Automata, Groups, Limit Spaces, and Tilings
arXiv:math/0412373 · doi:10.1016/j.jalgebra.2005.10.022
Abstract
We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering.
to appear in J. Algebra