Fractal Dimension of a Coral Reef at Ecological Scales

Abstract

Conventional analytical techniques do not cope adequately with multiscale processes. Mandelbrot's concept of fractal dimension, a novel approach to multiscale phenomena, is applied to the problem of coral reef topography. A fractal dimension D = 1.9-2.0 for a contour on the reef slope is obtained. This contrasts strongly with the well established value of D = 1.2-1.3 for coastlines. We speculate that in common with the human lung, another living surface with a high D value, the coral reef slope is maximizing its contact with the surrounding medium.