• DOI:10.1126/science.156.3775.636
Corpus ID: 15662830

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

@article{Mandelbrot1967HowLI,
  title={How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension},
  author={B. Mandelbrot},
  journal={Science},
  year={1967},
  volume={156},
  pages={636 - 638}
}

• B. Mandelbrot
• Published 1967
• Medicine, Mathematics
• Science

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.