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

Science  05 May 1967:
Vol. 156, Issue 3775, pp. 636-638
DOI: 10.1126/science.156.3775.636


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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