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 intinite 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 ot 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.
CITATION STYLE
Sadun, L. (1998). Some generalizations of the pinwheel tiling. Discrete and Computational Geometry, 20(1), 79–110. https://doi.org/10.1007/PL00009379
Mendeley helps you to discover research relevant for your work.