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Fractals, Chaos, Power Laws

Author: Manfred Schroeder
Publisher: Courier Corporation
ISBN: 0486472043
Category : Science
Languages : en
Pages : 448

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Book Description

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.

Fractals, Chaos, Power Laws

Author: Manfred Schroeder
Publisher: Courier Corporation
ISBN: 0486472043
Category : Science
Languages : en
Pages : 448

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Book Description
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.

Fractals, Chaos, Power Laws

Author: Manfred Robert Schroeder
Publisher: W H Freeman & Company
ISBN: 9780716721369
Category : Chaotic behavior in systems
Languages : en
Pages : 429

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Book Description

Heaven's Fractal Net

Author: William J. Jackson
Publisher: Wipf and Stock Publishers
ISBN: 1666737992
Category : Philosophy
Languages : en
Pages : 343

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Book Description
Heaven's Fractal Net explores the uniquely useful geometrical forms found in nature and in cultures of the world. The visual shapes of fractals attract eyes with their fascinating beauty. They appear in images and designs with reiterated patterns whose parts are self-similar to the whole pattern--just as a fern frond is structured with smaller and smaller self-similar branches. The fractal-like imagery in religious architecture has been used to symbolize infinity, consciousness, vertigo, and wonder. In nature fractals serve as dynamic configurations for circulation, including the branching shapes of trees and lungs, rivers and nerves. A wealth of fractal examples is found in arts, symbols, and decorations. Heaven's Fractal Net is a book which explores self-similarities in worldwide cultures, providing a rich background for examining many geometrical shapes used by humanity, exploring processes of creativity in wisdom traditions, and delving into archetypal images in depth psychology. Fractals offer an organizing principle for many different kinds of hierarchies and composites, and in recent years "fractal" has become a familiar household word for a new yet ancient geometry.

Waves with Power-Law Attenuation

Author: Sverre Holm
Publisher: Springer
ISBN: 3030149277
Category : Science
Languages : en
Pages : 312

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Book Description
This book integrates concepts from physical acoustics with those from linear viscoelasticity and fractional linear viscoelasticity. Compressional waves and shear waves in applications such as medical ultrasound, elastography, and sediment acoustics often follow power law attenuation and dispersion laws that cannot be described with classical viscous and relaxation models. This is accompanied by temporal power laws rather than the temporal exponential responses of classical models. The book starts by reformulating the classical models of acoustics in terms of standard models from linear elasticity. Then, non-classical loss models that follow power laws and which are expressed via convolution models and fractional derivatives are covered in depth. In addition, parallels are drawn to electromagnetic waves in complex dielectric media. The book also contains historical vignettes and important side notes about the validity of central questions. While addressed primarily to physicists and engineers working in the field of acoustics, this expert monograph will also be of interest to mathematicians, mathematical physicists, and geophysicists.

The Impact of Environmental Variability on Ecological Systems

Author: D.A. Vasseur
Publisher: Springer Science & Business Media
ISBN: 1402058519
Category : Science
Languages : en
Pages : 234

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Book Description
Fluctuations in the environmental conditions impacting life are ubiquitous. This book brings together contributions to provide readers with a comprehensive look at the challenges for ecological systems and ecological research alike. It offers a comprehensive range of topics, from environmental variability itself to its ecosystem-level impact.

Everyday Creativity and the Healthy Mind

Author: Ruth Richards
Publisher: Springer
ISBN: 1137557664
Category : Psychology
Languages : en
Pages : 390

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Book Description
As human beings we all have creative potential, a quality essential to human development and a vital component to healthy and happy lives. However this may often remain stifled by the choices we make, or ways in which we choose to live in our daily lives. Framed by the “Four Ps of Creativity” – product, person, process, press – this book offers an alternative understanding of the fundamentals of ordinary creativity. Ruth Richards highlights the importance of “process”, circumventing our common preoccupation with the product, or creative outcome, of creativity. By focusing instead on the creator and the creative process, she demonstrates how we may enhance our relationships with life, beauty, future possibilities, and one another. This book illustrates how our daily life styles and choices, as well as our environments, may enable and allow creativity; whereas environments not conducive to creative flow may kill creative potential. Also explored are questions of ‘normality’, beauty and nuance in creativity, as well as creative relationships.

Chaos and Fractals

Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1475747403
Category : Mathematics
Languages : en
Pages : 999

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Book Description
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.

Chaos and Fractals

Author: C.A. Pickover
Publisher: Elsevier
ISBN: 9780080528861
Category : Computers
Languages : en
Pages : 452

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Book Description
These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. 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. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. 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. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Physics of Fractal Operators

Author: Bruce West
Publisher: Springer Science & Business Media
ISBN: 0387217460
Category : Science
Languages : en
Pages : 354

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Book Description
This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.

Fractals, Graphics, and Mathematics Education

Author: Michael Frame
Publisher: Cambridge University Press
ISBN: 9780883851692
Category : Computers
Languages : en
Pages : 232

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Book Description
Fractal Geometry is a recent edition to the collection of mathematical tools for describing nature, and is the first to focus on roughness. Fractal geometry also appears in art, music and literature, most often without being consciously included by the artist. Consequently, through this we may uncover connections between the arts and sciences, uncommon for students to see in maths and science classes. This book will appeal to teachers who have wanted to include fractals in their mathematics and science classes, to scientists familiar with fractal geometry who want to teach a course on fractals, and to anyone who thinks general scientific literacy is an issue important enough to warrant new approaches.