Constructing Penrose-like tilings from a single prototile and the implications for quasicrystals
نویسندگان
چکیده
We present two sets of rules for constructing quasiperiodic tilings that suggest a simpler structural model of quasicrystals and a more plausible explanation of why quasicrystals form. First, we show that quasiperiodic tilings can be constructed from a single prototile with matching rules which constrain the way that neighbors can overlap. Second, we show that maximizing the density of a certain cluster of fat and thin tiles can force a Penrose tiling without imposing the usual Penrose matching rules. @S0163-1829~97!02706-9#
منابع مشابه
A Fractal Fundamental Domain with 12-fold Symmetry
Square triangle tilings are relevant models for quasicrystals. We introduce a new self-similar tile-substitution which yields the well-known nonperiodic square triangle tilings of Schlottmann. It is shown that the new tilings are locally derivable from Schlottmann’s, but not vice versa, and that they are mutually locally derivable with the undecorated square triangle tilings. Furthermore, the r...
متن کاملLocal Isomorphism, Landau Theory, and Matching Rules in Quasicrystals
Standing as the5 do in such striking contrast to the structures of classical crystallography, quasicrystals:], have generated a great deal of interest, both theoretically and experiment-ally. The exciting discovery of a rapidly rooled a l I o of AlMn-2: exhibiting sharp diffraction peaks in a n array with classical1~forbidden icosahedral rotation syrbmetry has been confirmed by man7 successive ...
متن کاملA Modification of the Penrose Aperiodic Tiling
From black and white linoleum on the kitchen floor to magnificent Islamic mosaic to the intricate prints of M.C. Escher, tilings are an essential component of the decorative arts, and the complex mathematical structure behind them has intrigued scientists, mathematicians, and enthusiasts for centuries. Johannes Kepler, most famous for his laws of planetary motion, was known to have been interes...
متن کاملMedieval 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 of these patterns, called girih tilings, first appeared in the 12 Century AD. Recent investigations show these medieval tilings contain symmetries similar to those found in aperiodic Penrose tilings firs...
متن کاملQuasicrystals and geometry: a Book Review
Penrose tilings (Fig. 1) are beautiful. They also suggest significant new mathematics, so it is about time someone wrote a book about them which is readable (in fact, eminently readable) by mathematicians. The book, Quasicrystals and geometry, by Marjorie Senechal, has an even broader goal: to present certain developments in crystallography from the past decade. The developments were generated ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997