[DSRP Evidence](https://dsrpevidence.org/)

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

## Details

**Authors** Mandelbrot, Benoît B.

**Year** 1967

**Publisher** Science

**Kind of work** article

**Discipline** Mathematics

**Secondary disciplines** Geography

**Applied** false

[Read it at the publisher](https://doi.org/10.1126/science.156.3775.636) 
10.1126/science.156.3775.636

## In authors' words

### What they set out to do (purpose)

To show that the length of geographical curves such as coastlines is often undefined and to propose a measure of their complication.

### What they found (results)

Geographical curves are so involved in detail that their lengths are often infinite or undefinable. Many are statistically self-similar, each portion resembling a reduced-scale image of the whole, and a fractional quantity D, exceeding 1, describes their degree of complication.

## Commentary

### In short

The paper shows that the measured length of a coastline has no single value, because it keeps growing as finer detail is included, and offers a fractional dimension to describe this.

### Response

Self-similarity makes each part resemble the whole (system), and the measured length depends on the scale of the measuring step (perspective). Caveats: only the abstract and publisher record were read; the fit to perspectives is an inference from scale-dependence of measurement and is arguable.

**Patterns it shows** S, P

Formal proof or model

**Added** 2026-10-26

**How to cite this** Mandelbrot, Benoît B. (1967). How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science.