The Limit Space of Self-similar Groups and Schreier graphs

The present paper investigates the limit G-space J₆ generated by the self-similar action of automatic groups on a regular rooted tree. The limit space J₆ is the Gromov-Hausdorff limit of the family of Schreier graphs ₍; therefore, J₆ can be approximated by Schreier graphs on level n-th when n tends to infinity. We propose a computer program whose code is written in Wolfram language computes the adjacency matrix of Schreier graph ₍ at each specified level of the regular rooted tree. In this paper, the Schreier graphs corresponding to each automatic group is computed by applying the program to some collection of automata groups, including classic automatic groups.