Search results for "FRACTAL"
showing 10 items of 329 documents
Encriptación óptica empleando llaves Weierstrass-Mandelbrot
2013
[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to enc…
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…
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…
Adding Synthetic Detail to Natural Terrain Using a Wavelet Approach
2002
Terrain representation is a basic topic in the field of interactive graphics. The amount of data required for good quality terrain representation offers an important challenge to developers of such systems. For users of these applications the accuracy of geographical data is less important than their natural visual appearance. This makes it possible to mantain a limited geographical data base for the system and to extend it generating synthetic data.In this paper we combine fractal and wavelet theories to provide extra data which keeps the natural essence of actual information available. The new levels of detail(LOD) for the terrain are obtained applying an inverse Wavelet Transform (WT) to…
Mixed-aspect fractal surfaces
2013
In order to provide accurate tools to model original surfaces in a Computer Aided Geometric Design context, we develop a formalism based on iterated function systems. This model enables us to represent both smooth and fractal free-form curves and surfaces. But, because of the self-similarity property underlying the iterated function systems, curves and surfaces can only have homogeneous roughness. The aim of our work was to elaborate a method to build parametric shapes (curves, surfaces, ...) with a non-uniform local aspect: every point is assigned a ''geometric texture'' that evolves continuously from a smooth to a rough aspect. The principle is to blend shapes with uniform aspects to defi…
Structural Study of Star Polyelectrolytes and Their Porous Multilayer Assembly in Solution
2015
Star polyelectrolytes with responsive properties to external stimuli, such as pH, temperature and ionic condition, were utilized to fabricate layer-by-layer (LbL) microcapsules . The microstructure of star polyelectrolytes was first studied in semi-dilute solution by in situ small-angle neutron scattering (SANS). These measurements show that with the addition of salts, arms of strong cationic star polyelectrolytes will contract and the spatial ordering of the stars would be interrupted. SANS measurements were also performed on the microcapsules in order to study their internal structure and responsive properties in solution. The results show that with the increase of shell thickness, microc…
SPATIAL MULTIFRACTALITY OF ELECTRONIC STATES AND THE METAL-INSULATOR TRANSITION IN DISORDERED SYSTEMS
1993
For the investigation of the spatial behavior of electronic wave functions in disordered systems, we employ the Anderson model of localization. The eigenstates of the corresponding Hamiltonian are calculated numerically by means of the Lanczos algorithm and are analyzed with respect to their spatial multifractal properties. We find that the wave functions show spatial multifractality for all parameter cases not too far away from the metal-insulator transition (MIT) which separates localized from extended states in this model. Exactly at the MIT, multifractality is expected to exist on all length scales larger than the lattice spacing. It is found that the corresponding singularity spectrum…
Fractional calculus in solid mechanics: local versus non-local approach
2009
Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
Classification of cat ganglion retinal cells and implications for shape-function relationship
2002
This article presents a quantitative approach to ganglion cell classification by considering combinations of several geometrical features including fractal dimension, symmetry, diameter, eccentricity and convex hull. Special attention is given to moment and symmetry-based features. Several combinations of such features are fed to two clustering methods (Ward's hierarchical scheme and K-Means) and the respectively obtained classifications are compared. The results indicate the superiority of some features, also suggesting possible biological implications.