Related papers: Fractal dimension evolution and spatial replacemen…
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…
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…
City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature…
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
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…
Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic…
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…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth,…
We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…
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…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…
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…