The Hitchin component is a preferred component of the space of homomorphisms from a surface group to PSL_n(R). I will describe a parametrization of this component that is well-adapted to a general geodesic lamination on the surface. This can be used to provide a very explicit description of the action on the Hitchin component of a pseudo-Anosov homeomorphism of the surface. This is joint work with Guillaume Dreyer.