Abstract
One well studied way to construct quasicrystalline tilings is via in ate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings the Penrose, octagonal, and pinwheel tilings are famous examples. We present a di erent model for generating hierarchical tilings we call fusion rules . In ate-and-subdivide rules are a special case of fusion rules, but general fusion rules are more exible 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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