无处不在的分形

出版时间：2009-1  出版社：世界图书出版公司  作者：巴恩斯利  页数：531  
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内容概要

Credlts for Figures and Color Plates Much has changed in the world of fractals, computer graphics and modem mathematics since the first edition of Fractals Everywhere appeared. The company Iterated Systems, Inc., founded by Michael Barnsley and Alan Sloan, is now competing in the image compression field with both hardware and software products that use fractal geometry to compress images. Indeed, there is now a plethora of texts on subjects like fractals and chaos, and these terms are rapidly becoming "household words.

作者简介

作者：(英国)巴恩斯利 (Barnsley.M.F)

书籍目录

Foreword.AcknowledgmentsChapter Ⅰ IntroductionChapter Ⅱ  Metrlc Spaces; Equlvolent Spaces; Clossificatlon of Subsets; and the Space of Froctols  1.Spaces  2.Metric Spaces  3.Cauchy Sequences, Limit Points, Closed Sets, Perfect Sets, and Complete Metric Spaces  4.Compact Sets, Bounded Sets, Open Sets, Interiors, and Boundaries  5.Connected Sets, Disconnected Sets, and Pathwise- Connected Sets  6.The Metric Space (74(X), h): The Place Where Fractals Live  7.The Completeness of the Space of Fractals  8.Additional Theorems about Metric SpacesChapter Ⅲ  Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals  1.Transformations on the Real Line  2.Affine Transformations in the Euclidean Plane  3.MObius Transformations on the Riemann Sphere  4.Analytic Transformations  5.How to Change Coordinates  6.The Contraction Mapping Theorem  7.Contraction Mappings on the Space of Fractals  8.Two Algorithms for Computing Fractals from Iterated Function Systems  9.Condensation Sets  10.How to Make Fractal Models with the Help of the Collage Theorem  11.Blowing in the Wind: The Continous Dependence of Fractals on ParametersChapter Ⅳ  Chaotic Dynamics on Fractals  1.The Addresses of Points on Fractals  2.Continuous Transformations from Code Space to Fractals  3.Introduction to Dynamical Systems  4.Dynamics on Fractals: Or How to Compute Orbits by Looking at Pictures  5.Equivalent Dynamical Systems  6.The Shadow of Deterministic Dynamics  7.The Meaningfulness of Inaccurately Computed Orbits is Established by Means of a Shadowing Theorem  8.Chaotic Dynamics on FractalsChapter Ⅴ  Fractal Dimension  1.Fractal Dimension  2.The Theoretical Determination of the Fractal Dimension  3.The Experimental Determination of the Fractal Dimension  4.The Hausdorff-Besicovitch DimensionChapter Ⅵ  FrocIoI Interpolation  1.Introduction: Applications for Fractal Functions  2.Fractal Interpolation Functions  3.The Fractal Dimension of Fractal Interpolation Functions  4.Hidden Variable Fractal Interpolation  5.Space-Filling CurvesChapter Ⅶ  Julia Sets  1.The Escape Time Algorithm for Computing Pictures of IFS Attractors and Julia Sets  2.Iterated Function Systems Whose Attractors Are Julia Sets  3.The Application of Julia Set Theory to Newton's Method  4.A Rich Source for Fractals: Invariant Sets of Continuous Open MappingsChapter Ⅷ  Parameter Spaces and Mandelbrot Sets  1.The Idea of a Parameter Space: A Map of Fractals  2.Mandelbrot Sets for Pairs of Transformations  3.The Mandelbrot Set for Julia Sets  4.How to Make Maps of Families of Fractals Using Escape TimesChapter Ⅸ  Measures on Fractals  1.Introduction to Invariant Measures on Fractals  2.Fields and Sigma-Fields  3.Measures  4.Integration  5.The Compact Metric Space (79(X), d)  6.A Contraction Mapping on (P(X))  7.Elton's Theorem  8.Application to Computer GraphicsChapter Ⅹ  Recurrent Iterated Function Systems  1.Fractal Systems  2.Recurrent Iterated Function Systems  3.Collage Theorem for Recurrent Iterated Function Systems  4.Fractal Systems with Vectors of Measures as Their Attractors  5.ReferencesReferencesSelected AnswersIndex

章节摘录

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《无处不在的分形(第2版)》由世界图书出版公司出版。

用户评论 (总计6条)

•   应该不错，但很专业，如果只是对分形感兴趣想了解下，还是算了
•   内容很好，涉及到了自己需要的方面。
•   认为书不错
•   刚买完就碰上搞活动 真想退了重买
•   真心有点难
•   书的内容很好，只是图片印刷质量太差。分形图本来是很优美的图像，结果印刷的很难看。