Overview
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. Simple, recursively applied rules can give rise to complex biological structures by a variety of methods. This suggests that genetic rules govern the general structuring of an organism, while rules implied by interactions at the biochemical, cellular, and tissue levels govern ontogenic development and therefore play the major role in the growth of an organism. Chaos, or non-linear dynamics, is introduced as a stimulating way to examine biological behavior at the cellular and whole animal levels, even though proof of the chaotic nature of normal physiologic events is as yet meager. The later chapters give sets of examples of structural and behavioral fractal phenomena in nerve and muscle, in the cardiovascular and respiratory systems and in growth processes. Why molecular interactions and complex systems give rise to fractals is explored and related to the ideas of emergent properties of systems operating at high levels of complexity.
The book contains black-and-white illustrations.
Editorials
From The Critics
Reviewer: William R. Law, PhD(University of Illinois at Chicago College of Medicine)Description: This book in the series Methods in Physiology deals with the complex field of fractals, or the mathematics of "chaos," as it applies to physiological systems.
Purpose: Its purpose is twofold. In the first part, properties of fractals and chaos are described and illustrated, providing a common ground knowledge base for its audience. In the second part, physiological applications are presented, along with new knowledge that has come from such applications.
Audience: The authors suggest, and I agree, that this book is written for research professionals and students who have had at least some calculus. Although targeted toward medical biologists, I believe the book would be of equal value to those in the fields of mathematics and bioengineering who are searching for physiological applications in their disciplines.
Features: The graphics used are clear and highlight particular concepts very well. Equations are presented in an easily read format, and the chapters are divided into logical sections that help organize ideas for the reader. The references are current. The book has a clean, professional appearance.
Assessment: This is an excellent book in its clear writing, thorough coverage of the topic, and timeliness. This emerging field of study is proving to be of immense importance, yet it is still a mystery to most medical biologists. This book represents a fine first step in clarifying a complex idea for professionals who will need it in the future. It belongs in the hands of every medical biologist and should be a part of every academic medical library.
William R. Law
This book in the series Methods in Physiology deals with the complex field of fractals, or the mathematics of chaos, as it applies to physiological systems. "Its purpose is twofold. In the first part, properties of fractals and chaos are described and illustrated, providing a common ground knowledge base for its audience. In the second part, physiological applications are presented, along with new knowledge that has come from such applications. "The authors suggest, and I agree, that this book is written for research professionals and students who have had at least some calculus. Although targeted toward medical biologists, I believe the book would be of equal value to those in the fields of mathematics and bioengineering who are searching for physiological applications in their disciplines. "The graphics used are clear and highlight particular concepts very well. Equations are presented in an easily read format, and the chapters are divided into logical sections that help organize ideas for the reader. The references are current. The book has a clean, professional appearance. "This is an excellent book in its clear writing, thorough coverage of the topic, and timeliness. This emerging field of study is proving to be of immense importance, yet it is still a mystery to most medical biologists. This book represents a fine first step in clarifying a complex idea for professionals who will need it in the future. It belongs in the hands of every medical biologist and should be a part of every academic medical library.5 Stars! from Doody