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Fractal Rivers in Fractal Landscapes

Authors: James M Bardeen;

Fractal Rivers in Fractal Landscapes

Abstract

In the spirit of the "fractal forgeries" of Mandelbrot and Voss, the centered tile midpoint displacement algorithm of Mandelbrot is modified to introduce fractal rivers into fractal landscapes. The rivers and river networks co-evolve with the landscape to produce valleys and gulleys. The rivers have fractal dimensions in the range 1.1–1.26, similar to real rivers. The fractal dimension is maximized by weighting the probability of wriggling right vs. wriggling left so the river tries to maintain a straight course downstream, much as with meanders of real rivers. The rivers are generated by randomly placed springs and by local depressions in the landscape filled with "water" to become "lakes". The topological properties of the river networks and the degree to which the landscapes with and without rivers approximate fractional Brownian motion are explored.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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