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

Entropy of the Land Parcel Mosaic as a Measure of the Degree of Urbanization

Quantifying the urbanization level is an essential yet challenging task in urban studies because of the high complexity of this phenomenon. The urbanization degree has been estimated using a variety of social, economic, and spatial measures. Among the spatial characteristics, the Shannon entropy of the landscape pattern has recently been intensively explored as one of the most effective urbanization indexes. Here, we introduce a new measure of the spatial entropy of land that characterizes its parcel mosaic, the structure resulting from the division of land into cadastral parcels. We calculate the entropies of the parcel areas’ distribution function in different portions of the urban systems. We have established that the Shannon and Renyi entropies R0 and R1/2 are most effective at differentiating the degree of a spatial organization of the land. Our studies are based on 30 urban systems located in the USA, Australia, and Poland, and three desert areas from Australia. In all the cities, the entropies behave the same as functions of the distance from the center. They attain the lowest values in the city core and reach substantially higher values in suburban areas. Thus, the parcel mosaic entropies provide a spatial characterization of land to measure its urbanization level effectively.

Extracting Backbone Structure of a Road Network from Raw Data

The representation of roads as a networked system of nodes and edges has attracted significant interest in the network literature, generating a large number of studies over the years. Such representation requires a proper identification of what constitute an edge or a node. Intuitively, nodes represent the junctions where roads intersect, and edges are the road segments connecting these junctions. In practice, however, such simplified presentation is not trivial to achieve due to extra details of individual roads. In this paper, we present a set of novel and efficient computational techniques based on elementary geometry and graph theory that can be employed to obtain the essential structure of a road network, while also retaining the crucial geometry of roads, such as shape and length. This is done by dissecting the network into clusters of nodes of degree other than 2 and curves, which contain consecutive nodes of degree 2, connecting these clusters. These clusters of nodes and curves will be collapsed into cleaned nodes and paths, respectively in a simplified mathematical graph. We apply this method to obtain the simplification of road network in Punggol new town in the northeast region of Singapore, and show that application of network analyses such as centrality measures could be performed in a more meaningful and concise manner than on the original road network.