## Description

The overlapping variation method algorithm is a restructuring of the standard variation method for estimating fractal dimensions as proposed by Benoit Dubuc in 1989. This restructuring was created to remove redundant computations from the variation method algorithm when attempting to compute many fractal dimension estimates for regions where the fractal windows overlap. Thus the overlapping variation method is more computationally efficient at computing overlapping fractal windows of a Digital Elevation Model or DEM in two dimensions than a brute force approach using the variation method. The algorithm opens up the possibility of handling much larger DEMs than was previously possible. This is accomplished by reducing the number of comparisons needed to compute the variation in surface roughness of the DEM by one to two orders of magnitude. This thesis focuses on DEMs of large areas of coral reefs as its primary data set. This is one of many possible applications of the overlapping variation method where researchers are interested in how the surface roughness varies from region to region. The result is the new algorithm can compute large sets of fractal dimension estimates one to two orders of magnitude faster than by using the standard variation method to compute the same data. Further the concept of data parallelization is applied to allow computation speed to scale with available resources. This two pronged approach to generating multiple fractal dimension estimates allows us to generate data in days instead of months or years