Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fusion: A general framework for hierarchical tilings   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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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con