How winding is the coast of Britain ? Conformal invariance of rocky shorelines

TL;DR

This paper demonstrates that rocky coastlines of Britain exhibit conformal invariance, linking their fractal geometry to statistical models like percolation, and uses this to predict pollutant distribution patterns.

Contribution

It provides the first empirical evidence of conformal invariance in natural rocky shorelines and connects coastal erosion models with statistical physics.

Findings

Rocky shorelines with fractal dimension 4/3 are conformally invariant.

Coastlines are statistically equivalent to percolation cluster boundaries.

Conformal invariance enables prediction of pollutant flux distribution.

Abstract

We show that rocky shorelines with fractal dimension 4/3 are conformally invariant curves by measuring the statistics of their winding angles from global high-resolution data. Such coastlines are thus statistically equivalent to the outer boundary of the random walk and of percolation clusters. A simple model of coastal erosion gives an explanation for these results. Conformal invariance allows also to predict the highly intermittent spatial distribution of the flux of pollutant diffusing ashore.