Search Results for "introducing-fractal-geometry"

Introducing Fractal Geometry

Introducing Fractal Geometry

  • Author: Nigel Lesmoir-Gordon,Will Rood
  • Publisher: Totem Books
  • ISBN: 9781840461237
  • Category: Study Aids
  • Page: 174
  • View: 2373
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Fractal geometry is the geometry of the natural world and is an extension of classical geometry.

Introducing Fractals

Introducing Fractals

A Graphic Guide

  • Author: Nigel Lesmoir-Gordon,Will Rood
  • Publisher: Icon Books Ltd
  • ISBN: 1848317832
  • Category: Mathematics
  • Page: 176
  • View: 3178
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From Zeno to Mandelbrot: explore this new language with which you can describe the shape of cloud as precisely as an architect can describe a house.

Fractal Geometry

Fractal Geometry

Mathematical Foundations and Applications

  • Author: Kenneth Falconer
  • Publisher: John Wiley & Sons
  • ISBN: 111876286X
  • Category: Mathematics
  • Page: 400
  • View: 9280
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The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Fractal Geometry and Applications: Analysis, number theory, and dynamical systems

Fractal Geometry and Applications: Analysis, number theory, and dynamical systems

  • Author: Benoit B. Mandelbrot
  • Publisher: American Mathematical Soc.
  • ISBN: 0821836374
  • Category: Ergodic theory
  • Page: 517
  • View: 2185
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This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Fractals: A Very Short Introduction

Fractals: A Very Short Introduction

  • Author: K. J. Falconer
  • Publisher: Oxford University Press
  • ISBN: 0199675988
  • Category: Mathematics
  • Page: 132
  • View: 3491
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An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original.

Fractal Geometry in Biological Systems

Fractal Geometry in Biological Systems

An Analytical Approach

  • Author: Philip M. Iannaccone,Mustafa Khokha
  • Publisher: CRC Press
  • ISBN: 9780849376368
  • Category: Science
  • Page: 384
  • View: 7826
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Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.

Fractal Geometry and Stochastics Two

Fractal Geometry and Stochastics Two

  • Author: Christoph Bandt,Siegfried Graf
  • Publisher: Springer Science & Business Media
  • ISBN: 9783764362157
  • Category: Mathematics
  • Page: 292
  • View: 2252
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The combination of fractal geometry and stochastic methods can be used to create convincing models in many different areas of science such as biology, chemistry, computer science, mathematics and physics. The present book deals with the mathematical theory needed for this purpose. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the field. The contributors were the main speakers at the conference Fractal Geometry and Stochastics II held at Greifswald/Koserow, Germany, in August 1998.The book is addressed to mathematicians and scientists who are interested in any of the following topics:· fractal dimensions· fractal measures and multifractals· self-similar and self-affine fractals· random fractals· stable processes· ergodic theory and dynamical systems· harmonic analysis and stochastic processes on fractalsThe readers will be introduced to the most recent results and problems on these subjects and also be treated to an overview of their historical development. Both researchers and graduate students will benefit from the clear expositions.

Fractal Geometry in Architecture and Design

Fractal Geometry in Architecture and Design

  • Author: Carl Bovill
  • Publisher: Springer Science & Business Media
  • ISBN: 9780817637958
  • Category: Mathematics
  • Page: 195
  • View: 4945
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na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.

Fractals and Chaos

Fractals and Chaos

An illustrated course

  • Author: Paul S. Addison
  • Publisher: CRC Press
  • ISBN: 9780750304009
  • Category: Science
  • Page: 256
  • View: 2941
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Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.

Die fraktale Geometrie der Natur

Die fraktale Geometrie der Natur

  • Author: B. Mandelbrot
  • Publisher: Springer-Verlag
  • ISBN: 3034850271
  • Category: Science
  • Page: 491
  • View: 6095
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Fractal Geometry and Stochastics III

Fractal Geometry and Stochastics III

  • Author: Christoph Bandt,Umberto Mosco,Martina Zähle
  • Publisher: Springer Science & Business Media
  • ISBN: 9783764370701
  • Category: Mathematics
  • Page: 262
  • View: 8929
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This up-to-date monograph, providing an up-to-date overview of the field of Hepatitis Prevention and Treatment, includes contributions from internationally recognized experts on viral hepatitis, and covers the current state of knowledge and practice regarding the molecular biology, immunology, biochemistry, pharmacology and clinical aspects of chronic HBV and HCV infection. The book provides the latest information, with sufficient background and discussion of the literature to benefit the newcomer to the field.

Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

  • Author: Nicola Senesi,Kevin J. Wilkinson
  • Publisher: John Wiley & Sons
  • ISBN: 0470511192
  • Category: Science
  • Page: 340
  • View: 1993
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This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and contrasted with the more classical approaches. The book will provide the fundamental knowledge necessary for solving practical environmental problems. Furthermore, it examinea how the fractal approach has been applied in order to understand the structure and reactivity of natural, environmental systems including flocs, sediments, soils, microorganisms and humic substances.

Complexity Science, Living Systems, and Reflexing Interfaces: New Models and Perspectives

Complexity Science, Living Systems, and Reflexing Interfaces: New Models and Perspectives

New Models and Perspectives

  • Author: Orsucci, Franco
  • Publisher: IGI Global
  • ISBN: 1466620781
  • Category: Computers
  • Page: 466
  • View: 7269
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There are new and important advancements in today’s complexity theories in ICT and requires an extraordinary perspective on the interaction between living systems and information technologies. With human evolution and its continuous link with the development of new tools and environmental changes, technological advancements are paving the way for new evolutionary steps. Complexity Science, Living Systems, and Reflexing Interfaces: New Models and Perspectives is a collection of research provided by academics and scholars aiming to introduce important advancements in areas such as artificial intelligence, evolutionary computation, neural networks, and much more. This scholarly piece will provide contributions that will define the line of development in complexity science.

