Negative refraction and tiling billiards

TL;DR

This paper introduces 'tiling billiards,' a new dynamical system modeling trajectories refracting through planar tilings, inspired by materials with negative refraction, and explores specific cases through computer experiments.

Contribution

It presents a novel dynamical system called tiling billiards, inspired by negative index materials, and analyzes special cases with computational experiments.

Findings

Identification of specific behaviors in tiling billiards systems

Insights into trajectories in line-divided planar tilings

Potential applications in understanding negative refraction phenomena

Abstract

We introduce a new dynamical system that we call "tiling billiards," where trajectories refract through planar tilings. This system is motivated by a recent discovery of physical substances with negative indices of refraction. We investigate several special cases where the planar tiling is created by dividing the plane by lines, and we describe the results of computer experiments.