HOW LONG IS COAST OF BRITAIN - STATISTICAL SELF-SIMILARITY AND FRACTIONAL DIMENSION
HOW LONG IS COAST OF BRITAIN - STATISTICAL SELF-SIMILARITY AND FRACTIONAL DIMENSION
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DOI：
10.1126/science.156.3775.636
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发表时间：
1967-01-01
期刊：
影响因子：
56.9
通讯作者：
MANDELBROT, B
中科院分区：
文献类型：
--
作者：
MANDELBROT, B
地理曲线的细节如此复杂，以至于它们的长度往往是无限的，或者更确切地说，是无法定义的。然而，许多是统计上的“自相似”，这意味着每个部分可以被认为是整体的缩小比例的图像。在这种情况下，复杂程度可以用一个数量D来描述，这个数量D具有“维数”的许多性质，尽管它是分数的;也就是说，它超过了与普通的、可求长的曲线相关联的值单位。
Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "self-similar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantityDthat has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves.