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Knight Tiles: Particles and Collisions in the Realm of 4-Way Deterministic Tilings

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Developments in Language Theory (DLT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8633))

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Abstract

Particles and collisions are convenient construction tools to compute inside tilings and enforce complex sets of tilings with simple tilesets. Locally enforceable particles being incompatible with expansivity in the orthogonal direction, a compromise has to be found to combine both notions in a same tileset. This paper introduces knight tiles: a framework to construct 4-way deterministic tilings, that is tilings completely determined by any infinite diagonal of tiles, for which local particles and collisions with many slopes can still be constructed while being expansive in infinitely many directions. The framework is then illustrated by an elegant yet simple construction to mark a diagonal with a 4-way deterministic knight tileset.

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Author information

Authors and Affiliations

  1. INSA Centre Val de Loire, LIFO EA 4022, Univ. Orléans, FR-45067, Orléans, France

    Bastien Le Gloannec & Nicolas Ollinger

Authors
  1. Bastien Le Gloannec
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  2. Nicolas Ollinger
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina, 51, 620000, Ekaterinburg, Russia

    Arseny M. Shur  & Mikhail V. Volkov  & 

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Le Gloannec, B., Ollinger, N. (2014). Knight Tiles: Particles and Collisions in the Realm of 4-Way Deterministic Tilings. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_20

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  • DOI: https://doi.org/10.1007/978-3-319-09698-8_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09697-1

  • Online ISBN: 978-3-319-09698-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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