Fractal World Coastlines

Using the data available from the GSHHS Database, A Global Self-consistent, Hierarchical, High-resolution Shoreline Database (created and maintened by Paul Wessel) we have computed the "local" fractal dimension of the whole world coastlines. To this aim we have considered a grid of points separated by 1 degree of latitude/longitude. At each grid point we have associated the fractal dimension (computed via box counting) of the coastlines contained in a squared angular region of 2 degrees of latitude/longitude side centered on the point.

The result is shown in the following picture:

You can also see a zoom on the single continental coasts:

• Eurasia
• North America
• South America
• Oceania
• Africa

Fractal Dimension of Rocky World Coasts

Rocky coasts are estimated to represent 75% of the world's f shorelines, but this includes beaches backed by rocks, with many different morphologies and several different dynamical processes in action. Nevertheless, there are many cases in which wave erosion is recongized as the main erosive process.

• Caption: Fractal Dimension between 1.2 and 1.4

In the figure we have reported all the sites where a measure of the fractal dimension, performed via box-counting on parcels of 2 degrees of latitude/longitude of side, risulted in a fractal dimension comprised between 1.2 and 1.4. Many of them are rocky coasts and surely the morphoogy of some of them could be described by our model.

We think for instance to Bermuda Islands or the North-East coast of Sardinia, the italian island, which display a fractal dimension extremely close to 4/3.

The analysis have been performed on the GSHHS Database, a A Global Self-consistent, Hierarchical, High-resolution Shoreline Database created and maintened by Paul Wessel.