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Coastline Paradox

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953). In fact, the answer depends on the length of the Ruler you use for the measurements. A shorter Ruler measures more of the sinuosity of bays and inlets than a larger one, so the estimated length continues to increase as the Ruler length decreases.

In fact, a coastline is an example of a Fractal, and plotting the length of the Ruler versus the measured length of the coastline on a log-log plot gives a straight line, the slope of which is the Fractal Dimension of the coastline (and will be a number between 1 and 2).


Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 29-31, 1991.

© 1996-9 Eric W. Weisstein