Research On The Length of Coastlines and Borders
While studying the causes of war between two countries, Richardson decided to search for a relation between the probability of two countries going to war and the length of their common border. While collecting data, he realised that there was considerable variation in the various gazetted lengths of international borders. For example, that between Spain and Portugal was variously quoted as 987 or 1214 km while that between the Netherlands and Belgium as 380 or 449 km.
As part of his research, Richardson investigated how the measured length of a border changes as the unit of measurement is changed. He published empirical statistics which resulted in a conjectured relationship. This research was quoted by mathematician Benoît Mandelbrot in his 1967 paper How Long Is the Coast of Britain?
Suppose the coast of Britain is measured using a 200 km ruler, specifying that both ends of the ruler must touch the coast. Now cut the ruler in half and repeat the measurement, then repeat again:
Notice that the smaller the ruler, the larger the result. It might be supposed that these values would converge to a finite number representing the "true" length of the coastline. However, Richardson demonstrated that the measured length of coastlines and other natural features appears to increase without limit as the unit of measurement is made smaller. This is known nowadays as the Richardson effect.
At the time, Richardson's research was ignored by the scientific community. Today, it is considered an element of the beginning of the modern study of fractals.
Read more about this topic: Lewis Fry Richardson
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