Applied and Computational Mathematics
Volume 9, Issue 2, April 2020, Pages: 26-29
Received: Apr. 29, 2019;
Accepted: May 21, 2019;
Published: May 19, 2020
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Levent Yilmaz, Nisantasi University Neocampus, Maslak, Istanbul, Turkey
Fractal dimension is a measure for the degree of complexity or that of fractals. An alternative to fractal dimension is ht-index, which quantifies complexity in a unique way. Back to your question, the physical meaning of fractal dimension is that many natural and social phenomena are nonlinear rather than linear, and are fractal rather than Euclidean. We need a new paradigm for studying our surrounding phenomena, Not Newtonian physics for simple systems, but complexity theory for complex systems, Not linear mathematics such as calculus, Gaussian statistics, and Euclidean geometry, but online mathematics including fractal geometry, chaos theory, and complexity science in general. A channel is characterized by its width, depth, and slope. The regime theory relates these characteristics to the water and sediment discharge transported bye the channel empirically. Empirical measurements are taken on channels and attempts are made to fit empirical equations to the observed data. The channel characteristics are related primarily to the discharge but allowance is also made for variations in other variables, such as sediment size.
Meandering Fractals in Water Resources Management, Applied and Computational Mathematics.
Vol. 9, No. 2,
2020, pp. 26-29.
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104 (3), 530–541.
Jiang B. (2015), Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity, GeoJournal, 80 (1), 1-13.
F. Moisy (2008) https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
Fractal Dimension and Self-Similarity https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
Longley, P. A. and Batty, M. (1996), Spatial Analysis: Modelling in a GIS Environment, https://books.google.com.tr/books?isbn=0470236159.
Normant, F. and Tricot, G., (1995) Fractals in Engineering https://www.google.com/search?q=Normant+and+Triart&tbm=isch&source=univ&sa=X&ved=2ahUKEwjgurqA5O_hAhVSyqQKHeK7ChAQsAR6BAgJEAE&biw=1366&bih=6.
Yilmaz, L., “Maximum Entropy Theory by Using the Meandering Morphological Investigation-II”, Journal of RMZ-Materials and Geoenvironment, 2007, CSA / ASCE, Printed also in CSA Illumina, CSA: Guide to Discovery, email@example.com.
Sierpinski, S. (2002) https://www.mathsisfun.com/sierpinski-triangle.html https://wwwmathworld.wolfram.com/SierpinskiSieve.html.
Kennedy, J. F., et al., Proc. Am. Soc. civ. Engrs, 97, 101–141 (1971).
Hey, R. D., UK geol. Soc. Misc. Pap. 3, 42–56 (1974).
Yalin, M. S., Mechanics of Sediment Transport (Pergamon, Oxford, 1972).
Leopold, L. B., and Wolman, M. G., Bull. geol. Soc. Am., 71, 769–793 (1960).
Leopold, L. B., Wolman, M. G., and Miller, J. P., Fluvial Processes in Geomorphology (Freeman, London, 1964).
Shen, H. W., and Komura, S., Proc. Am. Soc. civ. Engrs, 94, 997–1015 (1968).
Hey, R. D., and Thorne, C. R., Area, 7, 191–195 (1975).