Grigorchuk's group and aperiodic order
We discuss Grigorchuk’s group of intermediate growth, its natural action on a binary rooted tree and its substitution structure. We then present a construction of Grigorchuk, Lenz and Nagnibeda which relates the associated measurable dynamical system of graphs and its associated random Laplacian to a combinatorial dynamical system over the integers and an associated random Schrödinger operator.