Abstract
Wang tiles are unit size squares with colored edges. To know if a given finite set of Wang tiles can tile the plane while respecting colors on edges is undecidable. Berger’s proof of this result shows the equivalence between tilings and Turing machines and thus tilings can be seen as a computing model. We thus have tilings that are Turing-universal, but there lacks a proper notion of universality for tilings. In this paper, we introduce natural notions of universality and completeness for tilings. We construct some universal tilings and try to make a first hierarchy of tile sets with a universality criteria.
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Lafitte, G., Weiss, M. (2007). Universal Tilings. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_32
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DOI: https://doi.org/10.1007/978-3-540-70918-3_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70917-6
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