Finitely related nilsemigroups and aperiodic tilings

We use this technique to construct an example of an infinite finitely related nilsemigroup, which gives an answer to the question of L.N.Shvernik. In this construction each paths on a tiling becomes an element of a semigroup, and the structure of the tiling corresponds to the algebraic relations in this semigroup. A tiling should respect only a finite number of local constraints, which correspond to a finite number of relators in the semigroup. This construction is connected with the Goodman-Strauss theorem on aperiodic hierarchical tilings.