For an object to be considered a fractl, two requirements 一个对象可以被认为是一个分形，两个要求.docVIP

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For an object to be considered a fractl, two requirements 一个对象可以被认为是一个分形，两个要求.doc

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For an object to be considered a fractl, two requirements 一个对象可以被认为是一个分形，两个要求

Patterns within patterns: fractals and landscape ecology What are fractals? A central goal of landscape ecology is to detect patterns through space or time and to extrapolate those patterns across multiple scales (Urban et al. 1987, Turner 1989, Turner et al., 2001). Fractal geometry is a method used to aid in achieving these goals. This method is valuable to the field of landscape ecology not only because few tools are currently available that explicitly address and measure scale, but it additionally allows investigators to generalize a pattern across a range of scales. This detection of patterns can then enable investigators to entertain questions concerning the processes creating the observed patterns and to look for these processes at the appropriate scales. Analytically, the fractal dimension (D) is derived from the slope of a double log plot and describes shape complexity. It is a statistical descriptor like the mean and mode and therefore does not necessarily explain the process in question. Rather, it provides a way of describing a geometric shape. Any linkages made between D and an ecological process results from experiments studying the process of interest, not from D alone. For an object to be considered fractal, two requirements must be met. The first requirement is that a fractal must be “a shape made of parts similar to the whole in some way” (Mandelbrot 1986). As the grain of measurement increases or decreases for the self-similar object, the shape or pattern tends to repeat itself. Mandelbrot developed a broad definition for fractal geometry because of its usefulness as an analytical tool in fields such as physics, biology, mathematics and ecology. Furthermore, the definition purposely does not differentiate between exactly self-similar objects or statistically self-similar objects. Exact self-similar structures, such as the Sierpinski carpet and triangle (figure 1), only exist in the mathematical sense. In nature, there is an inher