My Extended Essay is about this topic. I am trying to measure the coastline of Norway by the use of fractals, which is something that is quite similar to what Benoît Mandebrot did in 1967. Mandelbrot then published the research paper “How long is the coast of Britain? Statistical Self-Similarity and Fractional Dimension“, where he explained a method for measuring coastlines, and an example with the coastline of Britain.
In simple steps, what I did was to unfold a giant map of Norway. By using a compass fixed to a certain value and go from point to point along the coastline from south to north (or the other way, if you like) I deduced the length of the coastline.
However, the length differed when differing the compass span!
This is more commonly known as the coastline paradox, and is the reason for why the values for the length of the coastline differ from various sources. I got results that differed from 2500km to 6600km, the latter with a span corresponding to 20 km in real life.
However, by comparing my values with literature accepted values and using a formula that is described in the link, I managed to find a result.
The coastline of Norway is, when using a 1 km measurement scale by the use of Mandelbrot’s formula as described in the wiki-article:
19 157.1 km
Post comments or questions if you like.
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