A self-similar aperiodic set of 19 Wang tiles

10 Jul 2019 Labbé Sébastien

We define a Wang tile set $\mathcal{U}$ of cardinality 19 and show that the set $\Omega_\mathcal{U}$ of all valid Wang tilings $\mathbb{Z}^2\to\mathcal{U}$ is self-similar, aperiodic and is a minimal subshift of $\mathcal{U}^{\mathbb{Z}^2}$. Thus $\mathcal{U}$ is the second smallest self-similar aperiodic Wang tile set known after Ammann's set of 16 Wang tiles... (read more)

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