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

1967/05/05 by Benoît B. Mandelbrot · 11 citations
Economics, Econometrics and Finance · Computer Science · Environmental Science · #Complex Systems and Time Series Analysis #Geochemistry and Geologic Mapping #Soil Geostatistics and Mapping

paper · doi:10.1126/science.156.3775.636

openalex publication_date 1967/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• The Variation of Certain Speculative Prices

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• Benoit Mandelbrot [wikipedia]
• Coast [wikipedia]
• Fractal [wikipedia]
• Fractal dimension [wikipedia]