This work presents the mathematical foundations of theNested Cellular Automata(nested-CA) model, a model of computation for multiple scaleLand Use and LandCover Changestudies. The main properties of neste-CA model are describedandcompared to the agent-based and cellular automata models of computation. Th nested-CA model has been implemented in a software environment, calledTerraME(TerraModeling Environment), which provides a high level modeling language for modeldescription, a set of spatiotemporal data structures for model representation andsimulation, a module for spatiotemporal data management and analysis integrated to ageographic information system, and a set of functions for model calibration andvalidation. We describe the main design choices involved in the developmentof theTerraMEmodeling environment. Its architecture is detailed and the main properties arecompared with other modeling tools:Swarm,STELLA, andGEONAMICA. Finally, theconcept ofnested-CAand theTerraMEarchitecture are demonstrated in twoapplications of land cover change in the Brazilian Amazon.

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