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Fractal analysis

About: Fractal analysis is a(n) research topic. Over the lifetime, 6829 publication(s) have been published within this topic receiving 141205 citation(s).

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Book
Michael F. Barnsley1Institutions (1)
01 Jan 1988-
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.

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Abstract: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section. A bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images.

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4,276 citations


Book
01 Jan 1989-
Abstract: Foreword, B. Mandelbrot introduction fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces cluster-cluster aggregation (CCA) computer simulations experiments on Laplacian growth new developments.

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1,960 citations


Journal ArticleDOI
Alex Pentland1Institutions (1)
TL;DR: The3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable and this characterization is stable over transformations of scale and linear transforms of intensity.

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Abstract: This paper addresses the problems of 1) representing natural shapes such as mountains, trees, and clouds, and 2) computing their description from image data. To solve these problems, we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are a good choice for modeling 3-D natural surfaces because 1) many physical processes produce a fractal surface shape, 2) fractals are widely used as a graphics tool for generating natural-looking shapes, and 3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. The 3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable. Furthermore, this characterization is stable over transformations of scale and linear transforms of intensity. The 3-D fractal model has been successfully applied to the problems of 1) texture segmentation and classification, 2) estimation of 3-D shape information, and 3) distinguishing between perceptually ``smooth'' and perceptually ``textured'' surfaces in the scene.

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1,864 citations


Journal ArticleDOI
TL;DR: Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process, and similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease.

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Abstract: According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era.

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1,773 citations


Book
01 Aug 1988-
TL;DR: Fractal Modelling of Real World Images and a Unified Approach to Fractal Curves and Plants are studied.

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Abstract: Contents: Foreword: People and Events Behind the "Science of Fractal Images".- Fractals in Nature: From Characterization to Simulation.- Algorithms for Random Fractals.- Color Plates and Captions.- Fractal Patterns Arising in Chaotic Dynamical Systems.- Fantastic Deterministic Fractals.- Fractal Modelling of Real World Images.- Fractal Landscapes Without Creases and with Rivers.- An Eye for Fractals.- A Unified Approach to Fractal Curves and Plants.- Exploring the Mandelbrot Set.- Bibliography.- Index.

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1,732 citations


Network Information
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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20225
2021160
2020178
2019213
2018182
2017238

Top Attributes

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Topic's top 5 most impactful authors

Ajit Sadana

62 papers, 360 citations

Herbert F. Jelinek

30 papers, 1.1K citations

Odemir Martinez Bruno

21 papers, 481 citations

Nebojša T. Milošević

16 papers, 199 citations

Tak Cheung

9 papers, 14 citations