Fractal Geometry in Digital Imaging

Fractal Geometry in Digital Imaging

  • Author: Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews
  • Publisher: Academic Press
  • ISBN: 9780127039701
  • Category: Mathematics
  • Page: 328
  • View: 4170
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This book presents the analysis of textured images using fractal geometry, and discusses its application to imaging science and computer vision when modeling natural objects. The authors explore the methods which can be used to simulate, analyze, and interpret coherent images, and demonstrate a new approach which segments each image into regions of similarity that can be characterized by a random fractal with a given fractal dimension. Fractal Geometry in Digital Imaging is based on a research project, but has been written with a broad coverage and user friendly math to make the book accessible to a wider audience. It includes real world experiences and applications using the techniques described. * Discusses the analysis of textured images using fractal geometry * Explores the methods used to simulate, analyze, and interpret coherent images * Contains coverage of real world experiences and applications * Written in a user friendly style

Fractals Everywhere

Fractals Everywhere

New Edition

  • Author: Michael F. Barnsley
  • Publisher: Courier Corporation
  • ISBN: 0486320340
  • Category: Mathematics
  • Page: 560
  • View: 8838
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Up-to-date text focuses on how fractal geometry can be used to model real objects in the physical world, with an emphasis on fractal applications. Includes solutions, hints, and a bonus CD.

Fractals and Dynamic Systems in Geoscience

Fractals and Dynamic Systems in Geoscience

  • Author: Jörn H. Kruhl
  • Publisher: Springer Science & Business Media
  • ISBN: 3662073048
  • Category: Science
  • Page: 421
  • View: 9259
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Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.

Applying Fractals in Astronomy

Applying Fractals in Astronomy

  • Author: Andre HECK,Jean M. Perdang
  • Publisher: Springer Science & Business Media
  • ISBN: 3540543538
  • Category: Science
  • Page: 212
  • View: 6442
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'Fractal geometry addressesitselfto questions that many people have been asking themselves. It con cerns an aspect of Nature that almost everybody had been conscious of, but could not address in a formal fashion. ' 'Fractal geometry seems to be the proper language to describe the complezity of many very compli cated shapes around us. ' (Mandelbrot, 1990a) 'I believe that fractals respond to a profound un easiness in man. ' (Mandelbrot, 1990b) The catchword fractal, ever since it was coined by Mandelbrot (1975) to refer to a class of abstract mathematical objects that were already known at the turn ofthe 19th century, has found an unprecedented resonance both inside and outside the scientific community. Fractal concepts, far more than the concepts of catastrophe theory introduced a few years earlier, are currently being applied not only in the physical sciences, but also in biology and medicine (Goldberger and West 1987). In the mid-eighties, Kadanoff (1986) asked the question: 'Why all the fuss about /ractals'! '. He offered a twofold answer: in the first place, it is 'because of the practical, technological importance of fractal objects'. Indeed he emphasised the relevance of these structures for materials scientists and oil drilling engineers, in search of structures with novel properties, or models for the flow of oil through the soil. His second answer was: 'Because of the intellectual interest of fractals '.

Fractal Apertures in Waveguides, Conducting Screens and Cavities

Fractal Apertures in Waveguides, Conducting Screens and Cavities

Analysis and Design

  • Author: Basudeb Ghosh,Sachendra Sinha,M.V. Kartikeyan
  • Publisher: Springer
  • ISBN: 3319065351
  • Category: Science
  • Page: 201
  • View: 3557
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This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no efforts were made to study the behavior of these fractal geometries for aperture coupling problems. The aperture coupling problem is an important boundary value problem in electromagnetics and used in waveguide filters and power dividers, slotted ground planes, frequency selective surfaces and metamaterials. The present book is intended to initiate a study of the characteristics of fractal apertures in waveguides, conducting screens and cavities. To perform a unified analysis of these entirely dissimilar problems, the “generalized network formulation of the aperture problems” by Mautz and Harrington was extended to multiple-aperture geometry. The authors consider the problem of coupling between two arbitrary regions coupled together via multiple apertures of arbitrary shape. MATLAB codes were developed for the problems and validated with the results available in the literature as well as through simulations on ANSOFT's HFSS.

Particle Technology and Applications

Particle Technology and Applications

  • Author: Sunggyu Lee,Kimberly H. Henthorn
  • Publisher: CRC Press
  • ISBN: 1439881685
  • Category: Science
  • Page: 342
  • View: 4739
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Particle Technology and Applications presents the theoretical and technological background of particle science and explores up-to-date applications of particle technologies in the chemical, petrochemical, energy, mechanical, and materials industries. It looks at the importance of particle science and technology in the development of efficient chemical processes and novel functional materials. With peer-reviewed chapters written by a select group of academic and industry experts, the book provides examples of particle technology and its advanced industrial applications. It includes the necessary scientific background of particle technology as well as relevant technological details of the application areas. This helps readers grasp specific details of the applied technology, since the advanced particle technology can directly or synergistically have an impact on outcomes, such as the development of a targeted functional material, enhancement of existing processing techniques, and modification of the properties of existing materials. Presenting a consistent scientific treatment of all topics, this comprehensive yet accessible book covers a variety of practical applications and relevant theoretical foundation of particle science and technology. It will help readers tackle new challenges in process and product development and create new methodologies in the clean technology sector.