Some Generalizations of the Pinwheel Tiling
Group Theory
2018-07-10 v1 Combinatorics
Metric Geometry
Abstract
We introduce a new family of nonperiodic tilings, based on a substitution rule that generalizes the pinwheel tiling of Conway and Radin. In each tiling the tiles are similar to a single triangular prototile. In a countable number of cases, the tiles appear in a finite number of sizes and an infinite number of orientations. These tilings generally do not meet full-edge to full-edge, but CAN be forced through local matching rules. In a countable number of cases, the tiles appear in a finite number of orientations but an infinite number of sizes, all within a set range, while in an uncountable number of cases both the number of sizes and the number of orientations is infinite.
Keywords
Cite
@article{arxiv.math/9712263,
title = {Some Generalizations of the Pinwheel Tiling},
author = {Lorenzo Sadun},
journal= {arXiv preprint arXiv:math/9712263},
year = {2018}
}
Comments
Plain TeX, 35 pages including 12 embedded postscript figures