Fractals: A User's Guide for the Natural Sciences

Fractals: A User's Guide for the Natural Sciences

by Harold M. Hastings, George Sugihara, Harold M. Hartings
     
 

ISBN-10: 0198545975

ISBN-13: 9780198545972

Pub. Date: 01/27/1994

Publisher: Oxford University Press, USA


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…  See more details below

Overview


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:
01/27/1994
Pages:
248
Product dimensions:
6.13(w) x 9.25(h) x 0.57(d)

Table of Contents

1Our view of nature7
2Fractals and power law scaling15
3Dimension of patterns36
4Dimension of graphs of functions56
5The Fourier transform62
6Modelling spatial and temporal patterns81
7Alternative models91
8Examples100
9Fractal analysis of time series109
10Case studies: pattern and process in vegetative ecosystems119
11Case study: scaling behaviour of density-dependent populations under random noise138
12Programs163
Annotated references225
Index233

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