Multifractal analysis of the street network and population: 15 largest brazilian cities

Abstract

By 2050, the world’s population is expected to reach 9.8 billion people. This will result in significant challenges related to housing, infrastructure, basic services, food security, health, education, employment, safety and natural resources at all urban levels. Faced with this alarming scenario, there is an urgent need to understand how cities work. This knowledge can greatly assist public agents in making decisions. However, the literature widely recognizes that cities are complex systems with many interacting components. How can we bridge the gap between decision-making and the complexity of cities? To address this question, we examined Brazil’s 15 largest cities in 2010 using fractal geometry, urban scaling and network science. We sought to demonstrate that both the street network and the population show multifractal patterns, indicating the existence of a non-linear dynamic governing the behavior of these patterns, which we suspect is closely related to their multifractal spectra. We believe that the shape of these spectra is closely linked to the geography and natural elements that make up the city. Furthermore, this study suggests that some urban laws of scale can be described in terms of endogenous variables such as population, area and fractal dimension by maximizing Shannon entropy, which is used to obtain the probability of interaction between two regions of the city. In addition, the generalized dimensions of the city can be considered to extend the scaling laws that take into account the notion of fractal dimension, in order to investigate which region or regions contribute most to the prediction of gross domestic product (GDP) and total street length. In addition, we sought to demonstrate that models which take endogenous factors into account to explain the economy and returns to scale can be simplified us- ing only macroscopic quantities such as population, total street length and urban area. This simplification was applied to the set of 5523 Brazilian cities. Finally, the data indi- cates that the fractal dimensions of the nodes, links and cyclomatic number of the street networks analyzed are equal to the fractal dimension of Bonacich’s centrality measure. Furthermore, the relationship between the topological quantities of this type of network remains constant, regardless of its size. In addition, there must be a close relationship be- tween decision-makers and the knowledge generated. Therefore, we believe that in order to promote quality of life in urban environments, it is important to understand how cities work. This can be achieved through the use of computational tools and a theoretical basis derived from various complex systems topics.