{
  "id": "1809.07876",
  "version": "v1",
  "published": "2018-09-20T21:50:39.000Z",
  "updated": "2018-09-20T21:50:39.000Z",
  "title": "Tiling Billards on Triangle Tilings, and Interval Exchange Transformations",
  "authors": [
    "Paul Baird-Smith",
    "Diana Davis",
    "Elijah Fromm",
    "Sumun Iyer"
  ],
  "comment": "31 pages, 19 figures, 2 appendices. Comments welcome!",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by an orientation-reversing three-interval exchange transformation on the circle, and that the behavior of all the trajectories on a given triangle tiling is described by a polygon exchange transformation. We show that, for a particular choice of triangle tiling, certain trajectories approach the Rauzy fractal, under rescaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T21:50:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E05",
      "37E35"
    ],
    "keywords": [
      "triangle tiling",
      "interval exchange transformations",
      "tiling billards",
      "orientation-reversing three-interval exchange transformation",
      "trajectory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}