Fixed-point tile sets and their applications

@article{Durand2012FixedpointTS,
  title={Fixed-point tile sets and their applications},
  author={B. Durand and A. Romashchenko and A. Shen},
  journal={J. Comput. Syst. Sci.},
  year={2012},
  volume={78},
  pages={731-764}
}
An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many fields, ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene@?s fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann@?s self-reproducing automata; similar ideas were also used by P… Expand
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