The Perimeter-Area Relation
Author:
Publisher
Springer US
Link
http://link.springer.com/content/pdf/10.1007/978-1-4899-2124-6_12
Reference1 articles.
1. We have recently shown (E. L. Hinrichsen, K. J. Måløy, J. Feder and T. Jøssang, J. Phys. A: Math. Gen. 22 L272–L277 (1989)) that DLA and experimental results on viscous fingering are self-similar in terms of branch orders, and that they have a fractal dimension given by D s = inr N/in(1/r L). Note that this expression for D s is analogous to the similarity dimension defined by equation (2.10) for Koch curves. Actually Horton and Hack label streams so that i = s for the main stream and i = 0 for streams with no tributaries. For numerical work our numbering is more convenient. We also use r N instead of r b for the branching ratio, and r L = 1/r l for the length ratio in the notation of Hack.
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