title: Pond fractals in a tidal flat.
abstract: 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.
authors.affiliation: Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA and Woods Hole Oceanographic Institution, 86 Water Street, Woods Hole, Massachusetts 02543, USA.
authors.forename: B B
authors.initials: BB
authors.lastname: Cael
authors.affiliation: Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA and Woods Hole Oceanographic Institution, 86 Water Street, Woods Hole, Massachusetts 02543, USA.
authors.forename: Bennett
authors.initials: B
authors.lastname: Lambert
authors.affiliation: Earth Research Institute, University of California, Santa Barbara, California 93106, USA.
authors.forename: Kelsey
authors.initials: K
authors.lastname: Bisson