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Fractal Analysis

Author : Fernando Brambila
Publisher : BoD – Books on Demand
ISBN 13 : 9535131915
Total Pages : 296 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Fractal Analysis by : Fernando Brambila

Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-06-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.

Intelligent Fractal-Based Image Analysis

Author : Soumya Ranjan Nayak
Publisher : Elsevier
ISBN 13 : 0443184690
Total Pages : 320 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Intelligent Fractal-Based Image Analysis by : Soumya Ranjan Nayak

Download or read book Intelligent Fractal-Based Image Analysis written by Soumya Ranjan Nayak and published by Elsevier. This book was released on 2024-05-27 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals are infinite, complex patterns used in modeling physical and dynamic systems. Fractal theory research has increased across different fields of applications including engineering science, health science, and social science. Recent literature shows the vital role fractals play in digital image analysis, specifically in biomedical image processing. Fractal graphics is an interdisciplinary field that deals with how computers can be used to gain high-level understanding from digital images. Integrating artificial intelligence with fractal characteristics has resulted in new interdisciplinary research in the fields of pattern recognition and image processing analysis. Intelligent Fractal-Based Image Analysis: Application in Pattern Recognition and Machine Vision provides insights into the current strengths and weaknesses of different applications as well as research findings on fractal graphics in engineering and science applications. The book aims to improve the exchange of ideas and coherence between various core computing methods and highlight the relevance of related application areas for advanced as well as novice-user application. The book presents an in-depth look at core concepts, methodological aspects, and advanced feature opportunities, focusing on major real time applications in engineering science and health science. The book will appeal to researchers, data scientists, industry professionals, and graduate students in the fields of fractal graphics and its related applications. - Investigates advanced fractal theories spanning neural networks, fuzzy logic, machine learning, deep learning, and hybrid intelligent systems in solving pattern recognition problems - Explores the application of fractal theories to a wide range of medical image processing modalities - Presents case studies that illustrate the application and integration of fractal theories into intelligent computing in the resolution of important pattern recognition and machine vision problems

Fractal Worlds

Author : Michael Frame
Publisher : Yale University Press
ISBN 13 : 030019787X
Total Pages : 536 pages
Book Rating : 4.3/5 (1 download)

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Book Synopsis Fractal Worlds by : Michael Frame

Download or read book Fractal Worlds written by Michael Frame and published by Yale University Press. This book was released on 2016-01-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this essential primer, mathematician Michael Frame, a close collaborator with Benoit Mandelbrot, the founder of fractal geometry, and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology

The Fractal Structure of Data Reference

Author : Bruce McNutt
Publisher : Springer Science & Business Media
ISBN 13 : 0306470349
Total Pages : 144 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis The Fractal Structure of Data Reference by : Bruce McNutt

Download or read book The Fractal Structure of Data Reference written by Bruce McNutt and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The architectural concept of a memory hierarchy has been immensely successful, making possible today's spectacular pace of technology evolution in both the volume of data and the speed of data access. Its success is difficult to understand, however, when examined within the traditional "memoryless" framework of performance analysis. The `memoryless' framework cannot properly reflect a memory hierarchy's ability to take advantage of patterns of data use that are transient. The Fractal Structure of Data Reference: Applications to the Memory Hierarchy both introduces, and justifies empirically, an alternative modeling framework in which arrivals are driven by a statistically self-similar underlying process, and are transient in nature. The substance of this book comes from the ability of the model to impose a mathematically tractable structure on important problems involving the operation and performance of a memory hierarchy. It describes events as they play out at a wide range of time scales, from the operation of file buffers and storage control cache, to a statistical view of entire disk storage applications. Striking insights are obtained about how memory hierarchies work, and how to exploit them to best advantage. The emphasis is on the practical application of such results. The Fractal Structure of Data Reference: Applications to the Memory Hierarchy will be of interest to professionals working in the area of applied computer performance and capacity planning, particularly those with a focus on disk storage. The book is also an excellent reference for those interested in database and data structure research.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891480
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Math with Bad Drawings

Author : Ben Orlin
Publisher : Black Dog & Leventhal
ISBN 13 : 0316509027
Total Pages : 556 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Math with Bad Drawings by : Ben Orlin

Download or read book Math with Bad Drawings written by Ben Orlin and published by Black Dog & Leventhal. This book was released on 2018-09-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.

