ARE MARSH SHORELINES FRACTAL?

Over the past twenty years, fractal geometry has gained acceptance as a valid method in describing complex patterns in nature. An important property of any fractal pattern is that it retains its complexity at different scales. The geometry of a shoreline is often cited as an example of a fractal pattern (e.g., Richardson, 1960; Mandelbrot, 1967; Simon and Simon, 1995; Jiang and Plotnick, 1998). As such, when the length of a shoreline is measured, the calculated distance will depend on the scale of the measuring device. Theoretically, the length of a shoreline would become infinite with an infinitely small measuring device. Previous studies on shoreline geometries have used relatively small-scale nautical charts, topographic maps, and aerial photographs (e.g., 1:625,000; 1:40,000; 1:10,000). In addition, the fractal nature of a changing shoreline geometry due to erosion has not been examined. This study, in contrast, investigates the fractal nature of six marsh shorelines in Rehoboth Bay, DE using very precise surveying equipment. This method produces relative large-scale maps on the order of 1:80, and detailed shoreline positions with a precision of about ± 4 cm. In addition, multiple surveys of the same shorelines, revealing erosional changes over a three-year period, provide a unique opportunity to investigate whether the fractal nature of a shoreline changes with time. Using the box-counting method, and ten different cell sizes, five fractal D values were calculated for each site (thirty in all) that range from 0.90 to 1.10, with a mean of 1.01. For each site, these values do not significantly change over time. Therefore, the data support the conclusion that these marsh shorelines do not represent a fractal geometry nor do they become fractal over time.