A single fractal pinwheel tile
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- by Christoph Bandt, Dmitry Mekhontsev and Andrei Tetenov PDF
- Proc. Amer. Math. Soc. 146 (2018), 1271-1285 Request permission
Abstract:
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based on partitions of triangles or rectangles. The fractal example of Frank and Whittaker requires 13 different types of tiles. We present an example of a single tile with fractal boundary and very simple geometric structure which has the same symmetry and spectral properties as the pinwheel triangle.References
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Additional Information
- Christoph Bandt
- Affiliation: Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany
- MR Author ID: 30465
- Email: bandt@uni-greifswald.de
- Dmitry Mekhontsev
- Affiliation: Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
- Email: mekhontsev@gmail.com
- Andrei Tetenov
- Affiliation: Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
- MR Author ID: 256679
- Email: a.tetenov@gmail.com
- Received by editor(s): November 23, 2016
- Received by editor(s) in revised form: March 2, 2017, and April 12, 2017
- Published electronically: September 13, 2017
- Communicated by: Jeremy Tyson
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1271-1285
- MSC (2010): Primary 52C20, 28A80
- DOI: https://doi.org/10.1090/proc/13774
- MathSciNet review: 3750238