Plaid model/ Richard Evan Schwartz

Includes bibliography and index

Introduction -- Part 1 The Plaid model -- Part 2 The Plaid pet -- Part 3 The Graph pet -- Part 4 The Plaid graph correspondence -- Part 5 The Distribution of orbits

The Plaid Model, which is a self-contained sequel to Richard Schwartz’s Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.

Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.

The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.