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• W19866239 abstract "The definition of a fractal has been successfully deduced from constructing the Kochcurve and the Cantor set. Principles of seven methods (the ruler, box-counting, spectral,structure function, intersection methods, cube-counting, and triangular prism methods) fordetermining the fractal dimensions are illustrated and verified by the Koch curve, Cantorset, and the simulated 1-dimensional and 2-dimensional ffim samples by comparing thecalculated with the theoretical D values of the theoretical fractal models. The application ofappropriate methods to self-similar or self-affme fractals is essential due to differenttheoretical assumptions of the methodologies. The ruler dimension is different from thespectral dimension. The application of Hanning window to the synthetic fBm samples(Hanning window weighted) is important to obtain correct fractal dimensions for thespectral method and structure function methods. The multi-scaling behaviour of a fractalcan be unveiled by revealing the difference between the 1st and 2nd order structure functionmethods. The zeroset theory is used to relate the D values of 1-d contour set with 2-dsurface by analyzing the DEM data.The results of fractal analysing 132 topographic contours digitized from differentAbstract vscales (1:200,000, 1:50,000, 1:20,000) of maps of the border area between Spain andPortugal show that contours are self-similar, and have a fractal dimension of about D = 1.23over length scales ranging from 30 m to 13 km scale (3 orders of magnitude). The thirteenfiled and map profiles from Dorset area of southern England has a D value of 1.03 derivedfrom the ruler method. The variations in D values are controlled by three geological factors:erosive processes, lithologies, and fractures. The dominant control is the erosive processand fractures, and lithologies can either result in significant difference or produce moresubtle variation in D values of coastlines and contours. For example, the river down-cuttingproduces higher D value (1.1 ~ 1.5) than the wave action or cliff retreat erosive processes(1.01-1.10).The results of the fractal analysis of the five TM sub-image of Qatar have shown thatD values of the TM images range from 2.10 to 2.96. The variations in D values arecontrolled by different types of surface, band variations, and methodologies. The study areaB of a single rock type has the lowest D value (D is about 2.25) and is significant differentfrom the other four study areas, whilst the urban area E yields the highest fractal dimension(about D = 2.6). Band 3 yields the highest fractal dimensions, followed by bands 4, 5, 1,and 6, and band 2 has the lowest D value. The difference between the D values derivedfrom the 2nd and 1st order structure function methods for all the six bands of five study areasis D2s,(q=2) - D2s(q=l) = 0.16 0.13 (the uncertainty is the standard deviation), and suggeststhat the TM imagery has a multi-scaling property." @default.
• W19866239 created "2016-06-24" @default.
• W19866239 creator A5014875991 @default.
• W19866239 date "1998-08-01" @default.
• W19866239 modified "2023-09-27" @default.
• W19866239 title "Fractal analysis of topography and reflectance surfaces" @default.
• W19866239 hasPublicationYear "1998" @default.
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