Substitutive Structure of Jeandel–Rao Aperiodic Tilings

@article{Labb2021SubstitutiveSO,
  title={Substitutive Structure of Jeandel–Rao Aperiodic Tilings},
  author={S. Labb{\'e}},
  journal={Discrete \& Computational Geometry},
  year={2021},
  volume={65},
  pages={800-855}
}
  • S. Labbé
  • Published 2021
  • Computer Science, Mathematics
  • Discrete & Computational Geometry
Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles, i.e., unit squares with colored edges, that admit valid tilings (contiguous edges of adjacent tiles have the same color) of the plane, none of them being invariant under a nontrivial translation. We study herein the Wang shift $$\Omega _0$$ Ω 0 made of all valid tilings using the set $$\mathcal {T}_0$$ T 0 of 11 aperiodic Wang tiles discovered by Jeandel and Rao. We show that there exists a minimal subshift $$X_0$$ X… Expand
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TLDR
A set of 16 Wang tiles is introduced that admits a valid tiling of the plane described by a deterministic finite automaton taking as input the representation of a position (m,n) ∈ Z and outputting a Wang tile. Expand
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