Overview
- Authors:
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James B. Bassingthwaighte
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Center for Bioengineering, University of Washington, Seattle, USA
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Larry S. Liebovitch
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Center for Complex Systems, Florida Atlantic University, Boca Raton, USA
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Bruce J. West
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Physics Department, University of North Texas, Denton, USA
- This volume delineates the use of fractal patterns and measures of fractal dimensions in describing and understanding general aspects of biology, particularly human physiology
- After describing the ubiquitous nature of fractal phenomena, the authors give examples of the properties of fractals in space and time
- Proceeding from mathematical definitions, they develop detailed practical methods for assessing the fractal characteristics of wave forms varying with time, tissue density variation, and surface irregularities
- Most importantly, the authors show how fractal variation defines internal spatial or temporal correlations within the fractal system or object
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Table of contents (13 chapters)
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Overview
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 3-7
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Properties of Fractals and Chaos
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 11-44
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 45-62
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 63-107
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 108-135
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 136-146
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 147-173
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Physiological Applications
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Front Matter
Pages 175-175
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 177-209
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 210-235
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 236-262
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 263-284
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 285-299
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- James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Pages 300-327
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Back Matter
Pages 328-364
About this book
I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.
