Self-stabilised fractality of sea-coasts through damped erosion
Andrea Gabrielli
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.