# Box-Counting the Dimension of Coastlines

Box-Counting the Dimension of Coastlines

This Demonstration uses the box-counting method [1] to estimate the fractal dimension of three coastlines. The box-counting dimension of a coastline can be computed using a mesh of evenly spaced squares laid over a map of the coastline.

Let be the number of squares that are required to cover the whole coastline and be the sidelength of one square of the mesh. Then the box-counting dimension is .

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A detailed description of the box-counting method used in this Demonstration can be found in [2].