Related papers: A Scaling Approach to Evaluating the Distance Expo…
The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be explained with the ideas from…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
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…
The attraction measure, scaling exponent, and impedance function of the gravity model are redefined using the concepts from fractals and spatial complexity. Firstly, the attraction measure of spatial interaction in human systems is defined…
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…
A pair of fractal gravity models can be derived from the spatial interaction models based on entropy maximizing principle and allometric scaling law. The models can be expressed as dual form in mathematics and are important for analyzing…
The area-perimeter allometric scaling is a basic and important approach for researching fractal cities and has been studied for a long time. However, the boundary dimension of a city is always numerically overestimated by the traditional…
Entropy is one of physical bases for fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using fractal dimension, we can describe urban growth and form and characterize spatial complexity. A…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e.\ a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of city-like…
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…
The conventional concept of geographical space is mainly referred to actual space based on landscape, maps, and remote sensing images. However, this notion of space is not enough to interpret different types of fractal dimension of cities.…
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…
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,…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
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…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
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…