Fractals : a user's guide for the natural sciences

Harold M. Hastings and George Sugihara

A unique explanation of how to use fractal geometry in ecology and biology. Beginning with the foundations of measurement in Euclidian geometry, this book progresses from analogues in the geometry of random fractals to illustrative applications spanning the natural sciences. Designed to enable students and researchers to master the methods of this hot current topic, it: Includes a toolbox of user-ready computer programs Provides a blend of motivation, geometry and detailed applications Presents detailed case studies in ecosystem patterns and fluctuations of small populations It is the only guide to using fractals in these areas and will prove an essential source for all natural scientists interested in working with fractals.

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Fractals: A User's Guide for the Natural Sciences explains Mandelbrot's fractal geometry and describes some of its applications in the natural world. Written to enable students and researchers to master the methods of this timely subject, the book steers a middle course between the formality of many papers in mathematics and the informality of picture-oriented books on fractals. It is both a logically developed text and a 'fractals for users' handbook. Fractal geometry exploits a characteristic property of the real world self-similarity - to find simple rules for the assembly of complex natural objects. Beginning with the foundations of measurement in Euclidean geometry, the authors progress from analogues in the geometry of random fractals to illustrative applications spanning the natural sciences: the developmental biology of neurons and pancreatic islets; fluctuations of bird populations; patterns in vegetative ecosystems; and even earthquake models. The final section provides a toolbox of user-ready programs. This volume is an essential resource for all natural scientists interested in working with fractals.

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[目次]

  • PART I. INTRODUCTION: OUR VIEW OF NATURE
  • PART II. THE MATHEMATICS OF RANDOM FRACTALS: FRACTALS AND POWER LAW SCALING
  • 1. Dimension of graphs of functions
  • 2. The Fourier transform
  • PART III. THE BRIDGE TO APPLICATIONS: MODELLING SPATIAL AND TEMPORAL PATTERNS
  • 3. Alternative models
  • 4. Examples
  • 5. Fractal analysis of time series
  • PART IV. CASE STUDIES: PATTERN AND PROCESS IN VEGETATIVE ECOSYSTEMS
  • 6. Scaling behaviour of density-dependent populations under random noise
  • PART V. THE TOOLBOX: PROGRAMS/ANNOTATED REFERENCES
  • Index

「Nielsen BookData」より

[目次]

  • I. INTRODUCTION. OUR VIEW OF NATURE
  • II. THE MATHEMATICS OF RANDOM FRACTALS. FRACTALS AND POWER LAW SCALING
  • 1. Dimension of graphs of functions
  • 2. The Fourier transform
  • 3. Alternative models
  • 4. Examples
  • 5. Fractal analysis of time series
  • IV. CASE STUDIES. PATTERN AND PROCESS IN VEGETATIVE ECOSYSTEMS
  • 6. Scaling behaviour of density-dependent populations under random noise
  • V. THE TOOLBOX. PROGRAMS/ANNOTATED REFERENCES
  • Index

「Nielsen BookData」より

この本の情報

書名 Fractals : a user's guide for the natural sciences
著作者等 Hastings, Harold M.
Sugihara, G.
Sugihara George
シリーズ名 Oxford science publications
出版元 Oxford University Press
刊行年月 1993
ページ数 xi, 235 p.
大きさ 24 cm
ISBN 0198545975
0198545983
NCID BA21393754
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言語 英語
出版国 イギリス
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