Variations in drainage basins analyses through the methods Box-Counting and SPA-BOX

Abstract

Drainage basins, like other plane images, can be analyzed by the fractal dimension; satellites images or images produced at soil level in topographical surveys have been analyzed through some methods that determine the fractal dimension, but, that technology is still not available for most technicians in the area. The objective of this work was to compare two methods, Box Counting and SPA-BOX, which determine the fractal dimension of images of drainage basins. The obtained results of fractal dimension (D) through the Box-Counting method wer 1.2912 + 0.0528,1.1515 + 0.0357, 1.2033 + 0.0609,1.1853 + 0.0552,1.1579 + 0.0162,1.1616 + 0.0125,1.1872 + 0.0583,1.1650 +0.0190. For SPA-BOX method the following values of D were obtained: 1.2192 + 0.0049,1.2280 + 0.0040,1.2521 + 0,0040,1.2229 + 0.0021,1.2330 + 0.0025,1.1868 + 0.0035,1.2468 + 0.0044, 1.2281 + 0.0016, for the drainage basins from 1 to 8 respectively. From these results, it was possible to infer that Box-Counting can lead to experimental mistakes, mainly, in relation to the insertion of the illustrations to be analyzed, while SPA-BOX is more accurate in that kind of analysis, but it has the inconvenience of being more difficult in its execution.