Search results for "Multifractal"

On the Multifractal Character of the Lorenz Attractor

1992

A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character

Des fractales pour des villes résilientes et économes

2019

National audience; L’étude des villes dans l’approche de la géographie théorique et quantitative est étroitement liée aux données disponibles pour les décrire : données de population (loi rang-taille, théorie évolutive des villes), données de cartographie des bâtiments (densités, analyses (multi)fractales, pour étudier de quelle manière les bâtiments remplissent l’espace), données de tracés des réseaux de transport. Depuis une dizaine d’années, des données détaillées de localisation d’activités, d’énergie, de transport, de climat, etc. complètent le spectre des applications.En mettant en avant l’articulation entre échelles L’approche fractale s’inscrit dans la logique d’un réductionnisme cl…

MULTIFRACTAL ELECTRONIC WAVE FUNCTIONS IN THE ANDERSON MODEL OF LOCALIZATION

1992

Investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints

2018

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce th…

On the multifractal analysis of measures

1992

La forme des villes françaises est-elle déterminée par les morphologies bâties et non bâties qui les environnent ? Éléments de réponse apportés par d…

2016

International audience; Des chercheurs en géographie ont montré, depuis les années 90, que les villes contemporaines partagent les caractéristiques morphologiques de certains objets fractals : les bordures urbaines sont très indentées à travers les échelles ; dans chaque ville, le nombre d’agrégats bâti et leur taille suivent une loi de puissance tandis que le nombre d’espaces non bâtis est relié à leur taille selon une autre loi de puissance (Batty & Longley, 1994 ; Frankhauser, 1994). Les dimensions fractales permettent de caractériser au moyen de mesures quantitatives les formes urbaines et ainsi de comparer aussi bien des villes entre elles que des quartiers d’une ville.Nous proposons i…

Multiscaling Properties of Large-Scale Structure in the Universe

1995

The large-scale distribution of galaxies and galaxy clusters in the universe can be described in the mathematical language of multifractal sets. A particularly significant aspect of this description is that it furnishes a natural explanation for the observed differences in clustering properties of objects of different density in terms of multiscaling, the generic consequence of the application of a local density threshold to a multifractal set. The multiscaling hypothesis suggests ways of improving upon the traditional statistical measures of clustering pattern (correlation functions) and exploring further the connection between clustering pattern and dynamics.

Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field

1992

In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.

Analysis of normal human retinal vascular network architecture using multifractal geometry

2017

AIM To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyse…

Reliability of fractal estimations on noisy patterns

2019

ECTQG 2019, European Colloquium of Theoretical and Quantitative Geography, Mondorf-les-Bains, LUXEMBOURG, 05-/09/2019 - 09/09/2019