An automaton generating parageometric automorphisms?

Automorphisms of the free group can be classified using their index. A maximal index indicates that the automorphism is rich as it would be geometric or parageometric. Geometric group automorphisms have been widely studied and are generated "easily". This cannot be said for parageometric automorphisms. Or could it be ?! The aim of the presentation is to introduce these different notions and to give a partial answer to the final question.