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2014 | 126 | 2 | 508-511
Article title

Tiling Spaces of Taylor-Socolar Tilings

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EN
Abstracts
EN
The Taylor-Socolar tiling has been introduced as an aperiodic mono-tile tiling. We consider a tiling space which consists of all the tilings that are locally indistinguishable from a Taylor-Socolar tiling and study its structure. It turns out that there is a bijective map between the space of the Taylor-Socolar tilings and a compact Abelian group of a Q-adic space (Q̅) except at a dense set of points of measure 0 in Q̅. From this we can derive that the Taylor-Socolar tilings have quasicrystalline structures. We make a parity tiling from the Taylor-Socolar tiling identifying all the rotated versions of a tile in the Taylor-Socolar tiling by white tiles and all the reflected versions of the tile by gray tiles. It turns out that the Taylor-Socolar tiling is mutually locally derivable from this parity tiling.
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EN
Publisher

Year
Volume
126
Issue
2
Pages
508-511
Physical description
Dates
published
2014-08
Contributors
author
  • Department of Mathematics Education, Kwandong University, Gangneung, Gyeonggi-do, 210-701, Korea
References
  • [1] J. Socolar, J. Taylor, J. Combinat. Theor., Series A 118, 2207 (2011), doi: 10.1016/j.jcta.2011.05.001
  • [2] J. Socolar, J. Taylor, Math. Intelligencer 34, 18 (2012), doi: 10.1007/s00283-011-9255-y
  • [3] R. Penrose, Twistor Newsletter, reprinted in Roger Penrose: Collected Works, Vol. 6, 1997-2003, Oxford University Press, New York 2010 http://people.maths.ox.ac.uk/lmason/Tn/
  • [4] R. Penrose, in: The Mathematics of Long-Range Aperiodic Order, Ed. R.V. Moody, NATO ASI Series C, Vol. 489, Kluwer Acad. Publ., Dordrecht (Netherlands) 1997, p. 467
  • [5] M. Baake, F. Gähler, U. Grimm, Symmetry 4, 581 (2012), doi: 10.3390/sym4040581
  • [6] F. Gähler, private communication
  • [7] J.-Y. Lee, R.V. Moody, 'A Relation between Two Aperiodic Hexagonal Tilings', preprint
  • [8] C. Radin, M. Wolff, Geometr. Dedic. 42, 355 (1992), doi: 10.1007/BF02414073
  • [9] J.-Y. Lee, R.V. Moody, Symmetry 5, 1 (2013), doi: 10.3390/sym5010001
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n221kz
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