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Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. 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 materials interactively and each theorem is accompanied by a computer demo.

Hyperbolic spaces. --- Singularities (Mathematics) --- Transformations (Mathematics) --- Geometry, Plane. --- Plane geometry --- Algorithms --- Differential invariants --- Geometry, Differential --- Geometry, Algebraic --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- 1-dimensional wordlines. --- Bad Tile Lemma. --- Box Theorem. --- Copy Lemma. --- Copy Theorem. --- Curve Turning Theorem. --- Graph Master Picture Theorem. --- Graph Master Theorem. --- Graph Reconstruction Lemma. --- Grid Geometry Lemma. --- Grid Supply Lemma. --- Horizontal Lemma. --- Intertwining Lemma. --- Master Picture Theorem. --- Matching Criterion. --- Orbit Equivalence Theorem. --- PET. --- Plaid Master Picture Theorem. --- Projection Theorem. --- Quasi-Isomorphism Theorem. --- Rectangle Lemma. --- Renormalization Theorem. --- Segment Lemma. --- Truchet Comparison Theorem. --- Truchet tile system. --- Vertical Lemma. --- anchor point. --- arithmetic alignment. --- arithmetic graph. --- auxiliary lemmas. --- capacities. --- capacity sequence. --- capacity. --- checkerboard partition. --- classifying map. --- compactification. --- congruence. --- continued fractions. --- convex polygon. --- convex polytopes. --- corner percolation. --- east edges. --- elementary number theory. --- embedded loops. --- equidistribution. --- even rational parameter. --- fundamental surface. --- geometric alignment. --- geometry. --- graph grid. --- grid lines. --- horizontal case. --- integer square. --- intersection points. --- kites. --- kits. --- lemma. --- lemmas. --- light point. --- light points. --- linear algebra. --- low capacity lines. --- map. --- maps. --- mass sequence. --- masses. --- number theory. --- orbit. --- oriented lines. --- outer billiards map. --- outer billiards. --- parallel lines. --- parallelotope. --- particle lines. --- pixelated spacetime diagrams. --- pixelated spacetime. --- pixilation. --- plaid PET map. --- plaid model. --- plaid polygon. --- plaid polygons. --- plane. --- planetary motion. --- planetary orbits. --- polygon. --- polytope exchange transformations. --- polytopes. --- prism structure. --- prism. --- proof. --- quarter turn compositions. --- remote adjacency. --- renormalization. --- scale information. --- sequences. --- slanting lines. --- spaces. --- spacetime diagrams. --- spacetime plaid surfaces. --- special billiards orbits. --- square tiling. --- stacking blocks. --- structural result. --- symmetries. --- symmetry. --- technical lemma. --- theorems. --- vertical case. --- vertical particles.