For a class of symbolic dynamical systems we give some geometrical models as dynamical systems defined on geodesic laminations on the hyperbolic disc. The symbolic systems studied here come from a family of minimal sequences on a $3$-symbol alphabet with complexity $2n+1$, which satisfy a special combinatorial property. These sequences were originally defined by P. Arnoux and G. Rauzy as a generalization of the binary sturmian sequences. We show some applications of these results to Rauzy fractals.