Fractal PhysiologyThis 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. |
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algorithm analysis application approach approximately attractor average behavior branching calculated called cells changes channel chaos chaotic Chapter closed complex constant continuous correlation curve defined density depends described determine dispersion distribution dynamics effective energy equal equation estimates et al example experimental Figure flow fluctuations fractal dimension frequency function given gives growth heart heterogeneity histograms increases independent initial intervals ion channel iteration kinetic length Mandelbrot mathematical mean measured mechanisms method nature neurons noise object observed organ original panel parameters patterns period phase space set physical physiological pieces plot potential power law probability processes produce properties protein random range regions relationship relative resolution result rules scaling self-similarity shown in Fig signal similar simple single slope spatial statistical structure surface unit values variables variation versus