Fixed Point Constructions in Tilings and Cellular Automata (Invited Talk)

Author Ilkka Törmä

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Ilkka Törmä
  • Department of Mathematics and Statistics, University of Turku, Finland

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Ilkka Törmä. Fixed Point Constructions in Tilings and Cellular Automata (Invited Talk). In 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The simulations are implemented entirely by computations of Turing machines embedded in the tilings or spacetime diagrams. We present an overview of the construction and list its applications in the literature.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Tilings
  • Wang tiles
  • cellular automata
  • multidimensional symbolic dynamics
  • self-simulation


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