  We study combinatorial properties of the subshift induced by the substitution
that describes Lysenok's presentation of Grigorchuk's group of intermediate
growth by generators and relators. This subshift has recently appeared in two
different contexts: on one hand, it allowed to embed Grigorchuk's group in a
topological full group, and on the other hand, it was useful in the spectral
theory of Laplacians on the associated Schreier graphs.
