal. The physicists' interest led to another approach which connected the Penrose tiling to extremal problems and proved it to be a model for the state with minimum energy in some systems. This development came after Petra Gummelt's demonstration that it is possible to build an aperiodic tiling with a single decagonal tile if overlapping is allowed and this construction reproduced the Penrose tiling.[5]

[자료출처]

• Page name: Penrose tiling
• Author: Wikipedia contributors
• Publisher: Wikipedia, The Free Encyclopedia.
• Date of last revision: 27 May 2007 02:59 UTC
• Date retrieved: 29 May 2007 05:29 UTC
• Permanent link: http://en.wikipedia.org/w/index.php?title=Penrose_tiling&oldid=133775306
• Page Version ID: 133775306