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Science 5 May 1967:
Vol. 156. no. 3775, pp. 636 - 638
DOI: 10.1126/science.156.3775.636
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Articles

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

Benoit Mandelbrot 1

1 International Business Machines, Thomas J. Watson Research Center, Yorktown Heights, New York 10598

Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," 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 D that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves.


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