Download or read book Frontiers of Fractal Analysis written by Santo Banerjee and published by CRC Press. This book was released on 2024-10-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Download or read book Measure Topology and Fractal Geometry written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

Download or read book Chaos and Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

Download or read book Frontiers of Fractal Analysis written by Santo Banerjee and published by CRC Press. This book was released on 2022-07-07 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Download or read book Fractals A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.

Download or read book Discovery of Cosmic Fractals written by Yurij Baryshev and published by World Scientific. This book was released on 2002 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a simple manner, explains the frontiers of astronomy, how fractals appear in cosmic physics, offers a personal view of the history of the idea of self-similarity and of cosmological principles and presents the debate which illustrates how new concepts and deeper observations reveal unexpected aspects of Nature.

Download or read book Differential Equations on Fractals written by Robert S. Strichartz and published by Princeton University Press. This book was released on 2006-08-20 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure, energy, and metric -- Laplacian -- Spectrum of the laplacian -- Postcritically finite fractals -- Further topics.

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Download or read book Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Weiyi Su and published by World Scientific. This book was released on 2017-08-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.

Download or read book The Beauty of Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 1986-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.

Download or read book Frontiers in Electromagnetics written by Douglas H. Werner and published by Wiley-IEEE Press. This book was released on 2000 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: "FRONTIERS IN ELECTROMAGNETICS is the first all-in-one resource to bring in-depth original papers on today's major advances in long-standing electromagnetics problems. Highly regarded editors Douglas H. Werner and Raj Mittra have meticulously selected new contributed papers from preeminent researchers in the field to provide state-of-the-art discussions on emerging areas of electromagnetics. Antenna and microwave engineers and students will find key insights into current trends and techniques of electromagnetics likely to shape future directions of this increasingly important topic. Each chapter includes a comprehensive analysis and ample references on innovative subjects that range from combining electromagnetic theory with mathematical concepts to the most recent techniques in electromagnetic optimization and estimation. The contributors also present the latest developments in analytical and numerical methods for solving electromagnetics problems. With a level of expertise unmatched in the field, FRONTIERS IN ELECTROMAGNETICS provides readers with a solid foundation to understand this rapidly changing area of technology. Topics covering fast-developing applications in electromagnetics include: * Fractal electrodynamics, fractal antennas and arrays, and scattering from fractally rough surfaces * Knot electrodynamics * The role of group theory and symmetry * Fractional calculus * Lommel and multiple expansions. Professors: To request an examination copy simply e-mail [email protected]." Sponsored by: IEEE Microwave Theory and Techniques Society, IEEE Antennas and Propagation Society.

Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-07-26 with total page 228 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. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book. Here we present the use of fractal geometry, in particular, fractal analysis in two sciences: health sciences and social sciences and humanities. Part 1 is Health Science. In it, we present the latest advances in cardiovascular signs, kidney images to determine cancer growth, EEG signals, magnetoencephalography signals, and photosensitive epilepsy. We show how it is possible to produce ultrasonic lenses or even sound focusing. In Part 2, we present the use of fractal analysis in social sciences and humanities. It includes anthropology, hierarchical scaling, human settlements, language, fractal dimension of different cultures, cultural traits, and Mesoamerican complexity. And in Part 3, we present a few useful tools for fractal analysis, such as graphs and correlation, self-affine and self-similar graphs, and correlation function. It is impossible to picture today's research without fractal geometry.

Download or read book New Frontiers in Nanochemistry Concepts Theories and Trends written by Mihai Putz and published by CRC Press. This book was released on 2020-05-10 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Frontiers in Nanochemistry: Concepts, Theories, and Trends, Volume 1: Structural Nanochemistry is the first volume of the new three-volume set that explains and explores the important concepts from various areas within the nanosciences. This first volume focuses on structural nanochemistry and encompasses the general fundamental aspects of nanochemistry while simultaneously incorporating crucial material from other fields, in particular mathematic and natural sciences, with specific attention to multidisciplinary chemistry. Under the broad expertise of the editor, the volume contains 50 concise yet comprehensive entries from world-renowned scholars, alphabetically organizing a multitude of essential basic and advanced concepts, ranging from algebraic chemistry to new energy technology, from the bondonic theory of chemistry to spintronics, and from fractal dimension and kinetics to quantum dots and tight binding—and much more. The entries contain definitions, short characterizations, uses and usefulness, limitations, references, and more.

Download or read book Fractal Patterns in Nonlinear Dynamics and Applications written by Santo Banerjee and published by CRC Press. This book was released on 2020-03-27 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.

Download or read book Fractal Analysis written by Clifford Brown and published by SAGE. This book was released on 2010-04-14 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: A specialized presentation of fractal analysis oriented to the social sciences This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior. Key Features Detailed examples help readers learn and understand the analytical methods presented. Matlab codes for programs allow users to implement, on their own, some of the techniques described in the text. Visit http://www.ccs.fau.edu/~liebovitch/larry.html for more details. Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material. This is the only book designed to introduce fractal analysis to a general social science audience. Learn more about “The Little Green Book” - QASS Series! Click Here

Download or read book Fractal Frontiers Fractals In The Natural And Applied Sciences written by Miroslav M Novak and published by World Scientific. This book was released on 1997-03-29 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, science has developed by reducing complex situations to simple ones, analyzing the components and synthesizing the original situation. While this 'reductionist' approach has been extremely successful, there are phenomena of such complexity that one cannot simplify them without eliminating the problem itself. Recently, attention has turned to such problems in a wide variety of fields. This is in part due to the development of fractal geometry. Fractal geometry provides the mathematical tools for handling complexity. The present volume is a collection of papers that deal with the application of fractals in both traditional scientific disciplines and in applied fields. This volume shows the advance of our understanding of complex phenomena across a spectrum of disciplines. While these diverse fields work on very different problems, fractals provide a unifying formalism for approaching these problems.