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A Computer Search for Planar Substitution Tilings with \(n\)-Fold Rotational Symmetry

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Abstract

We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of \(\pi /n\). We find new substitution rules admitting \(7\)-fold rotational symmetry at many different inflation factors.

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Acknowledgments

The first and third authors were partly supported by the German Research Council (DFG), CRC 701. The third author was also partly supported by the Fields Institute during a research visit.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße 25, D-33615, Bielefeld, Germany

    Franz Gähler

  2. Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA, 02138, USA

    Eugene E. Kwan

  3. School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    Gregory R. Maloney

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  1. Franz Gähler
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  2. Eugene E. Kwan
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  3. Gregory R. Maloney
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Correspondence to Gregory R. Maloney.

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Gähler, F., Kwan, E.E. & Maloney, G.R. A Computer Search for Planar Substitution Tilings with \(n\)-Fold Rotational Symmetry. Discrete Comput Geom 53, 445–465 (2015). https://doi.org/10.1007/s00454-014-9659-5

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  • DOI: https://doi.org/10.1007/s00454-014-9659-5

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