Fractals : a user's guide for the natural sciences
著者
書誌事項
Fractals : a user's guide for the natural sciences
（Oxford science publications）
Oxford University Press, 1993
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: pbk ISBN 9780198545972
内容説明
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.
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
- 巻冊次
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ISBN 9780198545989
内容説明
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.
目次
- PART I. INTRODUCTION: OUR VIEW OF NATURE
- PART II. THE MATHEMATICS OF RANDOM FRACTALS: FRACTALS AND POWER LAW SCALING
- PART III. THE BRIDGE TO APPLICATIONS: MODELLING SPATIAL AND TEMPORAL PATTERNS
- PART IV. CASE STUDIES: PATTERN AND PROCESS IN VEGETATIVE ECOSYSTEMS
- PART V. THE TOOLBOX: PROGRAMS/ANNOTATED REFERENCES
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