Schreier Graphs for a Self-Similar Action of the Heisenberg Group - Bondarenko, I.; Kravchenko, R. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital Schreier graphs of action on the boundary of the tree with different degrees of growth.