Search results for "Fractal analysis"
showing 10 items of 13 documents
From fractal urban pattern analysis to fractal urban planning concepts
2014
International audience; Fractal geometry can be used to develop a multiscale approach toinvestigate the spatial organization of urban fabrics. First, the concepts behindfractal reference models are introduced so as to provide a better understandingof the results obtained from empirical analyses of urban patterns. Then, differentmethods for conducting fractal analyses are presented and the results obtained forurban patterns are discussed. It turns out that, despite their irregular appearance,urban patterns are often organized by an inherent fractal order principle, at leastacross a certain range of scales. More detailed analysis of the findings reveals linksbetween these fractal properties a…
Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets
1998
Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension. Mutual relations between the three most popular fractal dimensions, namely: the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal …
Assessing forest landscape structure using geographic windows.
2001
Landscape structure, interpreted as indicator of functional processes, has become a main attribute of multiresource forest inventories, enhancing its value with respect to society needs. This approach implies effective use of earth observation techniques and geographic information systems to obtain a global view of the inventoried landscapes and to understand the ecological functions of large spatially-heterogeneous landscape mosaics. Landscape structure often reveal extremely complex patterns that can only be very roughly characterized by methods of Euclidean geometry. Conversely, fractals can be applied to adequately describe many of the irregular, fragmented patterns found in nature. In …
The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities
2015
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (g…
Diagnostic Performance of Muscle Echo Intensity and Fractal Dimension for the Detection of Frailty Phenotype
2021
To determine the relationship between muscle echo intensity (EI) and fractal dimension (FD), and the diagnostic performance of both ultrasound parameters for the identification of frailty phenotype. A retrospective interpretation of ultrasound scans from a previous cohort (November 2014–February 2015) was performed. The sample included healthy participants <60 years old, and participants ≥60 divided into robust, pre-frail, and frail groups according to Fried frailty criteria. A region of interest of the rectus femoris from the ultrasound scan was segmented, and histogram function was applied to obtain EI. For fractal analysis, images were processed using two-dimensional box-counting techniq…
Nanoscale Domain Structure in Relaxor PLZT x/65/35 Ceramics
2006
We present the experimental study of the geometry of the nanoscale domain structure in classical lead zirconate-titanate relaxor ceramics (Pb1 − x La x )(Zr0.65Ti0.35)O3 (PLZT) with La concentration from 5 to 10%. The analysis of the switching current data measured in rectangular pulses indicates the existence of random three-dimensional maze-type domain structure. High-resolution domain visualization performed using Piezoresponse Force Microscopy (PFM) reveals nanoscale domain patterns. The domain structures existing in PLZT ceramics after zero-field-cooling represent the nanoscale quasi-regular maze (“finger-print”). Statistical and fractal analysis of PFM images was performed for quantit…
Is there any scaling in the cluster distribution?
1994
We apply fractal analysis methods to investigate the scaling properties in the Abell and ACO catalogs of rich galaxy clusters. We also discuss different technical aspects of the method when applied to data sets with small number of points as the cluster catalogs. Results are compared with simulations based on the Zel'dovich approximation. We limit our analysis to scales less than 100 $\hm$. The cluster distribution show a scale invariant multifractal behavior in a limited scale range. For the Abell catalog this range is 15--60$\hm$, while for the ACO sample it extends to smaller scales. Despite this difference in the extension of the scale--range where scale--invariant clustering takes plac…
Analyse de la distribution spatiale des implantations humaines : apports et limites d’indicateurs multi-échelles et trans-échelles
2020
As human beings, it is easy for us to judge visually whether a distribution is dispersed or concentrated. However, the quantitative formalization of our impressions is problematic. It depends on the scales of the chosen analysis. This dependence of indicators on scales has changed. It is initially considered as a barrier to knowledge, it now reflects the multi-scale organisation of the distributions studied. The central objective of this thesis is to investigate the limits and contribution of multi-scale and trans-scale indicators to the study of the spatial distributions of human settlements.Spatial analysis aims at comparing spatial distributions to a uniform distribution. The way in whic…
Multiscale analyses and characterizations of surface topographies
2018
International audience; This work studies multiscale analyses and characterizations of surface topographies from the engineering and scientific literature with an emphasis on production engineering research and design. It highlights methods that provide strong correlations between topographies and performance or topographies and processes, and methods that can confidently discriminate topographies that were processed or that perform differently. These methods have commonalities in geometric characterizations at certain scales, which are observable with statistics and measurements. It also develops a semantic and theoretical framework and proposes a new system for organizing and designating …
Method of Discrimination of Surface Fractality
1993
Abstract A simple method for the discrimination of surface fractality is proposed. This method is based on the comparison of the nitrogen adsorption isotherm on a given sample with the "standard" isotherm on a smooth surface. The proposed comparative method makes it possible to determine the lower limit of the scale range of surface fractality. A thermodynamic method is recommended as a complement to fractal analysis in the scale range of about 10-1000 A. The results of the investigation of surface roughness are presented with examples of typical samples of silica gels, porous glasses, apatite, and coal.