Pond fractals in a tidal flat.

B B Cael,Bennett Lambert,Kelsey Bisson

doi:10.1103/physreve.92.052128

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.

Highlights

Power-law distributions are characteristic of scale-free phenomena and occur widely in nature [1]
A hallmark of the study of self-similar surfaces is the power-law distribution of areas enclosed by contours of level surfaces
The results strongly suggest a fractal pond pattern in tidal flats similar to those found in terrestrial lakes and Arctic melt ponds, albeit on different spatiotemporal scales and driven by different physical processes

Summary

INTRODUCTION

Power-law distributions are characteristic of scale-free phenomena and occur widely in nature [1]. A hallmark of the study of self-similar surfaces (e.g., continuum percolation theory and statistical topography) is the power-law distribution of areas enclosed by contours of level surfaces. This is widely observed in geophysical systems through both connected and closed bodies of water [2,3,4]. In the past decade, celebrated papers have demonstrated the existence of such power-law-distributed, fractal water bodies in geophysical systems [2,3,7,8,9]. These statistical quantities are robust to alterations of the image processing technique and reveal a system statistically similar to lakes and melt ponds

DATA COLLECTION AND ANALYSIS

RESULTS

DISCUSSION