Mathematics – Logic
Scientific paper
Aug 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005dps....37.3209g&link_type=abstract
American Astronomical Society, DPS meeting #37, #32.09; Bulletin of the American Astronomical Society, Vol. 37, p.687
Mathematics
Logic
Scientific paper
Prior research is equivocal on the existence and location of Martian coastlines. This study proposes a novel method of analyzing putative coastlines; fractal dimensions provide a quantitative measurement of the complexity and nature of a fractal. Geological evidence points to a coastline at the elevation of -3790 meters, called the Deuteronilus contact. It is hypothesized that the fractal dimensions of this putative Martian coastline will be comparable to those of Earth shorelines. A topographic map with a contour line at -3790 meters was obtained from the U. S. Geological Survey, reflecting the most recent Mars Orbiter Laser Altimeter data. The map was cropped into sixty and twenty degree segments, and the putative coastline was isolated from extraneous features. A program which used the box-counting method calculated the fractal dimensions of the putative shorelines. The 22 results were tabulated and compared to 17 fractal dimensions of Earth shorelines, collected from published articles. Ranges were 1.07 to 1.66 for Earth and 1.141 to 1.436 for Mars. The mean was 1.28 for the Mars data and 1.22 for the Earth data, a slight difference that asteroid craters could account for. An unpaired t-test could not prove that the two data sets were significantly different. Although the past existence of a coastline at the Deuteronilus contact cannot be definitively proven without on site investigations, the hypothesis that the fractal dimensions of the putative Martian coastline would be comparable to those of Earth's was accepted, thereby substantiating the claims for the existence of a large northern ocean.
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