Fractals, Chaos, Power Laws

Fractals, Chaos, Power Laws

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  • Author: Manfred Schroeder
  • Publisher: Courier Corporation
  • ISBN: 0486472043
  • Category : Science
  • Languages : en
  • Pages : 450

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

Fractals, Chaos, Power Laws

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


Waves with Power-Law Attenuation

Waves with Power-Law Attenuation

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  • Author: Sverre Holm
  • Publisher: Springer
  • ISBN: 3030149277
  • Category : Science
  • Languages : en
  • Pages : 338

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

The Impact of Environmental Variability on Ecological Systems

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  • Author: D.A. Vasseur
  • Publisher: Springer Science & Business Media
  • ISBN: 1402058519
  • Category : Science
  • Languages : en
  • Pages : 240

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.


Heaven's Fractal Net

Heaven's Fractal Net

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

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.


Everyday Creativity and the Healthy Mind

Everyday Creativity and the Healthy Mind

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

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.


How Nature Works

How Nature Works

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  • Author: Per Bak
  • Publisher: Springer Science & Business Media
  • ISBN: 1475754264
  • Category : Mathematics
  • Languages : en
  • Pages : 229

Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties. "...a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex systems...it will reward a sufficiently skeptical reader." -NATURE "...presents the theory (self-organized criticality) in a form easily absorbed by the non-mathematically inclined reader." -BOSTON BOOK REVIEW "I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST


Uncharted

Uncharted

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  • Author: Erez Aiden
  • Publisher: Penguin
  • ISBN: 1101632119
  • Category : Science
  • Languages : en
  • Pages : 288

“One of the most exciting developments from the world of ideas in decades, presented with panache by two frighteningly brilliant, endearingly unpretentious, and endlessly creative young scientists.” – Steven Pinker, author of The Better Angels of Our Nature Our society has gone from writing snippets of information by hand to generating a vast flood of 1s and 0s that record almost every aspect of our lives: who we know, what we do, where we go, what we buy, and who we love. This year, the world will generate 5 zettabytes of data. (That’s a five with twenty-one zeros after it.) Big data is revolutionizing the sciences, transforming the humanities, and renegotiating the boundary between industry and the ivory tower. What is emerging is a new way of understanding our world, our past, and possibly, our future. In Uncharted, Erez Aiden and Jean-Baptiste Michel tell the story of how they tapped into this sea of information to create a new kind of telescope: a tool that, instead of uncovering the motions of distant stars, charts trends in human history across the centuries. By teaming up with Google, they were able to analyze the text of millions of books. The result was a new field of research and a scientific tool, the Google Ngram Viewer, so groundbreaking that its public release made the front page of The New York Times, The Wall Street Journal, and The Boston Globe, and so addictive that Mother Jones called it “the greatest timewaster in the history of the internet.” Using this scope, Aiden and Michel—and millions of users worldwide—are beginning to see answers to a dizzying array of once intractable questions. How quickly does technology spread? Do we talk less about God today? When did people start “having sex” instead of “making love”? At what age do the most famous people become famous? How fast does grammar change? Which writers had their works most effectively censored by the Nazis? When did the spelling “donut” start replacing the venerable “doughnut”? Can we predict the future of human history? Who is better known—Bill Clinton or the rutabaga? All over the world, new scopes are popping up, using big data to quantify the human experience at the grandest scales possible. Yet dangers lurk in this ocean of 1s and 0s—threats to privacy and the specter of ubiquitous government surveillance. Aiden and Michel take readers on a voyage through these uncharted waters.


Lumen Naturae

Lumen Naturae

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  • Author: Matilde Marcolli
  • Publisher: MIT Press
  • ISBN: 0262358328
  • Category : Mathematics
  • Languages : en
  • Pages : 390

Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.


Physics of Fractal Operators

Physics of Fractal Operators

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  • Author: Bruce West
  • Publisher: Springer Science & Business Media
  • ISBN: 0387217460
  • Category : Science
  • Languages : en
  • Pages : 355

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.