An Anosov family is a sequence of diffeomorphisms along compact manifolds such that the tangent bundles split into expanding and contracting subspaces, thus generalizing an Anosov map of a manifold. The main examples are the {\em multiplicative } families, related to the multiplicative continued fraction expansion. Geometrically, the multiplicative families imbed in a flow on a torus fiber bundle over the unit tangent bundle of the Teichm\"uller space of the torus, extending the classical modular flow. Equivalently, this flow (the scenery flow) describes the process of zooming toward the renormalization small-scale structure of irrational circle rotations. The scenery flow has as a cross-section a random dynamical system (i.e. a skew product transformation) constructed from the additive generators; by the above result, it codes as a random shift of finite type built from exactly the same matrices.