Knight tiles: particles and collisions in the realm of 4-way deterministic tilings

Bastien Le Gloannec (1) , Nicolas Ollinger (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Mots clés: Deterministic tiles; Domino Problem; Tiling Problem; Expansive Subdynamics; Particles; Wang tiles

Domaines: Autre [cs.OH]; Théorie et langage formel [cs.FL]

Bastien Le Gloannec, Nicolas Ollinger. Knight tiles: particles and collisions in the realm of 4-way deterministic tilings. Developments in Language Theory (DLT), Aug 2014, Ekaterinburg, Russia. pp 227-238, ⟨10.1007/978-3-319-09698-8_20⟩. ⟨hal-00960244⟩