Fractal Analysis and Synergetics of Catalysis in Nanosystems

Author : G. V. Kozlov
Publisher : Nova Publishers
ISBN 13 : 9781604563641
Total Pages : 178 pages
Book Rating : 4.5/5 (636 download)

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Book Synopsis Fractal Analysis and Synergetics of Catalysis in Nanosystems by : G. V. Kozlov

Download or read book Fractal Analysis and Synergetics of Catalysis in Nanosystems written by G. V. Kozlov and published by Nova Publishers. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanochemistry is a science connected with obtaining and studying of physical-chemical properties of particles having sizes on the nanometer scale. This book addresses polymer synthesis which, according to Melikhov's classification, is automatically part of nanochemistry. This is determined as far as polymeric macromolecules (more precisely macromolecular coils) belong to nanoparticles and polymeric sols and gels - to nanosystems. Catalysis on nanoparticles is one of the most important sections of nanochemistry. The majority of catalytic systems are nanosystems. At heterogeneous catalysis the active substance is tried to deposit on carrier in nanoparticles form in order to increase their specific surface. At homogeneous catalysis active substance molecules have often in themselves nanometer sizes. The most favorable conditions for homogeneous catalysis are created when reagent molecules are adsorbed rapidly by nanoparticles and are desorbed slowly but have high surface mobility and, consequently, high reaction rate on the surface and at the reaction molecules of such structure are formed at which desorption rate is increased sharply. If these conditions are realised in nanosystem with larger probability than in macrosystem, then nanocatalyst has the raising activity that was observed for many systems.

Encyclopedia of Public Administration and Public Policy: A-J

Author : Jack Rabin
Publisher : CRC Press
ISBN 13 : 9780824709464
Total Pages : 734 pages
Book Rating : 4.7/5 (94 download)

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Book Synopsis Encyclopedia of Public Administration and Public Policy: A-J by : Jack Rabin

Download or read book Encyclopedia of Public Administration and Public Policy: A-J written by Jack Rabin and published by CRC Press. This book was released on 2003 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Nuremberg trials to the Civil Service Reform Act of 1978 to recent budget reconciliation bills, the Encyclopedia of Public Administration and Public Policy provides detailed coverage of watershed policies and decisions from such fields as privatization, biomedical ethics, education, and diversity. This second edition features a wide range of new topics, including military administration, government procurement, social theory, and justice administration in developed democracies. It also addresses current issues such as the creation of the Department of Homeland Security and covers public administration in the Middle East, Africa, Southeast Asia, the Pacific, and Latin America.

Fractal Modelling

Author : Jaap A. Kaandorp
Publisher : Springer Science & Business Media
ISBN 13 : 3642579221
Total Pages : 234 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Fractal Modelling by : Jaap A. Kaandorp

Download or read book Fractal Modelling written by Jaap A. Kaandorp and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, methods from fractal geometry are applied to model growth forms, taking as a case study a type of growth process which can be found among various taxonomic classes such as sponges and corals. These models can be used, for example, to understand the amazing variety of forms to be found in a coral reef and to simulate their growth with 2D and 3D geometrical objects. Models which mimic the growth of forms and the environmental influence on the growth process are also useful for ecologists, as a combination of simulation models together with the actual growth forms can be used to detect the effects of slow changes in the environment.

The Fractal Geometry of the Brain

Author : Antonio Di Ieva
Publisher : Springer Nature
ISBN 13 : 3031476069
Total Pages : 999 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis The Fractal Geometry of the Brain by : Antonio Di Ieva

Download or read book The Fractal Geometry of the Brain written by Antonio Di Ieva and published by Springer Nature. This book was released on with total page 999 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractal Dimensions of Networks

Author : Eric Rosenberg
Publisher : Springer Nature
ISBN 13 : 303043169X
Total Pages : 530 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Fractal Dimensions of Networks by : Eric Rosenberg

Download or read book Fractal Dimensions of Networks written by Eric Rosenberg and published by Springer Nature. This book was released on 2020-07-07 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.

Fractals Everywhere

Author : Michael F. Barnsley
Publisher : Academic Press
ISBN 13 : 148325769X
Total Pages : 565 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fractals Everywhere by : Michael F. Barnsley

Download or read book Fractals Everywhere written by Michael F. Barnsley and published by Academic Press. This book was released on 2014-05-10 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals Everywhere, Second Edition covers the fundamental approach to fractal geometry through iterated function systems. This 10-chapter text is based on a course called "Fractal Geometry", which has been taught in the School of Mathematics at the Georgia Institute of Technology. After a brief introduction to the subject, this book goes on dealing with the concepts and principles of spaces, contraction mappings, fractal construction, and the chaotic dynamics on fractals. Other chapters discuss fractal dimension and interpolation, the Julia sets, parameter spaces, and the Mandelbrot sets. The remaining chapters examine the measures on fractals and the practical application of recurrent iterated function systems. This book will prove useful to both undergraduate and graduate students from many disciplines, including mathematics, biology, chemistry, physics, psychology, mechanical, electrical, and aerospace engineering, computer science, and geophysical science.

