Related papers: Multifractal portrayal of the Swiss population
Multifractality is one of the patterns observed in spatial distributions of populations. In this study, we performed multifractal analysis for populations by age group in the capital area of Japan. Each population group generally exhibited…
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
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…
Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension…
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…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
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…
Different techniques were developed to extract urban agglomerations from a big dataset. The urban agglomerations are used to understand the structure and growth of cities. However, the major challenge is to extract urban agglomerations from…
The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
Central place systems have been demonstrated to possess self-similar patterns in both the theoretical and empirical perspectives. A central place fractal can be treated as a monofractal with a single scaling process. However, in the real…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…