Contents

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface xi
4. Introduction 1
5. Part 1. The Plaid Model
6. Chapter 1. Definition of the Plaid Model 15
7. Chapter 2. Properties of the Model 25
8. Chapter 3. Using the Model 35
9. Chapter 4. Particles and Spacetime Diagrams 45
10. Chapter 5. Three-Dimensional Interpretation 57
11. Chapter 6. Pixellation and Curve Turning 71
12. Chapter 7. Connection to the Truchet Tile System 81
13. Part 2. The Plaid PET
14. Chapter 8. The Plaid Master Picture Theorem 93
15. Chapter 9. The Segment Lemma 103
16. Chapter 10. The Vertical Lemma 111
17. Chapter 11. The Horizontal Lemma 119
18. Chapter 12. Proof of the Main Result 125
19. Part 3. The Graph PET
20. Chapter 13. Graph Master Picture Theorem 135
21. Chapter 14. Pinwheels and Quarter Turns 143
22. Chapter 15. Quarter Turn Compositions and PETs 153
23. Chapter 16. The Nature of the Compactification 161
24. Part 4. The Plaid-Graph Correspondence
25. Chapter 17. The Orbit Equivalence Theorem 173
26. Chapter 18. The Quasi-Isomorphism Theorem 185
27. Chapter 19. Geometry of the Graph Grid 195
28. Chapter 20. The Intertwining Lemma 199
29. Part 5. The Distribution of Orbits
30. Chapter 21. Existence of Infinite Orbits 213
31. Chapter 22. Existence of Many Large Orbits 219
32. Chapter 23. Infinite Orbits Revisited 227
33. Chapter 24. Some Elementary Number Theory 239
34. Chapter 25. The Weak and Strong Case 245
35. Chapter 26. The Core Case 253
36. References 265
37. Index 267