We present a graph-theoretic model for dynamical systems given by a homeomorphism f on the Cantor set X. This construction gives a bijective correspondence between such dynamical systems (X,f) and a subclass of two-colored Bratteli separated graphs. We use this construction in order to write any dynamical system of our interest as an inverse limit of a sequence of (what we call) generalized finite shifts. This enables us to compute the associated Steinberg algebra (resp. C*-algebra) of the dynamical systems as colimits of the graph algebras (resp. graph C*-algebras) associated with the different levels of the corresponding separated graph. In subsequent work we plan to apply this theory to relate the type semigroup of the dynamical system with the graph monoid of the corresponding separated graph, and with the non-stable K-theory of the Steinberg algebra. This is joint work with Pere Ara (Universitat Autònoma de Barcelona).