How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
- 5 May 1967
- journal article
- other
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 156 (3775) , 636-638
- https://doi.org/10.1126/science.156.3775.636
Abstract
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 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.Keywords
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