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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

Nonlinear Physics for Beginners

Author: Lui Lam
Publisher: World Scientific Publishing Company
ISBN: 9813103701
Category : Science
Languages : en
Pages : 348

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Book Description
Almost all real systems are nonlinear. For a nonlinear system the superposition principle breaks down: The system's response is not proportional to the stimulus it receives; the whole is more than the sum of its parts. The three parts of this book contains the basics of nonlinear science, with applications in physics. Part I contains an overview of fractals, chaos, solitons, pattern formation, cellular automata and complex systems. In Part II, 14 reviews and essays by pioneers, as well as 10 research articles are reprinted. Part III collects 17 students projects, with computer algorithms for simulation models included. The book can be used for self-study, as a textbook for a one-semester course, or as supplement to other courses in linear or nonlinear systems. The reader should have some knowledge in introductory college physics. No mathematics beyond calculus and no computer literacy are assumed. Request Inspection Copy

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.

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.

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.

Heaven's Fractal Net

Author: William Joseph Jackson
Publisher: Indiana University Press
ISBN: 9780253216205
Category : Religion
Languages : en
Pages : 346

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Book Description
Accompanying DVD contains ... "Two hours of Supercomputed frame-by-frame fractal animation. Includes Mandelbrot Zooms, Julia Promenades, Cascade maps and the Lorenz Attractor. Forty six scenes with original music."--[container of 1990 VHS release].

Fractals, Graphics, and Mathematics Education

Author: Michael Frame
Publisher: Cambridge University Press
ISBN: 9780883851692
Category : Computers
Languages : en
Pages : 206

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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.

Fractals for the Classroom

Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1461244064
Category : Mathematics
Languages : en
Pages : 500

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Book Description
Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.