Advertisement

Discrete & Computational Geometry

, Volume 20, Issue 1, pp 79–110 | Cite as

Some Generalizations of the Pinwheel Tiling

  • L. Sadun

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

Finite Number Infinite Number Countable Number Matching Rule Substitution Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • L. Sadun
    • 1
  1. 1.Mathematics Department, University of Texas, Austin, TX 78712, USA sadun@math.utexas.edu US

Personalised recommendations