Author by : Paul S. 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. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics. Widely spread subjects which the author has encountered hitherto are briefly addressed in the book, as chaos and fractal science is a frontier of new research fields nowadays. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences.
Two chapters analyzing the standard one-dimensional examples. Interest continues to grow among scientists and, rather surprisingly, artists and designers. Author by : Michael F. Readership: Biomedical and physical scientists and students. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. The computer programs are now in Matlab.
The book provides a comprehensive overview of a nascent theory of medicine, including a new chapter on the theory of complex networks as they pertain to medicine. Integrating the work of leading mathematicians, physicists, chemists, and engineers, this research-level monograph discusses different aspects of the concepts of chaos and fractals from both experimental and theoretical points of view. The third part highlights the applications of chaotic dynamics and fractals. The book can be used as a textbook for an undergraduate course. The areas covered are mathematical frontiers, the predictability and control of chaos, detection and classification, advance applied signal processing methods, stochastic resonance, machine diagnostics, turbulence, geophysics, medicine, and new methods for modeling nonlinear systems. Author by : David P. It is not presented as a purely theoretical treatise but shows mathematics at a workshop, so to speak, through important applications originating in a deep pure mathematical theory.
Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals. It shows how these subjects continue to grow within mathematics and in many other disciplines. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry.
Whether for scholars and researchers, Higher Ed instructors, students, or professionals, our books help define fields of study, nurture curiosity, and give readers the competitive edge. In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs that have occurred in the intervening years are emphasized. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. It shows how these subjects continue to grow within mathematics and in many other disciplines. The book concludes with the famous Julia sets and the Mandelbrot set. This conference deals with the research area of chaos, dynamical systems, and fractal geometry.
A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. The book can be used as a text for undergraduate courses or for self-study. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. These books provide prompt access to the latest innovations in research and technology in their respective fields.
The second edition contains much new material and has been thoroughly revised. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. Devaney Languange : en Publisher by : American Mathematical Soc. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.
It is explained why the continuum approach leads to predictions that are not necessarily realized in computations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J. One chapter each on two-dimensional examples Hénon, horseshoe , fractals, and differential equations. The authors represented here are some of the top experts in this field.
Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. Author by : Robert L. It shows how these subjects continue to grow within mathematics and in many other disciplines. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. In addition, plenty of problems are provided to test understanding. The book may be used in part or as a whole to form an introductory course in either or both subject areas.