Related papers: Fractal Texture and Structure of Central Place Sys…
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…
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…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
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…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
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.…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
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…
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show…
A standard scientific study comprises two processes: one is to describe a thing, and the other is to understand how the thing works. In order to understand the principle of urban growth, a number of shape indexes are proposed to describe…
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…
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…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
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 time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the growth rate formula and…