Drawing Limit Sets of Kleinian Groups Using Finite State Automata

Greg McShane John R. Parker Ian Redfern

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 Teichmüller space of the punctured torus.