Tests Of A Fractal Model Of Topography

This thesis tested a fractal model of topography using a variety of measurement techniques (including the variogram method, the cell counting method, and the dividers method) applied to a range of surface types. The methods were first tested for reliability and accuracy by applying them to simulated surfaces of known fractal dimensions. Then, the methods were applied to 58 datasets obtained from U.S.G.S. Digital Elevation Models which covered 9 physiographic provinces in the United States.;The fractal model was found to be a valid model. It fit some topographic datasets well but did not consistently fit all datasets. The fractal dimension was found to vary depending on elevation, direction, and sample size. Those methods which were applied to individual contours were found to consistently produce different dimensions than those methods which were applied to the surfaces. However, it was found that the physiographic provinces could be statistically distinguished using the fractal dimension (D). In addition, it was discovered that the intercepts obtained from the variogram analyses could also be used to separate landform types.;An interesting result of this thesis research was that the fractal model analyses brought to light differences within physiographic provinces that were otherwise not visible using traditional morphometric parameters.;New avenues of research have been identified as a result of the findings of this research