Back to the page of origin
## How long are the world’s coasts?

The estimates for the global length of coastlines found in the literature vary widely. This is not surprising because the projected length of a coast depends upon the measurement scale applied. Reference to this fact was made in an article by the mathematician Benoît Mandelbrot published in 1967 in the journal Science. In his article, entitled “How long is the coast of Britain?”, he also concluded that the answer to this question depended on the magnitude of the measurement scale selected. Using a coarser scale that does not take into account the length of shorelines in the bays, for example, results in a shorter total length. Applying a finer scale for measuring, taking into account smaller embay-
ments, gives a longer coastline. Benoît Mandelbrot later linked his work to the mathematical concept of fractals, a term also coined by him.

A fractal is a mathematical object that is constructed from a repeating structural pattern down to the smallest dimension. In this sense, a coastline can also be resolved to an infinitely fine scale. It is thus theoretically possible when measuring a coastline to include the dimensions of every pebble or sand grain that makes up the coasts. There is a difference here with respect to mathematical fractals in that the structures do not repeat identically at all size scales.

A fractal is a mathematical object that is constructed from a repeating structural pattern down to the smallest dimension. In this sense, a coastline can also be resolved to an infinitely fine scale. It is thus theoretically possible when measuring a coastline to include the dimensions of every pebble or sand grain that makes up the coasts. There is a difference here with respect to mathematical fractals in that the structures do not repeat identically at all size scales.

fig. 1.18 > The finer the scale used to measure a coastline, the greater the calculated length becomes.