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arXiv · 1311.5555

Fusion: A general framework for hierarchical tilings

Natalie Priebe Frank
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Abstract

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.

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Natalie Priebe Frank. 2013-11-21. Fusion: A general framework for hierarchical tilings. https://arxiv.org/abs/1311.5555

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