Related papers: Describing urban evolution with the fractal parame…
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…
The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric…
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…
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…
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 gravity model is one of important models of social physics and human geography, but several basic theoretical and methodological problems remain to be solved. In particular, it is hard to explain and evaluate the distance exponent using…
The concept of allometric growth is based on scaling relations, and it has been applied to urban and regional analysis for a long time. However, most allometric analyses were devoted to the single proportional relation between two elements…
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…
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…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
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…
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 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…
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…
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…
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 growth curves of fractal dimension of urban form take on squashing effect and can be described by sigmoid functions. The fractal dimension growth of urban form in western countries can be modeled by Boltzmann's equation and logistic…
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 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…
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…