Meandering Fractals in Water Resources Management

Levent Yilmaz

doi:doi:10.11648/j.acm.20200902.12

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Meandering Fractals in Water Resources Management

Levent Yilmaz

Published in Applied and Computational Mathematics (Volume 9, Issue 2)

Received: 29 April 2019 Accepted: 21 May 2019 Published: 19 May 2020

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Abstract

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.

Published in	Applied and Computational Mathematics (Volume 9, Issue 2)
DOI	10.11648/j.acm.20200902.12
Page(s)	26-29
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Natural Dimensions, Nonlinearity, Fractals, Meanders

References

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[2]	Jiang B. (2015), Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity, GeoJournal, 80 (1), 1-13.
[3]	F. Moisy (2008) https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
[4]	Fractal Dimension and Self-Similarity https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
[5]	Longley, P. A. and Batty, M. (1996), Spatial Analysis: Modelling in a GIS Environment, https://books.google.com.tr/books?isbn=0470236159.
[6]	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.
[7]	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, enews@csa.com.
[8]	Sierpinski, S. (2002) https://www.mathsisfun.com/sierpinski-triangle.html https://wwwmathworld.wolfram.com/SierpinskiSieve.html.
[9]	Kennedy, J. F., et al., Proc. Am. Soc. civ. Engrs, 97, 101–141 (1971).
[10]	Hey, R. D., UK geol. Soc. Misc. Pap. 3, 42–56 (1974).
[11]	Yalin, M. S., Mechanics of Sediment Transport (Pergamon, Oxford, 1972).
[12]	Leopold, L. B., and Wolman, M. G., Bull. geol. Soc. Am., 71, 769–793 (1960).
[13]	Leopold, L. B., Wolman, M. G., and Miller, J. P., Fluvial Processes in Geomorphology (Freeman, London, 1964).
[14]	Shen, H. W., and Komura, S., Proc. Am. Soc. civ. Engrs, 94, 997–1015 (1968).
[15]	Hey, R. D., and Thorne, C. R., Area, 7, 191–195 (1975).

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APA Style

Levent Yilmaz. (2020). Meandering Fractals in Water Resources Management. Applied and Computational Mathematics, 9(2), 26-29. https://doi.org/10.11648/j.acm.20200902.12

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ACS Style

Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl. Comput. Math. 2020, 9(2), 26-29. doi: 10.11648/j.acm.20200902.12

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Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl Comput Math. 2020;9(2):26-29. doi: 10.11648/j.acm.20200902.12

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@article{10.11648/j.acm.20200902.12,
  author = {Levent Yilmaz},
  title = {Meandering Fractals in Water Resources Management},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {2},
  pages = {26-29},
  doi = {10.11648/j.acm.20200902.12},
  url = {https://doi.org/10.11648/j.acm.20200902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200902.12},
  abstract = {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.},
 year = {2020}
}

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TY  - JOUR
T1  - Meandering Fractals in Water Resources Management
AU  - Levent Yilmaz
Y1  - 2020/05/19
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200902.12
DO  - 10.11648/j.acm.20200902.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - 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.
VL  - 9
IS  - 2
ER  -

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Author Information

Levent Yilmaz

Nisantasi University Neocampus, Maslak, Istanbul, Turkey

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APA Style

Levent Yilmaz. (2020). Meandering Fractals in Water Resources Management. Applied and Computational Mathematics, 9(2), 26-29. https://doi.org/10.11648/j.acm.20200902.12

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ACS Style

Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl. Comput. Math. 2020, 9(2), 26-29. doi: 10.11648/j.acm.20200902.12

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AMA Style

Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl Comput Math. 2020;9(2):26-29. doi: 10.11648/j.acm.20200902.12

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@article{10.11648/j.acm.20200902.12,
  author = {Levent Yilmaz},
  title = {Meandering Fractals in Water Resources Management},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {2},
  pages = {26-29},
  doi = {10.11648/j.acm.20200902.12},
  url = {https://doi.org/10.11648/j.acm.20200902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200902.12},
  abstract = {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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Meandering Fractals in Water Resources Management
AU  - Levent Yilmaz
Y1  - 2020/05/19
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200902.12
DO  - 10.11648/j.acm.20200902.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 26
EP  - 29
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200902.12
AB  - 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.
VL  - 9
IS  - 2
ER  -

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