Dissipative structures known from non-equilibrium thermodynamics can form patterns. Cities are regarded as open, dissipative structures due to their self-organisation and thus in theory are also capable of pattern formation. In a first step to understand similarities between nonlinear pattern formation and inter-urban systems, we investigate how inter-urban structures are arranged. We use data from the Global Urban Footprint to identify spatial regularities in seven regions (Argentina, China, Egypt, France, India, Ghana and USA) and to quantitatively describe settlement patterns by number of objects and density. We find that small areas of the examined data sets show a regular arrangement, the density and number of settlements differ widely between the different regions and the portion of regular areas within this regions strongly correlates with these two parameters. The results can be used to develop mathematical models that describe inter-urban pattern formation on the one hand and to investigate to what extent the respective settlement patterns are related to infrastructural, economic or political boundary conditions on the other.

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