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Showing 1 to 20 of 68 for “"Fractals."”.
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Dimensions of Self-Similar Fractals
… and Hausdorff dimensions of self-similar fractals that are the invariant sets of iterated function systems. We start with the Contraction Mapping Theorem, which will give us a constructive method in which to find fractals using iterated function systems. We then define the Hausdorff metric …
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Fractals in mechanics of materials
… is introduced to reflect the mass scaling on fractals. We propose a product measure consistent with generally anisotropic fractals and also simplify previous formulations from decoupling of coordinate variables. Two continuum models are developed – the classical continuum and the micropolar …
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Applications of fractals to image data compression
… with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity …
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Fractals in elastic-plastic transitions of random heterogeneous materials
… characteristics, very little work was done on fractals in elasto-plasticity, and so this study is one of the first attempts in that direction. Fractal patterns have been found to form in 2D aggregates of grains of either elastic-perfectly plastic type, or elastic-hardening-plastic type, or …
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Data comparison schemes for Pattern Recognition in Digital Images using Fractals
Pattern recognition in digital images is a common problem with application in remote sensing, electron microscopy, medical imaging, seismic imaging and astrophysics for example. Although this subject has been researched for over twenty years there is still no general solution which can be compared …
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FRACTALS IN PUPILLARY OSCILLATION PATTERNS: FROM GRAY IMAGES TO JACKSON POLLOCK PAINTINGS
… Kiselev, Hahn, & Auer, 2003; Mandelbrot, 1982). Fractals are structures which are self-similar at varying magnification and can be either statistical (meaning they are not identical when magnification varies but are self-similar by some statistical measure) or mathematical (the structure remains …
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Dynamics of frustrated magnetic systems – Emergent fractals and anomalous magnetic noise in spin ice
… It is by hosting the monopole motion that the fractals bequeath the magnetic noise with an anomalous exponent and cause a slow-down of the relaxation. The spatial properties of the fractals thus manifest themselves in the time dependence of the magnetisation – and the anomalous dynamics …
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First Order Differential Operators and Equations of Continuity and Transport-Type on metric Graphs and Fractals
… study continuity and transport-type equations on fractals as well as related first order differential operators of gradient and divergence-type with an additional modulation by a divergence-free minimal energy-dominant differential one-form. A key tool is a new integration by parts formula which …
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Convergence of Gibbs measures and the behavior of shrinking tubular neighborhoods of fractals and algebraic sets
… measure equally distributed along self-similar fractals with Hutchinson's Open Set Condition. In Chapter 3 we study spaces of concentric circles (which we call targets) in the plane, and examine how the sequence of probability measures distributes over the targets. By varying the number of …
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Distributed intelligent systems for a swarm of robots
… a distributed robotic swarm formation using fractals. Fractals have the properties of self-similarity, allowing for an equal distribution of the robots, and recursiveness, allowing for a gradual expansion of a swarm formation. Utilising the properties of fractals allow for a robotic swarm to …
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Dynamics of Iterated Functions Systems: Hausdorff Dimension and Related Topics
… formula to compute the Hausdorff dimension of fractals generated by a finite family of disjoint similar IFS, where by disjoint we mean the IFS satisfies the open set condition. In the first part of this thesis, we extend Hutchinson's formula by removing the open set condition. We introduce a …
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Characterization of functionally graded materials through fractal geometry
… and characteristics of the FGM in terms of fractals. There has been no prior literature on linking FGM and fractals. We characterize the interfaces between the two- phase FGM using fractals and estimate an interfacial fractal dimension for varying degrees of coarseness. Also, the variation …
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Microscopic Chaos, Fractals, and Transport in Nonequilibrium Steady States. - (Die Veröffentlichung einer ergänzten und überarbeiteten Version bei "World Scientific Publishing" ist für 2005/06 geplant.)
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this thesis we summarize recent theoretical advances along these lines. We focus on two different approaches to nonequilibrium …
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Dimensions in Random Constructions.
We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that …
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Dynamical statistics for power series and polynomials with restricted coefficients
… In the first part, we consider a family of fractals arising as limit sets of pairs of similitudes; these fractals are closely related to power series with all coefficients equal to ±1. Motivated by the Julia–Mandelbrot correspondence, we construct a natural measure in the parameter space …
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F-TRIDYN: A Monte-Carlo, BCA code for modeling ion-surface interactions with rough materials and coupling plasma and material codes
… be consistently and realistically modeled with fractals, using the fractal dimension and fractal length scale as the sole input parameters to control surface morphology and roughness. F-TRIDYN includes a robust fractal surface algorithm that is more computationally efficient than those in …
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Estimating the Hausdorff dimension
The use of fractals in fields such as molecular biology, epidemiology, landscape, ecology, geology, physics, etc., is becoming more common. In order to use fractals to model many phenomena, the researcher requires the knowledge of the fractal, or Hausdorff-Besicovitch, dimension. However, no …
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Multifractal Complexity of Hippocampal Memory Processing
… within ensembles of hippocampal neurons. Fractals, omnipresent in biological and physical systems, often manifest when systems are iterative or reverberatory, and consequently are detectable in spike trains of hippocampal neurons. This dissertation focuses on strengthening the association …
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African river basins : their present geometry and recent past as a framework for their evolution
Fractals and scaling laws abound in nature, and it is said that geometry of river networks and basins is an epitome of this. This study investigates how on the tectonically unique African continent, scaling parameters, and in particular deviations from 'perfect fractal patterns' relate to …
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