Digraph Self-Similar Sets and Aperiodic Tilings

Self-similarity is a concept often associated with fractal geometry. There are many interesting self-similar sets in the plane which would not generally be considered fractal, however (although their boundaries might be fractal). Such sets provide a fresh way of looking at tilings of the plane. Furthermore, a generalization of self-similarity, called digraph self-similarity, provides a way to construct aperiodic tilings.