ESTIMATING FRACTAL DIMENSION WITH THE DIVIDER METHOD IN GEOMORPHOLOGY

In order to investigate sources of error in using the divider method to estimate the fractal dimension of geomorphic phenomena, the divider method is applied to two river channel traces, a topographic contour line and a coastline. The lines were chosen to represent a variety of types of geomorphic phenomena. Three sources of error are examined. These include the problem of the last partial step in a divider walk, of varying the starting point of a divider walk, and of nonlinearity in the relationship between measured length and steplength, and/or number of steps and steplength. The amount of error in estimates of fractal dimension that results from each of these sources is difficult to determine. Procedures that can reduce the error are identified; however, error from these sources cannot be eliminated entirely. Therefore, it is suggested that researchers use greater care when employing the divider method to produce estimates of fractal dimension for use in geomorphic analyses.