Self-stabilised fractality of sea-coasts through damped erosion

TL;DR

This paper presents a model demonstrating how the interplay between coastal erosion and wave damping can lead to the self-stabilization of irregular, fractal-shaped sea coasts, revealing a natural tendency towards a fractal geometry.

Contribution

It introduces a simple dynamical model showing the emergence of stationary fractal coastlines through self-stabilization mechanisms involving erosion and wave damping.

Findings

Coastlines evolve into fractal shapes with a dimension near 4/3.

The model links fractal coast geometry to percolation theory.

Self-stabilization results from mutual feedback between erosion and wave damping.

Abstract

Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea-waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilisation of the waves amplitude together with the irregular morphology of the coast. A simple model of such stabilisation is studied. It leads, through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry.