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2014 | 126 | 2 | 461-466
Article title

Fusion: a General Framework for Hierarchical Tilings

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Content
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EN
Abstracts
EN
One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings-the Penrose, octagonal, and pinwheel tilings are famous examples. We present a different model for generating hierarchical tilings we call "fusion rules". Inflate-and-subdivide rules are a special case of fusion rules, but general fusion rules are more flexible and allow for defects, changes in geometry, and even constrained randomness. A condition that produces homogeneous structures and a method for computing frequency for fusion tiling spaces are discussed.
Keywords
EN
Publisher

Year
Volume
126
Issue
2
Pages
461-466
Physical description
Dates
published
2014-08
Contributors
author
  • Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, U.S.A.
References
  • [1] R. Lifshitz, J. Alloys Comp. 342, 186 (2002)
  • [2] M. Baake, U. Grimm, Aperiodic Order, A Mathematical Invitation, in: Encyclopedia of Mathematics and its Applications, Vol. 1, Cambridge University Press, Cambridge 2013
  • [3] N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics, Combinatorics, Lecture Notes in Mathematics, Vol. 1794, Springer-Verlag, Heidelberg, 2002
  • [4] E.A. Robinson, Proc. Sympos. Appl. Math. 20, 81 (2004)
  • [5] N.P. Frank, Expo. Math. 26, 295 (2008), doi: 10.1016/j.exmath.2008.02.001
  • [6] N.P. Frank, L. Sadun, Geom. Dedicata 171, 38 (2013), doi: 10.1007/s10711-013-9893-7
  • [7] M. Baake, U. Grimm, Chem. Soc. Rev. 41, 6821 (2012), doi: 10.1039/C2CS35120J
  • [8] N.P. Frank, L. Sadun, Topol. Proc. 43, 235 (2014)
  • [9] D. Damanik, M. Embree, A. Gorodetski, to appear in Directions in Aperiodic Order, in series Progress in Mathematics, Eds. J. Kellendonk, D. Lenz, J. Savinien, Birkhauser 2014
  • [10] L. Sadun, Topology of Tiling Spaces, University Lecture Series, American Mathematical Society, Providence 2008
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n209kz
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