Fractal geometry : mathematical foundations and applications

Bibliographic Information

Fractal geometry : mathematical foundations and applications

Kenneth Falconer

Wiley, c1990

  • : hbk
  • : pbk

Available at  / 108 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 278-283) and index

Description and Table of Contents

Volume

: hbk ISBN 9780471922872

Description

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.

Table of Contents

FOUNDATIONS. Mathematical Background. Hausdorff Measure and Dimension. Alternative Definitions of Dimension. Techniques for Calculating Dimensions. Local Structure of Fractals. Projections of Fractals. Products of Fractals. Intersections of Fractals. APPLICATIONS AND EXAMPLES. Fractals Defined by Transformations--Self-Similar and Self-Affine Sets. Examples from Number Theory. Graphs of Functions. Examples from Pure Mathematics. Dynamical Systems. Iteration of Complex Functions--Julia Sets. Random Fractals. Brownian Motion and Brownian Surfaces. Multifractal Measures. Physical Applications. References. Index.
Volume

: pbk ISBN 9780471967774

Description

This paperback edition of Fractal Geometry provides an accessible treatment of the mathematics of fractals and their dimensions. It is aimed at those wanting to use fractals in their own areas of mathematics or science. The first part of the book covers the general theory of fractals and their geometry. Results are stated precisely, but technical measure theoretic ideas are avoided and difficult proofs are sketched. The second part contains a wide variety of examples and applications in mathematics and physics. The book contains numerous diagrams and illustrative examples. Each chapter ends with self-study exercises and suggestions for further reading. The author provides an intuitive as well as a mathematical insight into the subject.

Table of Contents

  • Part I Foundations: mathematical background
  • Hausdorff measure and dimension
  • alternative definitions of dimension
  • techniques for calculating dimensions
  • local structure of fractals
  • projections of fractals
  • products of fractals
  • intersections of fractals. Part II Applications and examples: fractals defined by transformations
  • examples from number theory
  • graphs of functions
  • examples from pure mathematics
  • dynamical systems
  • iteration of complex functions-Julia sets
  • random fractals
  • Brownian motion and Brownian surfaces
  • multifractal measures
  • physical applications.

by "Nielsen BookData"

Details

  • NCID
    BA07951784
  • ISBN
    • 0471922870
    • 0471967777
  • LCCN
    89037981
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Chichester, West Sussex, England
  • Pages/Volumes
    xxii, 288 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
Page Top

AltStyle によって変換されたページ (->オリジナル) /