The Bratteli diagram is an infinite graph which reflects the structure of projections in an AF-algebra. We prove that every strictly ergodic unimodular Bratteli diagram of rank 2 g+ m−1 gives rise to a minimal geodesic lamination with the m principal regions on a hyperbolic surface of genus g≥1. The proof is based on a Morse theory of the recurrent geodesics on the hyperbolic surfaces.