The Fractal Nature of Planetary Landforms and Implications to Geologic Mapping

The primary product of planetary geologic and geomorphologic mapping is a group of lines and polygons that parameterize planetary surfaces and landforms. Many different research fields use those shapes to conduct their own analyses, and some of those analyses require measurement of the shape's perimeter or line length, sometimes relative to a surface area. There is a general lack of discussion in the relevant literature of the fact that perimeters of many planetary landforms are not easily parameterized by a simple aggregation of lines or even curves, but they instead display complexity across a large range of scale lengths; in fewer words, many planetary landforms are fractals. Because of their fractal nature, instead of morphometric properties converging on a single value, those properties will change based on the scale used to measure them. Therefore, derived properties can change—in some cases, by an order of magnitude or more—just when the measuring length scale is altered. This can result in significantly different interpretations of the features. Conversely, instead of a problem, analysis of the fractal properties of some landforms has led to diagnostic criteria that other remote sensing data cannot easily provide. This paper outlines the basic issue of the fractal nature of planetary landforms, gives case studies where the effects become important, and provides the recommendation that geologic mappers consider characterizing the fractal dimension of their mapped units via a relatively simple, straightforward calculation.