# Box-Counting the Dimension of Coastlines

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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.

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Contributed by: Erik Mahieu (January 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

References

[1] V. Kaurov. "Measuring Fractal Dimension of Natural Object from Digital Images." *Mathematica Stack Exchange*. (Oct 16, 2012) mathematica.stackexchange.com/questions/13125/measuring-fractal-dimension-of-natural-objects-from-digital-images.

[2] M. Mitchell et al. "Introduction to Complexity: 3.6 Box-Counting Dimension." *Complexity Explorer*. (2013) www.complexityexplorer.org/online-courses/3.

## Permanent Citation

"Box-Counting the Dimension of Coastlines"

http://demonstrations.wolfram.com/BoxCountingTheDimensionOfCoastlines/

Wolfram Demonstrations Project

Published: January 14 2014