We present a geometric approach to groups defined by transducers via the notion of enriched dual. We prove that the boundary dynamics $Q^{\omega}$ of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to have a finite Schreier graph in the boundary of the enriched dual pointed at some essentially non-trivial point, i.e., a point which ``represents'' elements on the Gromov boundary $\widehat{F_{Q}}$ of the free group $F_{Q}$. With this approach we address the problem of finding examples of non-bireversible transducers defining free groups. We show examples of transducers with sink accessible from every state which generate free groups and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties. Finally, we address the problem of finding examples of transducers which define groups whose dynamics in the boundary is essentially non-free without critical points. We show connections with this problem and the problem of tiling the plane with aperiodic Wang's tiles. (This is a joint work with D. D'Angeli).