Spatial point pattern and urban morphology: Perspectives from entropy, complexity, and networks.

Spatial organization of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterize the spatial pattern of urban locations based on the idea of entropy maximization is proposed. Three spatial length scales in the system with discerning interpretations in terms of the spatial arrangement of the locations are calculated. Using these length scales, two quantities are introduced to quantify the system's spatial pattern, namely, mass decoherence and space decoherence, whose combination enables the comparison of different cities in the world. The comparison reveals different types of urban morphology that could be attributed to the cities' geographical background and development status.