Social Simulation allows us to experiment in the social arena while avoiding unnecessary expenses and potential threats; a clear example of this is reflected in the simulation of urban growth, particularly if done without losing sight of the sustainable development necessary for maintaining the overall equilibrium of a city. This article provides a hybrid methodology using Distributed Agencies, cellular automaton, and dynamical systems to model the social processes of urban growth; raking in the most important data of the methodology through a corresponding method of data mining. Through the use of a qualitative and quantitative method we provide some important advancements in the field for the development of an appropriate understanding of social, economic and environmental aspects of urban growth.