Periodicity and ergodicity in the trihexagonal tiling
Metric Geometry
2018-07-24 v2
Abstract
We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almost every ray of light is dense in a region of a particular form: the regions have infinite area and consist of the plane with a periodic family of triangles removed. We also completely describe initial conditions for periodic and drift-periodic light rays.
Keywords
Cite
@article{arxiv.1609.00772,
title = {Periodicity and ergodicity in the trihexagonal tiling},
author = {Diana Davis and W. Patrick Hooper},
journal= {arXiv preprint arXiv:1609.00772},
year = {2018}
}
Comments
36 pages, 19 figures