Units of measurement for fractal extent, applied to the coastal distribution of bald eagle nests in the Aleutian Islands, Alaska

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Abstract
Attempts to measure the nesting density or territory size of bald eagles led to a fundamental difficulty, inherent in all such measurements on organisms which are distributed along an irregular boundary, such as a coastline. The “length” of such a boundary is not a meaningful measure, and neither can a meaningful “area” be associated with each nest. Mandelbrot's (1983) fractal geometry applies to the problem, but has not previously supplied practical units of measurement for fractals such as coastlines or rugged surfaces. A practical method is given for measuring the “extent” of such fractals, introducing a unit of variable dimension, the “metron”, which includes the existing SI units of length, area and volume as special cases. A linear measure, the “spacing” allows densities on fractals of different dimensions to be compared directly. The method is applied to the distribution of bald eagle nests along the coastlines of two islands in the Aleutians, and an extension of the method to handle distributions on mountainsides and island surfaces is indicated.