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.
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Received April 9, 1996, and in revised form September 16, 1996.
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Sadun, L. Some Generalizations of the Pinwheel Tiling . Discrete Comput Geom 20, 79–110 (1998). https://doi.org/10.1007/PL00009379
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DOI: https://doi.org/10.1007/PL00009379