Central place systems have been demonstrated to possess self-similarity in both the theoretical and empirical perspectives. A central place model can be treated as a monofractal with a single scaling process. However, a real system of human settlements is a complex network with multi-scaling...

<i>Urban form takes on properties similar to random growing fractals and can be described in terms of fractal geometry. However, a model of simple fractals is not effectual enough to characterize</i> <i>both the global and local features of urban patterns. In this paper</i> multifractal measurements are...

Zipf’s law can be used to describe the rank-size distribution of cities in a region. It has seldom been employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf’s law and can be characterized with the rank-size...

NaP zeolite was synthesized via ultrasonic-assisted hydrothermal synthesis. The methods for Cu or Fe doping were screened while exploring element distributions in liquid and solid phases. Oxidation process of methylene blue (MB) and methyl violet-6B (MV-6B) by doped NaP zeolites was surveyed....

The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical...

This paper contributes to the demonstration that the self-similar city hierarchies with cascade structure can be modeled with a pair of scaling laws reflecting the recursive process of urban systems. First we transform the Beckmann's model on city hierarchies and generalize Davis's 2^<i>n</i>-rule to an...

The rank-size regularity known as Zipf’s law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely...

Using fractal theory and urban land-use maps for 1949, 1959, 1980, and 1996, this study is devoted to analyzing the evolutionary features of urban form and land-use structure in Hangzhou, China. We find that self-similarity exists in both the built-up area and the municipal area, and fractal...