How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension¶
Mandelbrot, B. (1967). How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 156(3775), 636-638.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Fractal Geometry
- A coastline is fractal, as Mandelbrot (1967) originally argued in Science, from meters to perhaps hundreds of kilometers, not at molecular scales (where solid-mechanics smoothness dominates) and not at continental scales (where tectonic-plate structure dominates).
Supported in partVerified against the publisher's abstract
Mandelbrot's 1967 Science abstract backs self-similarity and a fractional dimension for geographical curves, but is silent on the claim's finite scale range and its excluded molecular and continental regimes.
“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”
- A coastline is fractal, as Mandelbrot (1967) originally argued in Science, from meters to perhaps hundreds of kilometers, not at molecular scales (where solid-mechanics smoothness dominates) and not at continental scales (where tectonic-plate structure dominates).
- Scale
Domain-specific¶
- Coastline Paradox
- The coastline paradox is the observation, originating with Lewis Fry Richardson (1961) and given mathematical form by Benoît Mandelbrot in his 1967 paper "How Long Is the Coast of Britain?"
This sourceMandelbrot's estimate of D = 1.25 for the west coast of Great Britain. Mandelbrot (1967) reports Richardson's finding that measured length grows as the measuring unit shrinks, and that reference works disagree about how long a border is.
Supported in partVerified against a saved copy of the source
“Such a formula, of an entirely empirical character, was proposed by Lewis F. Richardson (2) but unfortunately it attracted no attention.”
- The coastline paradox is the observation, originating with Lewis Fry Richardson (1961) and given mathematical form by Benoît Mandelbrot in his 1967 paper "How Long Is the Coast of Britain?"
Verification¶
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