ABSTRACT
As stated by Hastings and Sugihara (1993), the rst key steps in fractal analysis are (1) the choice of an appropriate power law, (2) the application of log transforms, and (3) the use of linear regression to t a log-transformed linear model. In Chapters 3 and 4, we thus summarize some of the more commonly used methods, together with more original ones, for estimating the fractal dimension DF of both self-similar and self-afne natural objects. Formal mathematical derivations and proofs have been omitted; readers interested in fractal theory should consult Mandelbrot (1983), Voss (1985, 1988), Falconer (1985, 1993), Frontier (1987), Feder (1988), Sugihara and May (1990a), Schroeder (1991), Peitgen et al. (1992), Hastings and Sugihara (1993), Tricot (1995), and Gouyet (1996). Note, however, that some of the methods used to estimate the fractal dimension are empirically, not mathematically, derived. Other reviews that have summarized fractal dimension estimation methods include Loehle (1983), Frontier (1987), Milne (1988, 1991), Kaye (1989, 1994), Williamson and Lawton (1991), Kenkel and Walker (1993), Klinkenberg (1993), Nonnenmacher et al. (1994), Johnson et al. (1995), and Seuront (1998). Most of these reviews have been somewhat selective or have focused on a specic subdiscipline within the biological sciences. The diversity of available approaches for determining the fractal dimension reects differences in objectives and in the type of data analyzed.
