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A single fractal pinwheel tile


Authors: Christoph Bandt, Dmitry Mekhontsev and Andrei Tetenov
Journal: Proc. Amer. Math. Soc. 146 (2018), 1271-1285
MSC (2010): Primary 52C20, 28A80
DOI: https://doi.org/10.1090/proc/13774
Published electronically: September 13, 2017
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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.


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Additional Information

Christoph Bandt
Affiliation: Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany
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
Email: a.tetenov@gmail.com

DOI: https://doi.org/10.1090/proc/13774
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
Article copyright: © Copyright 2017 American Mathematical Society

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