Related papers: Dynamical Fractal: Theory and Case Study
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
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…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…
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…
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 central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies.…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…
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 things surrounding us vary dramatically, which implies that there are far more small things than large ones, e.g., far more small cities than large ones in the world. This dramatic variation is often referred to as fractal or scaling.…
The famous Laplace's Demon is not only of strict physical determinism, but also related to the power of differential equations. When deterministically extended structures are taken into consideration, it is admissible that fractals are…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
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…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
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…
The emerging field of the Science of Cities has unveiled previously undiscovered facets of urban life. Contrary to the expectation of chaotic behaviour influenced solely by cultural and geographic factors, cities globally exhibit universal…