Abstract
Wang tiles are unit size squares with colored edges. By using a fixed-point theorem à la Kleene for tilings we give novel proofs of classical results of tilings problems’ undecidability by way of diagonalization on tilings (made possible by this theorem). Then, we present a general technique to construct aperiodic tile sets, i.e., tile sets that generate only aperiodic tilings of the plane. Our last construction generalizes the notion of self-simulation and makes possible the construction of tile sets that self-simulate via self-similar tilings, showing how complex the self-simulation can be.
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Lafitte, G., Weiss, M. (2009). Constructing New Aperiodic Self-simulating Tile Sets. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_31
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DOI: https://doi.org/10.1007/978-3-642-03073-4_31
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