Drawing limit sets of Kleinian groups using finite state automata

Abstract

The theory of automatic groups (groups that can be treated by means of finite-state automata), and in particular the techniques of automatic coset enumeration developed by Redfern, are applied to the problem of computing limit sets of a large class of Kleinian groups. We discuss in detail the case of groups in the Maskit embedding of the \tspace/ of the punctured torus.