Fusion: A general framework for hierarchical tilings
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.
Keywords
Cite
@article{arxiv.1311.5555,
title = {Fusion: A general framework for hierarchical tilings},
author = {Natalie Priebe Frank},
journal= {arXiv preprint arXiv:1311.5555},
year = {2013}
}
Comments
This paper is to appear in the proceedings of the 12th International Conference on Quasicrystallography. It is written as an introduction for non-mathematicians