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Fractals and Chaos

Fractals and Chaos
Author: Benoit Mandelbrot
Publisher: Springer Science & Business Media
Total Pages: 321
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475740174

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Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.


Fractals And Beyond: Complexities In The Sciences

Fractals And Beyond: Complexities In The Sciences
Author: Miroslav M Novak
Publisher: World Scientific
Total Pages: 374
Release: 1998-08-25
Genre:
ISBN: 9814544507

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One of the ways to understand the complexity in scientific disciplines is through the use of fractal geometry. Tremendous progress has been made in this field since its inception some two decades ago. This book collects the papers at the cutting-edge, reflecting the current status of fractals. With its special emphasis on the multidisciplinary research, the book represents a unique contribution to the understanding of the complex phenomena in nature.


Fractals

Fractals
Author: Jens Feder
Publisher: Springer Science & Business Media
Total Pages: 305
Release: 2013-11-11
Genre: Science
ISBN: 1489921249

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This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.


Chaos and Fractals

Chaos and Fractals
Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
Total Pages: 1013
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475747403

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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.


The Fractal Geometry of Nature

The Fractal Geometry of Nature
Author: Benoit Mandelbrot
Publisher: Echo Point Books & Media, LLC
Total Pages: 0
Release: 2021-07-16
Genre:
ISBN: 9781648370410

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Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.


The Fractal Self

The Fractal Self
Author: John L. Culliney
Publisher: University of Hawaii Press
Total Pages: 257
Release: 2017-07-31
Genre: Science
ISBN: 0824866649

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Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.


Beyond the Sage on the Stage

Beyond the Sage on the Stage
Author: S. L. Seethaler
Publisher: University of Toronto Press
Total Pages: 293
Release: 2024-01-31
Genre: Education
ISBN: 1487547528

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Communication failures are ubiquitous. Exacerbating the situation, much communication advice is superficial, and the vast research base that should inform best practices in communication is difficult to navigate. Beyond the Sage on the Stage translates lessons from carefully documented scholarship into lucid prose with meaningful examples that illustrate readily applicable communication strategies. This user-friendly guide provides a unique cross-disciplinary approach to developing the knowledge, skills, and habits of mind to achieve evolving communication goals. Topics include optimizing language and visuals, designing comparisons, composing logic stories, conveying authenticity, clarifying data and uncertainty, supporting reasoning and decision-making, avoiding backfires, reading body language, and cultivating empathy. The book is constructed with a clear progression of logic based on a proven educational framework and provides guidance for communication about both uncontroversial and controversial topics. Demonstrating how commonly dispensed communication advice is often counterproductive, Beyond the Sage on the Stage is an innovative toolkit for being understood, fostering trust and genuine connection, and building a foundation for more effective, inclusive communication.


Fractals, Graphics, and Mathematics Education

Fractals, Graphics, and Mathematics Education
Author: Michael Frame
Publisher: Cambridge University Press
Total Pages: 232
Release: 2002-06-20
Genre: Computers
ISBN: 9780883851692

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Fractals for the Classroom

Fractals for the Classroom
Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
Total Pages: 468
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475721722

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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.


A Tale of Two Fractals

A Tale of Two Fractals
Author: A.A. Kirillov
Publisher: Springer Science & Business Media
Total Pages: 148
Release: 2013-04-23
Genre: Mathematics
ISBN: 0817683828

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Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.