Publication Date


Document Type


Committee Members

Chris Barton (Committee Chair), Mateen Rizki (Committee Member), Sarah Tebbens (Committee Member)

Degree Name

Master of Science (MS)


Previous fractal analyses of shoreline roughness have measured the fractal dimension of long segments of shoreline, e.g. Mandelbrot (1983) quantified the shoreline of the west coast of Britain and Feder (1988) quantified the shoreline of Norway. Consequently, changes in roughness along short segments are not captured by the analysis. In this study, the fractal dimension of the mainland shoreline of the contiguous United States has been measured in 125, 250, and 375 km segments using the box-counting method. The box counting method is based on the equation N = c x b where N is number of occupied boxes, C is a constant, x is box side length, and b is the fractal dimension (scaling exponent). A MATLAB code was written to measure the fractal dimension using the box-counting method. The fractal dimension measures the scaling property of a pattern not at any one length but over a range of lengths. In this study, the box-counting method counts occupied boxes over a range of box sizes along a segment of shoreline to measure the fractal dimension as it changes at different scales along the shoreline. The result is that the fractal dimension of the shoreline will continue to change as the segment length decreases. Thus, the single value of the fractal dimension reported by Richardson (1961) and Mandelbrot (1983) for the shoreline of the west coast of Britain or by Feder (1988) for the shoreline of Norway are each an approximation of the average fractal dimensions at smaller segment lengths. The shoreline analyzed in this study is the NOAA Medium Resolution Shoreline. Source map scales range from 1:10,000 to 1:600,000 with an average of 1:70,000. In the current study, sequentially numbered X-Y coordinate points in UTM Zone 18N, spaced 50 meters apart, as measured continuously along the shoreline comprised the shoreline. Fractal scaling was found on every section of the contiguous United States shoreline for each segment length (125, 250, 375 km) sampled. The range of fractal dimensions is 1.0 - 1.5. Fractal dimensions from 1.1 to 1.4 are consistently found in bays and rias. River banks have fractal dimensions ranging between 1.0-1.2, and never higher. Long stretches of smooth shoreline outside of bays that face towards open water have consistently low fractal dimensions of 1.0 to 1.1. Shorelines that double back on themselves, such as those of the Chesapeake Bay and Seattle Bay, Washington, have high fractal dimensions of 1.3 to 1.4. Low fractal dimensions were found along the Pacific shoreline, which is an emergent shoreline on a tectonically active plate margin. Low fractal dimensions are consistently measured on the Great Lakes shorelines. The high fractal dimensions observed along the Atlantic and Gulf shorelines may in part be due to high storm activity and the annual hurricane season. The Atlantic and Gulf of Mexico shorelines are both on tectonically passive margins.

Page Count


Department or Program

Department of Earth and Environmental Sciences

Year Degree Awarded