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

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

May 1967

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1967sci...156..636m&link_type=abstract

Science, Volume 156, Issue 3775, pp. 636-638

Computer Science

148

Scientific paper

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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