Fusion: a General Framework for Hierarchical Tilings

• Authors: N. Frank
• Languages of publication: 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

61.44.Br; 02.40.Gh

Discipline

• 02.40.Gh: Noncommutative geometry
• 61.44.Br: Quasicrystals

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 461-466

Dates

published

2014-08

Contributors

author

N. Frank

• Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, U.S.A.

References

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Identifiers

DOI

10.12693/APhysPolA.126.461