Spatial Analysis of Settlement Structures to Identify Pattern Formation Mechanisms in Inter-Urban Systems

Abstract

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.

Towards the Identification of Simple Mechanisms Describing the Development of Settlements

“…The economically successful settlers are able to suppress weaker actors and even take over their property, leading to a regular distribution of equally sized ranches in A. Apart from theory, all three arrangement of settlements can be found in distributions of settlements in agriculturally dominated regions [10][11][12][13], suggesting that settlements could follow certain mechanisms, be they attractive, random or repulsive processes. An particularly interesting feature of these regions is the existence of regularities in settlement distributions.…”

Spatio-Temporal Interurban Regularities in the Global South

“…For the investigation four different regions of the Global South, partly intersecting with regions analyzed by [16], are chosen. Those agriculturally dominated regions are placed in India, Egypt, Nigeria and Argentina (See Figure 2, for coordinates see Table A1).…”

“…area or population This can be executed by abstracting objects to their mass center position and assigning the size of the object to its mass center. In case of built-up structures this procedure is straightforward as geometrical mass centers can be determined trivially [16]. In contrast, the determination for population density objects can not be done in the same manner as for concentrations density centers have to be considered that they do not correspond to geometrically determined mass centers.…”

“…With the now prepared point patterns, we can determine what point processes are dominant in empirical structures. In the field of urban studies such investigations commonly utilize the Average Nearest Neighbor (ANN) index by [30] which is able to quantitatively describe the regularity of a point pattern [16,31,32]. A major drawback of the ANN is its dependency on the chosen excerpt size.…”

“…At this point we can exploit a recurrently identifiable feature in urban mechanisms that is regularity. Regularity can be found in various spatial and temporal processes, just to mention congestion [14], travel [15] or settlement distribution patterns [16]. Furthermore, regularity is a core property and starting point in a variety of urban models based on cellular automates [17], agent based models [18] or pattern formation mechanisms [19].…”