Abstract
The research problem is about to generate artificial fractal landscape surfaces from the Digital Elevation Model (DEM) using a stochastic algorithm by Geographic Resources Analysis Support System Geographic Information System (GRASS GIS) software. Fractal surfaces resemble appearance of natural topographic terrain and its structure using random surface modelling. Study area covers Kuril-Kamchatka region, Sea of Okhotsk, North Pacific Ocean. Techniques were included into GRASS GIS modules (r.relief, d.rast, r.slope.aspect, r.mapcalc) for raster calculation, processing and visualization. Module 'r.surf.fractal' was applied for generating synthetic fractal surface from ETOPO1 DEM GeoTIFF using algorithm of fractal analysis. Three tested dimensions of the fractal surfaces were automatically mapped and visualized. Algorithm of the automated fractal DEM modelling visualized variations in steepness and aspect of the artificially generated slopes in the mountains. Controllable topographic variation of the fractal surfaces was applied for three dimensions: dim=2.0001, 2.0050, 2.0100. Auxiliary modules were used for the visualization of DEMs (d.rast, r.colors, d.vect, r.contour, d.redraw, d.mon). Modules 'r.surf.gauss' and 'r.surf.random' were applied for artificial modelling as Gauss and random based mathematical surfaces, respectively. Univariate statistics for fractal surfaces were computed for comparative analysis of maps representing continuous fields by module 'r.univar': number of cells, min/max, range, mean, variance, standard deviation, variation coefficient and sum. The paper includes 9 maps and GRASS GIS codes used for visualization.
Highlights
Fractals are infinitely complex patterns of the dynamic systems, self-similar across different scales created by repeating a recursive iterative process in a feedback loop (Briggs, 1992; Mandelbrot, 1982)
The results were made using 'r.surf.fractal' module of GRASS GIS to generate multi-dimensional surfaces from the initial Digital Elevation Model (DEM) based on the ETOPO1
The paper started by the description of a theoretical background regarding fractal theory and its practical applications in natural sciences and in geoinformatics, followed by the developed methodology using various software approaches (e.g. R, Python, Matlab, GRASS GIS)
Summary
Fractals are infinitely complex patterns of the dynamic systems, self-similar across different scales created by repeating a recursive iterative process in a feedback loop (Briggs, 1992; Mandelbrot, 1982). As commonly used and described both in pure mathematical and nature sciences (Edgar, 2007; Falconer, 2003; Feder, 2013; Gordon, 2000; Muzy, Bacry, & Arneodo, 1993; Panchev, 1971); fractal algorithms are well applicable in geographic studies for spatial analysis aimed at classifying and investigating variations in Earth’s relief. The phenomenon of Earth’s topography consists in its partial self-similarity repeating fractal structure of the landscapes at various dimensions where the theory of fractals is well applicable. Mandelbrot suggested computing the complexity (curvature) of a line by applying a single dimension between 1 and 2 for a line, or between 2 and 3 in a surface (Mandelbrot, 1967, 1975)
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