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How complexity emerges in urban systems: Theory of urban morphology.

Human beings develop the land and transform land use patterns, constructing artificial structures. Among them, the city is a representative system and its morphology has attracted much attention. While most existing studies have been devoted to individual dynamics and focused on the proximity of specific areas of a city, we here pay attention to the city as a complex system, where interactions between individuals give rise to emergent properties. Specifically, analyzing the big data on every building in Seoul City, we specify the relevant interactions among constituents and probe the emergence of complex land use patterns. In particular, based on the empirical observations, we illustrate that interactions between land uses are frustrated, which serves as a basic postulate of the theory of urban morphology. We examine this conjecture with the help of a layered Ising-type model and disclose that the actual land use pattern emerges at the criticality of the system in the presence of heterogeneously distributed fields. It is also remarked that our model, allowing quantitative predictions, can easily be applied to other cities around the world.