This chapter aims to frame the complexity of spatial interactions using the structure of space; imagined as a network of spatial channels built up by interacting flows. The first assumption is that space is a productive system represented by flows that justify, build up and maintain the channels, the same way as income justifies, constructs and preserves capital. The second assumption is that either there is (self-adapting) evolution of the territory that maximizes the size of channels, like a city that puts most of its income in urban infrastructure, or there is human rationality that optimizes the size of the channels to maximize human interaction flows. Using an entropy function, we can explain the relation between channel sizes and the flows that move along them. On the other hand, we use the integral of the entropy function to explain how the size of channels are built-up through the accumulated flows they generate. Finally, entropy functions that explain flows and channels are opened up to include distance constraints and external impacts. The demonstration of these conceptual and operational models of complex spatial systems comes in the last part of the chapter: first, with the calibration of a model that explains the spread of infectious diseases to exemplify the organic maximization of infection channels; and second, with the estimation of a regional economic model that maximizes flows subject to the spatial structure of channels, confined by policy measures.
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