Related papers: How the geometry of cities explains urban scaling …
Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
The emerging field of the Science of Cities has unveiled previously undiscovered facets of urban life. Contrary to the expectation of chaotic behaviour influenced solely by cultural and geographic factors, cities globally exhibit universal…
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…
The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…
The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map…
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…
Despite the rapid growth of cities in the past century, our quantitative, in-depth understanding of how cities grow remains limited due to a consistent lack of historical data. Thus, the scaling laws between a city's features and its…
The recent availability of data for cities has allowed scientists to exhibit scalings which present themselves in the form of a power-law dependence with population of various socio-economical and structural indicators. We propose here a…
A good understanding of cities is crucial to implement urban planning policies leading to social and economic sustainability and an efficient use of resources. While urban concentration has been associated with both positive and negative…
The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential…
Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal…
We study the connection between urban scaling, fundamental allometry (between city population and city area), and per capita vs.\ population density scaling. From simple analytical derivations we obtain the relation between the 3 involved…
Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using…
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model…
The law of allometric growth is one of basic rules for understanding urban evolution. The general form of this law is allometric scaling law. However, the deep meaning and underlying rationale of the scaling exponents remain to be brought…