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On the Application of Fractal Geometry to
Stream NetworksCalculating and Comparing Fractal Dimensions
Adam ZhangGeorgia Institute of Technology
Mathematics of Stream NetworksQuantitative framework for stream networks
Horton-Strahler Stream Ordering System
Streams as fractals
Fractals and Fractal DimensionsSelf-similarity and Heavy Tails
Fractal Dimension
Complexity and Space-filling
Fractal methods in streams
Different values
Validity
Divider (Richardson) Method
Functional-Box Counting
As a function of bifurcation and length
H.J. Andrews
Bifurcation jpg
ImplicationsGenerally fractal
Similar to values across watersheds
Techniques create varying ranges of dimension
Only divider method illustrates sinuosity vs branching
Higher fractal dimensions have higher drainage densities
More space-filling
Further StudySimulate Tree Networks of Similar Dimension
Probability Distribution in Statistical Fractals
Catchment Area vs Bifurcation Ratio
AcknowledgementsMentors and Facilitators-
Dr. Desiree Tullos, Dr. Julia Jones, Dr. Fred Swanson, Dr. Catalina Segura, Cara Walter
EISI Group-
Sashka, Brent, Pete, Malia, Josh, Jane, Lydia, Elaina, Andrew, Stephanie
H.J. Andrews and Oregon State University
ReferencesB. B. Mandelbrot, “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” Science, New Series, Vol. 156, No. 3775, 1967, pp. 636-638.
La Barbera, P., and R. Rosso. 1990. On fractal dimension of stream networks, Reply to Tarboton et al., Water. Resour. Res., 26(9), 2245-2248.
Lovejoy, S., D. Schertzer, and A. A. Tsonis. 1987. Functional box counting and multiple elliptical dimensions in rain, Science, 235, 1036-1038.
Horton, R. E. 1932. Drainage-basin characteristics, EOS Trans. AGU, 13, 350-361.
I. Rodriguez and A. Rinaldo, “Fractal River Basins (Chance and Self-Organization),” Cambridge University Press, Cambridge, 1997.
Strahler, A. N. 1952. Hypsometric (area altitude) analysis of erosional topography, Geol. Soc. Am. Bull., 63, 1117-1142.
Tarboton, D. G., R. L. Bras, and I. Rodgriquez-Iturbe. 1988. The fractal nature of river networks, Water. Resour. Res., 24(8), 1317-1322
Z. Khanbabaei, A. Karam, and G. Rostamizad, "Studying relationships between the fractal dimension of the drainage basins and some of their geomorphological characteristics", Int. J. Geosci., vol. 4, pp. 636-642, 2013.
DiscussionAdam Zhang
School of Mathematics
Georgia Institute of Technology, c/o 2018
