Evolution and entropy in the organization of urban street patterns

Abstract

The street patterns of cities are the result of long-term evolution and interaction between various internal, social and economic, and external, environmental and landscape, processes and factors. In this article, we use entropy as a measure of dispersion to study the effects of landscapes on the evolution and associated street patterns of two cities: Dundee in Eastern Scotland and Khorramabad in Western Iran, cities which have strong similarities in terms of the size of their street systems and populations but considerable differences in terms of their evolution within the landscape. Landscape features have strong effects on the city shape and street patterns of Dundee, which is primarily a shoreline city, while Khorramabad is primarily located within mountainous and valley terrain. We show how cumulative distributions of street lengths when graphed as log–log plots show abrupt changes in their straight-line slopes at lengths of about 120 m, indicating a change in street functionality across scale: streets shorter than 120 m are primarily local streets, whereas longer streets are mainly collectors and arterials. The entropy of a street-length population varies positively over its average length and length range which is the difference between the longest and the shortest streets in a population. Similarly, the entropies of the power law tails of the street populations of both cities have increased during their growth, indicating that the distribution of street lengths has gradually become more dispersed as these cities have expanded.