Erosion and fractal coasts


Erosion and fractal coasts


Submitted by


Michel Darche
Regis Goiffon

In the 60’s, it was noticed that the geometry of rocky coasts is also fractal: this means that, when zooming on a photo, whatever the zoom, we see new details appearing that have the same character as the large scale details.

Why is this geometry fractal?

The sea destroys first the most fragile rocks. When it starts forming a small cove, the sea violently comes in and increases it. But then, the length of the coast increases, and the strength of the waves is spread along a longer coast. Hence, it is commonly admitted that the erosion is weaker along fractal coasts.
Geographers have modelled the evolution of the coastal morphology when erosion destroys the softer rocks, and hence increasing the irregularities of the coastline. In their model, the strength of waves is inversely proportional to the length of the coast.
The process stabilizes with the final coast having a fractal dimension exactly equal to 4/3 = 1.333.

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