APERIODIC TILES

被引：125

作者：

AMMANN, R

GRUNBAUM, B

SHEPHARD, GC

机构：

[1] UNIV WASHINGTON,SEATTLE,WA 98195

[2] UNIV E ANGLIA,NORWICH NR4 7TJ,NORFOLK,ENGLAND

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 1992年 / 8卷 / 01期

关键词：

D O I：

10.1007/BF02293033

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A set of tiles (closed topological disks) is called aperiodic if there exist tilings of the plane by tiles congruent to those in the set, but no such tiling has any translational symmetry. Several aperiodic sets have been discussed in the literature. We consider a number of aperiodic sets which were briefly described in the recent book Tilings and Patterns, but for which no proofs of their aperiodic character were given. These proofs are presented here in detail, using a technique with goes back to R. M. Robinson and Roger Penrose.

引用

页码：1 / 25

页数：25

共 18 条

[1]

Beenker F.P.M., 1982, 82WSK04 EINDH U TECH

[2] 3-DIMENSIONAL ANALOGS OF THE PLANAR PENROSE TILINGS AND QUASICRYSTALS [J].

DANZER, L .

DISCRETE MATHEMATICS, 1989, 76 (01) :1-7

[3]

DEBRUIJN NG, 1981, P K NED AKAD A MATH, V84, P39

[4]

DEBRUIJN NG, REMARKS BEENKER PATT

[5]

Gardner M., 1977, SCI AM, V236, P110, DOI DOI 10.1038/SCIENTIFICAMERICAN0177-110

[6]

Grunbaum B., 1986, TILINGS PATTERNS

[7] THEORY OF MATCHING RULES FOR THE 3-DIMENSIONAL PENROSE TILINGS [J].

KATZ, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 118 (02) :263-288

[8]

KATZ A, 1988, AM MATH SOC, V9, P437

[9] QUASI-CRYSTALS .1. DEFINITION AND STRUCTURE [J].

LEVINE, D ;

STEINHARDT, PJ .

PHYSICAL REVIEW B, 1986, 34 (02) :596-616

[10]

MACKAY AL, 1982, PHYS A, V114, P606

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