The Schelling segregation models are “agent based” population models, where individual members of the population (agents) interact directly with other agents and move in space and time. In this note we study one-dimensional Schelling population models as finite dynamical systems. We define a natural notion of entropy which measures the complexity of the family of these dynamical systems. The entropy counts the asymptotic growth rate of the number of limit states. We find formulas and deduce precise asymptotics for the number of limit states, which enable us to explicitly compute the entropy. ∗Supported by the SFB-grant F1305 and the grant P16613-N12 of the Austrian FWF. †This work was partially supported by NSF grants DMS-0355180 and INT-0104675 ‡Supported by the SFB-grant F1301 of the Austrian FWF.