相关论文: Fractal Scaling of Population Counts Over Time Spa…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
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…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
The study of human dynamics has attracted much interest from many fields recently. In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library…
We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated…