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The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical…
We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization…
Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a…
Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D,…
The dynamics of city's spatial structures are determined by the coupling of functional components (such as restaurants and shops) and human beings within the city. Yet, there still lacks mechanism models to quantify the spatial distribution…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number…
A good understanding of cities is crucial to implement urban planning policies leading to social and economic sustainability and an efficient use of resources. While urban concentration has been associated with both positive and negative…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
Urban systems are primarily relational. The uneven intensities and distribution of flows between systems of cities results in hierarchically organised complex networks of urban exchange. Distinct urban spatial structures reflect the…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
The spatial distribution of population and activities within urban areas, or urban form at the mesoscopic scale, is the outcome of multiple antagonist processes. We propose in this paper to benchmark different models of urban morphogenesis,…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…