Related papers: Cities and space: Common power laws and spatial fr…
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of…
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size…
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 law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in…
We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents…
This paper focuses on the challenge of interactively modeling street networks. In this work, we extend the simple fractal model, which is particularly useful for describing small cities or individual districts, by constructing random cities…
How does transport cost affect the spatial organization of economic activities? This study develops a theoretical framework that distinguishes between two types of dispersion forces in spatial models: "local" dispersion forces acting within…
The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical…
This study develops a statistical model that integrates economic agglomeration theory and power-law distributions of city sizes to project future population distribution on 1-km grid cells. We focus on Japan -- a country at the forefront of…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Galaxy structures are certainly fractal up to a certain crossover scale \lambda_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures…
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…
In this article, the relationship between two well-accepted empirical propositions regarding the distribution of population in cities, namely, Gibrat's law and Zipf's law, are rigorously examined using the Chinese census data. Our findings…
Urban development is shaped by historical, geographical, and economic factors, presenting challenges for planners in understanding urban form. This study models commute flows across multiple U.S. cities, uncovering consistent patterns in…
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be…
There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized,…
Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained…
Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the…
Driven by access to large volumes of movement data, the study of human mobility has grown rapidly over the past decades. The field has shown that human mobility is scale-free, proposed models to generate scale-free moving distance…