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Fractals: A User's Guide for the Natural Sciences

1 rating: 3.0
A book by Harold M. Hastings

'take the novitiate in a given discipline through the subtleties of fractal dimension, random fractals, Hurst exponents and so on, in a way that illuminates the field of study, thereby making it a working tool for the would be practitioner ... an excellent … see full wiki

Author: Harold M. Hastings
Publisher: Oxford University Press, USA
1 review about Fractals: A User's Guide for the Natural...

For mathematicians, not for beginners

  • Jan 7, 2007
The rise of fractal processes is the result of success and failure. It has been known for decades that continuous models were inadequate to simulate many phenomena. To paraphrase Benoit Mandelbrot, the father of fractals, "clouds are not spheres, mountains are not cones and trees are not lollipops." However, there were very few alternatives. Some early work on structures now recognized as fractal was done decades ago, but technical factors limited the scope. It was necessary for inexpensive computers and graphical devices to arise before fractals could truly be explored. The confluence of these two forces has led to a flood of work on fractals, the consequences of which will not be known for many years to come. However, it is clear that some knowledge of fractals is rapidly becoming a requirement in many disciplines, from physics to economics.
The authors here eschew a popular treatment of fractals, relying on mathematical explanations with few pictures. One immediately realizes that it is a scholarly work when a quick scan reveals that there are no color plates. Applications are used throughout. Earthquakes, pancreatic islets, temperature variations, rainfall data and vegetative ecosystems are some of the topics examined using fractals. But be prepared to perform some mathematics if you wish to understand.
And that is the outstanding feature of this book. There are a growing number of popular mathematics books that contain sections on fractals. Unfortunately, it is always more of the same. A description of the generation of the Mandelbrot and Julia sets, with color pictures. This book is designed to teach the working scientist the techniques needed to apply fractal models to their specific discipline. The mathematics is hard, complete and applicable. Listings of the many programs used to generate fractals are at the end of the book and the language is Turbo Pascal.
If your goal is to learn fractals for scientific applications, then this is the book for you. Otherwise, your best choice is one of the many popular books that use verbal explanations.

Originally published in School Science and Mathematics, reprinted with permission.

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