A Counterexample to Nivat's Conjecture for a Non-Convex Window of Full Affine Span

Abhishek Khetan

We construct an exact cluster $F\subseteq {\mathbb{Z}}^2$ of cardinality $8$ with full affine span, together with an $F$-tiling $T$, such that the orbit closure of $T$ in $\{0,1\}^{\m…