Fractals: A User's Guide for the Natural Sciences

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This insightful work explains Mandelbrot's fractal geometry and describes some of its most interesting applications. 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 applications spanning the natural sciences, including the developmental biology of neurons and pancreatic islets, fluctuations of bird populations, patterns in vegetative ecosystems, and even earthquake models. 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-orientated books on fractals. It is both a logically developed text and an essential "fractals for users" handbook. It is an essential resource for researchers and students in ecology, biology, applied mathematics, and plant and environmental sciences.

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Product Details

  • ISBN-13: 9780198545972
  • Publisher: Oxford University Press, USA
  • Publication date: 1/27/1994
  • Pages: 248
  • Product dimensions: 6.13 (w) x 9.25 (h) x 0.57 (d)

Meet the Author

Hofstra College

Scripps Institute of Oceanography, La Jolla, California

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Table of Contents

1 Our view of nature 7
2 Fractals and power law scaling 15
3 Dimension of patterns 36
4 Dimension of graphs of functions 56
5 The Fourier transform 62
6 Modelling spatial and temporal patterns 81
7 Alternative models 91
8 Examples 100
9 Fractal analysis of time series 109
10 Case studies: pattern and process in vegetative ecosystems 119
11 Case study: scaling behaviour of density-dependent populations under random noise 138
12 Programs 163
Annotated references 225
Index 233
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