In this paper the modelling formalism of cellular automata (CA) is generalized and extended within Geo-Algebra, a mathematical generalization of map algebra capable of expressing a variety of dynamic spatial models and spatial data manipulations within a common framework. Map dynamics, that is, the integration of the spatial dynamics reflected in CA and the spatial data handling capabilities of map algebra, constitutes a critical element within a wider project which sets out to formulate a general framework for simultaneously supporting spatial database manipulations and static and dynamic modelling within GIS. Map dynamics can also allow the modelling of additional dynamic behaviours and phenomena such as adaptation, design, learning and gaming not currently expressible as GIS models.