Miles of Tiles

Cover 1
Title 4
Copyright 5
Contents 8
List of Figures 10
Preface 12
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Cover 1
Title 4
Copyright 5
Contents 8
List of Figures 10
Preface 12
Introduction 14
Chapter 1. Ergodic Theory 30
1. The idea behind ergodic theory 30
2. Some mathematical structure 33
3. Substitution tilings 38
4. Finite type tilings 46
Chapter 2. Physics (for Mathematicians) 68
1. Diffraction of light waves 68
2. Statistical mechanics 71
Chapter 3. Order 76
1. Spectrum and order 76
Chapter 4. Symmetry 82
1. Substitution and rotational symmetry 82
2. Spectrum and X-rays 94
3. 3-dimensional models 99
Chapter 5. Conclusion 112
Appendix I. Geometry 116
Appendix II. Algebra 118
Appendix III. Analysis 122
References 126
List of Symbols 130
Subject Index 132
A 132
D 132
F 132
G 132
H 132
I 132
K 132
L 132
M 132
N 132
P 132
Q 132
R 132
S 132
T 133
U 133
W 133
Back Cover 134
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