Fractals A Very Short Introduction
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Fractals A Very Short Introduction
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Author : K. J. Falconer
language : en
Publisher: Oxford University Press
Release Date : 2013-09-26
Fractals A Very Short Introduction written by K. J. Falconer and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
This essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, and explains how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century.
Fractals A Very Short Introduction
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Author : Kenneth Falconer
language : en
Publisher: OUP Oxford
Release Date : 2013-09-26
Fractals A Very Short Introduction written by Kenneth Falconer and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
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.
Fractal Geometry In Human Geography And Planning
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Author : Cécile Tannier
language : en
Publisher: John Wiley & Sons
Release Date : 2024-07-19
Fractal Geometry In Human Geography And Planning written by Cécile Tannier and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-19 with Social Science categories.
The aim of this book is to provide an overview of the concepts and methods used in fractal analysis and modeling in order to study the spatial distribution of human settlements. The main concepts and mathematical tools are reviewed, and emphasis is placed on the practical benefits of their application and the pitfalls to be avoided when using them. The first part of the book is devoted to the basic concepts and geometric reference figures required for fractal analysis in human geography. In the second part, the principles of four major families of analysis methods are explained in detail: fractal analyses of point sequences, fractal methods for morphological delineation of urban agglomerations, multifractal analyses and cross scale signatures. The third part of the book is devoted to applications of fractal geometry in urban and regional planning.
Chaos And Dynamical Systems
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Author : David P. Feldman
language : en
Publisher: Princeton University Press
Release Date : 2019-08-06
Chaos And Dynamical Systems written by David P. Feldman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Mathematics categories.
Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
Kitchen Science Fractals A Lab Manual For Fractal Geometry
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Author : Michael Frame
language : en
Publisher: World Scientific
Release Date : 2021-10-04
Kitchen Science Fractals A Lab Manual For Fractal Geometry written by Michael Frame and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-04 with Young Adult Nonfiction categories.
This book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.
Fractal Geometry
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Author : Kenneth Falconer
language : en
Publisher: John Wiley & Sons
Release Date : 2014-02-03
Fractal Geometry written by Kenneth Falconer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-03 with Mathematics categories.
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 www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)
Assouad Dimension And Fractal Geometry
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Author : Jonathan M. Fraser
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-29
Assouad Dimension And Fractal Geometry written by Jonathan M. Fraser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-29 with Mathematics categories.
The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Systems Cybernetics Control And Automation
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Author : Spyros G. Tzafestas
language : en
Publisher: CRC Press
Release Date : 2022-09-01
Systems Cybernetics Control And Automation written by Spyros G. Tzafestas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.
Systems, cybernetics, control, and automation (SCCA)are four interrelated and overlapping scientific and technological fields that have contributed substantially to the development, growth, and progress of human society. A large number of models, methods, and tools were developed that assure high efficiency of SCCA applied to practical situations. The real-life applications of SCCA encompass a wide range of man-made or biological systems, including transportations, power generation, chemical industry, robotics, manufacturing, cybernetics organisms (cyborgs), aviation, economic systems, enterprise, systems, medical/health systems, environmental applications, and so on. The SCCA fields exhibit strong influences on society and rise, during their use and application, many ethical concerns and dilemmas. This book provides a consolidated and concise overview of SCCA, in a single volume for the first time, focusing on ontological, epistemological, social impact, ethical, and general philosophical issues. It is appropriate for use in engineering courses as a convenient tutorial source providing fundamental conceptual and educational material on these issues, or for independent reading by students and scientists.Included in the book is:• Background material on philosophy and systems theory• Major ontological, epistemological, societal and ethical/philosophical aspects of the four fields that are considered in the book• Over 400 references and a list of 130 additional books in the relevant fields • Over 100 colored photos and 70 line figures that illustrate the text
Dynamical Systems With Applications Using Matlab
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Author : Stephen Lynch
language : en
Publisher: Springer
Release Date : 2014-07-22
Dynamical Systems With Applications Using Matlab written by Stephen Lynch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD. Features new to the second edition include · sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; · chapters on image processing and binary oscillator computing; · hundreds of new illustrations, examples, and exercises with solutions; and · over eighty up-to-date MATLAB program files and Simulink model files available online. These files were voted MATLAB Central Pick of the Week in July 2013. The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics. Praise for the first edition Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing. —OR News/Operations Research Spectrum The MATLAB programs are kept as simple as possible and the author's experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes.... I recommend ‘Dynamical Systems with Applications using MATLAB’ as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering. —Mathematica
Fractal Dimensions Of Networks
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Author : Eric Rosenberg
language : en
Publisher: Springer Nature
Release Date : 2020-07-07
Fractal Dimensions Of Networks written by Eric Rosenberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Computers categories.
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.