Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 16 3 2009 10.5194/npg-16-419-2009 http://www.nonlin-processes-geophys.net/16/419/2009/ http://www.nonlin-processes-geophys.net/16/419/2009/npg-16-419-2009.html http://www.nonlin-processes-geophys.net/16/419/2009/npg-16-419-2009.pdf 419 429 2009-06-23 Quantitative analysis of randomness exhibited by river channels using chaos game technique: Mississippi, Amazon, Sava and Danube case studies G. Žibret gorazd.zibret@geo-zs.si T. Verbovšek Geological Survey of Slovenia, Ljubljana, Slovenia University of Ljubljana, Faculty of Natural Sciences and Engineering, Department of Geology, Ljubljana, Slovenia This paper presents a numerical evaluation of the randomness which can be observed in the geometry of major river channels. The method used is based upon that of generating a Sierpinski triangle via the chaos game technique, played with the sequence representing the river topography. The property of the Sierpinski triangle is that it can be constructed only by playing a chaos game with random values. Periodic or chaotic sequences always produce an incomplete triangle. The quantitative data about the scale of the random behaviour of the river channel pathway was evaluated by determination of the completeness of the triangle, generated on the basis of sequences representing the river channel, and measured by its fractal dimension. The results show that the most random behaviour is observed for the Danube River when sampled every 715 m. By comparing the maximum dimension of the obtained Sierpinski triangle with the gradient of the river we can see a strong correlation between a higher gradient corresponding to lower random behaviour. Another connection can be seen when comparing the length of the segment where the river shows the most random flow with the total length of the river. 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