Periodicity and ergodicity in the trihexagonal tiling

@article{Davis2018PeriodicityAE,
  title={Periodicity and ergodicity in the trihexagonal tiling},
  author={Diana Davis and William P. Hooper},
  journal={Commentarii Mathematici Helvetici},
  year={2018}
}
  • D. Davis, W. Hooper
  • Published 3 September 2016
  • Mathematics
  • Commentarii Mathematici Helvetici
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. 
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