An aperiodic set of 11 Wang tiles

Emmanuel Jeandel (1) , Michael Rao (2)

1 MOCQUA - Designing the Future of Computational Models
2 MC2 - Modèles de calcul, Complexité, Combinatoire

We present a new aperiodic tileset containing 11 Wang tiles on 4 colors, and we show that this tileset is minimal, in the sense that no Wang set with either fewer than 11 tiles or fewer than 4 colors is aperiodic. This gives a definitive answer to the problem raised by Wang in 1961.

Domaines: Mathématique discrète [cs.DM]; Théorie et langage formel [cs.FL]

Emmanuel Jeandel, Michael Rao. An aperiodic set of 11 Wang tiles. Advances in Combinatorics, 2021, ⟨10.19086/aic.18614⟩. ⟨hal-01166053v4⟩