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) and sometimes known as the Richardson effect (Mandelbrot 1983, p. 28). 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).

REFERENCES

Gleick, J. Chaos: Making a New Science. New York: Penguin Books, pp. 94-95, 1988.

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

Mandelbrot, B. B. "How Long Is the Coast of Britain." Ch. 5 in The Fractal Geometry of Nature. New York: W. H. Freeman, pp. 25-33, 1983.

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 109-110, 1999.