An Algebra for Modeling and Simulation of Continuous Spatial Changes

Continuous change models are commonly based on the Systems Dynamics paradigm. However, this paradigm does not provide support for an explicit and heterogeneous representation of geographic space, nor its topological (neighborhood) structure. Therefore, using it in modeling spatial changes still remains a challenge. In this context, this paper presents an algebra that extends the Systems Dynamics paradigm to the development of spatially explicit models of continuous change. The proposed algebra provides types and operators to represent flows of energy and matter between heterogeneous regions of geographic space. To this end, algebraic sets of operations similar to those in Map Algebras are introduced, allowing the representation of local, focal and zonal flows. Finally, case studies are presented to evaluate the usefulness, expressiveness and computational efficiency of the proposed algebra.