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Fractals, Scaling and Growth Far from Equilibrium
  • Language: en
  • Pages: 700

Fractals, Scaling and Growth Far from Equilibrium

A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.

Fractals: A Very Short Introduction
  • Language: en
  • Pages: 153

Fractals: A Very Short Introduction

  • Type: Book
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  • Published: 2013-09-26
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  • Publisher: OUP Oxford

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.

Fractals: Theory and Applications in Engineering
  • Language: en
  • Pages: 336

Fractals: Theory and Applications in Engineering

Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

A Random Walk Through Fractal Dimensions
  • Language: en
  • Pages: 452

A Random Walk Through Fractal Dimensions

Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin

Fractals for the Classroom
  • Language: en
  • Pages: 528

Fractals for the Classroom

Published in cooperation with the National Council of Teachers of Mathematics

Fractals and Chaos
  • Language: en
  • Pages: 308

Fractals and Chaos

  • Type: Book
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  • Published: 2013-03-12
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  • Publisher: Springer

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 Disordered Systems
  • Language: en
  • Pages: 428

Fractals and Disordered Systems

Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.

Dynamics of Fractal Surfaces
  • Language: en
  • Pages: 496

Dynamics of Fractal Surfaces

In the last few years there has been an explosion of activity in the field of the dynamics of fractal surfaces, which, through the convergence of important new results from computer simulations, analytical theories and experiments, has led to significant advances in our understanding of nonequilibrium surface growth phenomena. This interest in surface growth phenomena has been motivated largely by the fact that a wide variety of natural and industrial processes lead to the formation of rough surfaces and interfaces. This book presents these developments in a single volume by bringing together the works containing the most important results in the field.The material is divided into chapters c...

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot
  • Language: en
  • Pages: 592

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Fraktály
  • Language: cs
  • Pages: 64

Fraktály

  • Type: Book
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  • Published: 2021-01-01
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  • Publisher: Dokořán

Ojedinělý průvodce po chaosu v přírodě a matematice pro každého, kdo kdy toužil porozumět vzorcům uspořádání listů nebo vytváření sněhových vloček. Eukleides z Alexandrie před více než 2 000 lety vytvořil postup pro měření a mapování světa pomocí přímek, kruhů, koulí a kuželů. Jeho model měření vedl k vynálezu geometrie a k teoriím Isaaca Newtona a ovlivnil obory tak rozdílné, jako je ekonomie či etika. Eukleidova elegantní řešení však většinou neodpovídala realitě přírody a při vývoji moderních technologií, jako je satelitní navigace, vyvstala potřeba přesnějších metod měření tvarů, které se neskládají z přímek nebo snadno měřitelných křivek. Řešení se objevilo v roce 1982 a dostalo název fraktály.