A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on classical tilings plane due to Raphael Robinson. Extending those group by exploiting group’s structure and posing additional local rules prune out remaining periodic behavior, we maintain rich projective subdynamics Z2 cosets. In addition, obtained factors onto aperiodic, minimal sofic shift via map that is invertible dense set configurations.