Our reflections and the numerous works concerning the city, its planning and its transformations, showed all its complexity. The overall process of spatial development of the city system results from the interaction of social, political and economic factors, some being activators of its development and others inhibitors. In front of such a complexity and such a profusion of factors, it is difficult to produce a rigorous explanatory theory. Hence, in a parsimony perspective, we make the central hypothesis, that comes true rather widely through the simulations, that the great majority of the factors which pilot urban development are linked to processes that have spatial designs which reveal them. More exactly, urban processes (as sub urbanization, large housing estates construction, business park development, etc,) are appearing from specific spatial configurations but are also producing characteristic spatial patterns. Rather than producing a fine spatial analysis which tries to isolate the contributory factors, that is almost impossible because of their intricacy, we adopted a constructive approach by developing SpaCelle. This cellular automata platform obliges the modeller to a certain conceptual parsimony. It was developed on urban growth issues; nevertheless, it remains very general and can be used in other research fields concerned by spatial dynamics. SpaCelle is based on a classical cellular automata paradigm which means that each cell is only reactive. Indeed, contrarily to a more general agent based model, at each iteration a cell cannot do anything other than change its internal state from its previous state and that of its neighbours. Therefore, no flow can be modelled. This means that we can't modelize interactions since it requires a simultaneous exchange between two or more cells. In addition, the use of the platform requires no computer skills: a one click installation, graphical interface, no algorithmic programming. The dynamic model is defined by a list (unordered) of transition rules close to the natural language which permits to test explicit hypotheses of evolution of land use. The user must first build an initial spatial configuration by importing the different layers containing geographical data (grid for the land use or the topography, vector layer for networks, etc.). Then he has to build the base of knowledge of the cellular automata which defines the different states in each cellular layer and the dynamics of the model using two kind of transition rules: environmental rules and life rules. These rules reflect the spatial aspects of processes in action. They are at every moment and in every place in competition with each other. It can thus handle the complexity of influences and constraints, often antagonistic that are overlapping in space. An important feature of this type of modelling comes from the verbal aspect of the formulation of the dynamic model, which provides by construction, an explanatory aspect by induction. Indeed most of the urban growth models are based either on deterministic dynamics that adjusts series of evolution curves or action curves according to the distance (as a potential), or on stochastic laws as Markov chains, methods that are not directly explanatory. The cellular automata SpaCelle helped to enlarge and further improve our reflection on the city construction. The modelisation was applied to the Rouen area. The reflection was carried out from two directions. The first, based on a retro-simulation approach, led to a model that improved the general understanding of urban dynamics during the second half of the twentieth century. We identified some ten processes, more or less old, that have animated urban spaces since the Second World War. It was validated using different methods. The second, based on a prospective approach, aims at assist management of urban areas. It compares the simulations of different scenarios proposed by policy makers and local planners for 2025. Prospective scenarios were realized using the retrosimulation model, on which alternatives scenarios were constructed. The results of these scenarios were discussed with city planners who could appreciate visually some possible effects of the different political orientations. Finally, the platform SpaCelle is not limited to the urban growth issues; it permits to simulate a wide variety of situations from the game of life to the spatial spread of epidemics, through ecological or climatic models.
