Related papers: Modeling Fractal Structure of Systems of Cities Us…
Passenger flows in a traffic network reflect spatial interaction patterns in an urban systems. Gravity models can be employed to quantitatively describe and predict spatial flows. However, how to model passenger flows and reveal the deep…
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…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
Many approaches have dealt with the hypothesis that the environment contain information, mostly focusing on how humans decode information from the environment in visual perception, navigation, and spatial decision-making. A question yet to…
Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three…
As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time…
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
This paper endeavors to show how a fractal-based approach can offer an alternative to differential equations for describing rates of interaction in complex systems. The specific example given is for combat analysis. This concerns a scenario…
Entropy relates the fast, microscopic behaviour of the elements in a system to its slow, macroscopic state. We propose to use it to explain how, as complexity theory suggests, small scale decisions of individuals form cities. For this, we…
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…
Self-organisation in territories leads to the emergence of patterns in urban systems that shape the interactions between cities, resulting in a hierarchical organisation. Governance follows as well a hierarchical structure, breaking the…
This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical…
Quantifying the spatial organization of human settlements is fundamental to understanding the complexity of urban systems. However, the quantitative patterns of the distribution of villages, towns, and cities that lie between random and…
Fourier analysis and cross-correlation function are successfully applied to improving the conventional gravity model of interaction between cities by introducing a time variable to the attraction measures (e.g., city sizes). The traditional…
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…
We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion and coalescence of masses. We find that the spatial correlations…
The presented model provides an explanation to several empirically observed phenomena in spatial economics. By representing the system as a complex network of fixed-size land areas connected by trade between harbored activities, city size…
Urban-induced microclimate variations, such as urban heat islands and air pollution, scale with city size, producing distinctive relations between average climate variables and city-scale quantities (e.g., total population). However, these…