How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

DOI Web Site 被引用文献39件
  • Benoit Mandelbrot
    International Business Machines, Thomas J. Watson Research Center, Yorktown Heights, New York 10598

説明

<jats:p> 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 quantity <jats:italic>D</jats:italic> that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves. </jats:p>

収録刊行物

  • Science

    Science 156 (3775), 636-638, 1967-05-05

    American Association for the Advancement of Science (AAAS)

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