J. B. Bassingthwaighte, D. A. Beard, D. B. Percival and G. M. Raymond (1996), `Fractal Structures and Processes,' in Chaos and the Changing Nature of Science and Medicine: An Introduction (AIP Conference Proceedings, No. 376), edited by D. E. Herbert, Woodbury, New York: AIP Press, pp. 54-79.
Fractals and chaos are closely related. Many chaotic systems have fractal features. Fractals are self-similar or self-affine structures, which means that they look much the same when magnified or reduced in scale over a reasonably large range of scales, at least two orders of magnitude and preferably more (Mandelbrot, 1983). The methods for estimating their fractal dimensions or their Hurst coefficients, which summarize the scaling relationships and their correlation structures, are going through a rapid evolutionary phase. Fractal measures can be regarded as providing a useful statistical measure of correlated random processes. They also provide a basis for analyzing recursive processes in biology such as the growth of arborizing networks in the circulatory system, airways, or glandular ducts.
Arborizing networks growth; Circulatory system; Correlated random processes; Glandular ducts; Hurst coefficient; Self-affine structures; Self-similar structures
Go to next summary or home page for Don Percival