Fractals in physical geography

Abstract

Since the fractal concept was introduced to measuring coastline length over three decades ago, fractal analysis has been prolifically applied to many topographic studies. A number of mathematical algorithms are now available to determine the fractal dimension for both linear and areal features. These determination methods require one or more straight-line segments to fit the Richardson's plot. A close examination of the literature shows that not all topographic features are fractal at all scales studied. While the multifractal nature of some geographical phenomena has been explored in great depth, it is not completely understood why some terrains are better modelled with fractal geometry than others. Fractal analysis has been successfully used to measure and characterize irregular linear features such as coastlines and shorelines, to describe and characterize landforms, and to delineate landform regions statistically. Fractal analysis can also be used to produce terrain simulations with a known dimension against which hypotheses can be tested. These studies fail to link fractal dimensions to the underlying geomorphic processes. The failure stems from the fact that there is no one-to-one relationship between geomorphic processes and the landforms they shape.