TL;DR
This paper presents the Plaid Model, a combinatorial framework for generating embedded polygons in the plane, connecting various mathematical systems like outer billiards, percolation, and tilings.
Contribution
It introduces the Plaid Model and establishes foundational results linking it to multiple existing mathematical systems.
Findings
The Plaid Model produces embedded polygons with specific properties.
Connections between the Plaid Model and outer billiards on kites are established.
The model relates to corner percolation, Truchet tiles, and polyhedron exchange transformations.
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Stochastic processes and statistical mechanics