© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Physical Review E Statistical, Nonlinear, and Soft Matter Physics 92 (2015): 052128, doi: 10.1103/PhysRevE.92.052128.
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 2388357, the Gordon and Betty Moore Foundation, and the National Science Foundation, Award No. OCE-1315201.
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