Introducing the Plaid Model

Abstract

We introduce and prove some basic results about a combinatorial model which produces embedded polygons in the plane. The model is closely related to outer billiards on kites, and also is related to corner percolation, to Hooper's Truchet tile system, to self-similar tilings, and to polyhedron exchange transformations.Comment: 68 pages. This is an more polished version of the original submission. The connection to polytope exchanges is developed and one of the speculative sections has been eliminated. Otherwise, it has the same result