Fractal Analyses: Statistical And Methodological Innovations And Best Practices

Author : John G. Holden
Publisher : Frontiers E-books
ISBN 13 : 2889191389
Total Pages : 149 pages
Book Rating : 4.8/5 (891 download)

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Book Synopsis Fractal Analyses: Statistical And Methodological Innovations And Best Practices by : John G. Holden

Download or read book Fractal Analyses: Statistical And Methodological Innovations And Best Practices written by John G. Holden and published by Frontiers E-books. This book was released on 2013-06-03 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many statistical and methodological developments regarding fractal analyses have appeared in the scientific literature since the publication of the seminal texts introducing Fractal Physiology. However, the lion’s share of more recent work is distributed across many outlets and disciplines, including aquatic sciences, biology, computer science, ecology, economics, geology, mathematics, medicine, neuroscience, physics, physiology, psychology, and others. The purpose of this special topic is to solicit submissions regarding fractal and nonlinear statistical techniques from experts that span a wide range of disciplines. The articles will aggregate extensive cross-discipline expertise into comprehensive and broadly applicable resources that will support the application of fractal methods to physiology and related disciplines. The articles will be organized with respect to a continuum defined by the characteristics of the empirical measurements a given analysis is intended to confront. At one end of the continuum are stochastic techniques directed at assessing scale invariant but stochastic data. The next step in the continuum concerns self-affine random fractals and methods directed at systems that entail scale-invariant or 1/f patterns or related patterns of temporal and spatial fluctuation. Analyses directed at (noisy) deterministic signals correspond to the final stage of the continuum that relates the statistical treatments of nonlinear stochastic and deterministic signals. Each section will contain introductory articles, advanced articles, and application articles so readers with any level of expertise with fractal methods will find the special topic accessible and useful. Example stochastic methods include probability density estimation for the inverse power-law, the lognormal, and related distributions. Articles describing statistical issues and tools for discriminating different classes of distributions will be included. An example issue is distinguishing power-law distributions from exponential distributions. Modeling issues and problems regarding statistical mimicking will be addressed as well. The random fractal section will present introductions to several one-dimensional monofractal time-series analysis. Introductory articles will be accompanied by advanced articles that will supply comprehensive treatments of all the key fractal time series methods such as dispersion analysis, detrended fluctuation analysis, power spectral density analysis, and wavelet techniques. Box counting and related techniques will be introduced and described for spatial analyses of two and three dimensional domains as well. Tutorial articles on the execution and interpretation of multifractal analyses will be solicited. There are several standard wavelet based and detrended fluctuation based methods for estimating a multifractal spectrum. We hope to include articles that contrast the different methods and compare their statistical performance as well. The deterministic methods section will include articles that present methods of phase space reconstruction, recurrence analysis, and cross-recurrence analysis. Recurrence methods are widely applicable, but motivated by signals that contain deterministic patterns. Nonetheless recent developments such as the analysis of recurrence interval scaling relations suggest applicability to fractal systems. Several related statistical procedures will be included in this section. Examples include average mutual information statistics and false nearest neighbor analyses.

Fractal Geometry in Biological Systems

Author : Philip M. Iannaccone
Publisher : CRC Press
ISBN 13 : 9780849376368
Total Pages : 448 pages
Book Rating : 4.3/5 (763 download)

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Book Synopsis Fractal Geometry in Biological Systems by : Philip M. Iannaccone

Download or read book Fractal Geometry in Biological Systems written by Philip M. Iannaccone and published by CRC Press. This book was released on 1996-07-25 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Control and Its Applications

Author : Shu Tang Liu
Publisher : Springer Nature
ISBN 13 : 9811554595
Total Pages : 364 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Fractal Control and Its Applications by : Shu Tang Liu

Download or read book Fractal Control and Its Applications written by Shu Tang Liu and published by Springer Nature. This book was released on 2020-07-11 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on fractal control and applications in various fields. Fractal phenomena occur in nonlinear models, and since the behaviors depicted by fractals need to be controlled in practical applications, an understanding of fractal control is necessary. This book introduces readers to Julia set fractals and Mandelbrot set fractals in a range of models, such as physical systems, biological systems and SIRS models, and discusses controllers designed to control these fractals. Further, it demonstrates how the fractal dimension can be calculated in order to describe the complexity of various systems.Offering a comprehensive and systematic overview of the practical issues in fractal control, this book is a valuable resource for readers interested in practical solutions in fractal control. It will also appeal to researchers, engineers, and graduate students in fields of fractal control and applications, as well as chaos control and applications.

Fractal Functions, Dimensions and Signal Analysis

Author : Santo Banerjee
Publisher : Springer Nature
ISBN 13 : 3030626725
Total Pages : 132 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Fractal Functions, Dimensions and Signal Analysis by : Santo Banerjee

Download or read book Fractal Functions, Dimensions and Signal Analysis written by Santo Banerjee and published by Springer Nature. This book was released on 2020-12-14 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

The Fractal Dimension of Architecture

Author : Michael J. Ostwald
Publisher : Birkhäuser
ISBN 13 : 3319324268
Total Pages : 429 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis The Fractal Dimension of Architecture by : Michael J. Ostwald

Download or read book The Fractal Dimension of Architecture written by Michael J. Ostwald and published by Birkhäuser. This book was released on 2016-09-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.