How would you approach a most accurate measurement of the "length" of a coastline?
From this kind of wondering comes the idea of self-similarity that inspired folks like Julia and Mandelbrot. A bit of googling might help...
What is your definition of the length of a coastline ? At which tide ?
I'm not sure "googling" would be of benefit in establishing the PF readership opinions on how they might approach the problem.
Fractal geometries are intrinsically a part of the problem, and largely exemplify the biggest of such problems. This is pretty much given that lengths of coastlines and attempted or purported measurements thereof are often used to describe fractals.
I thank you for your contribution that it appears you are making that establishing the definition of 'coastline' is one of the primary steps in your approach.
The length will always depend on your definition. Typically a fixed length scale is chosen, and the coast is smoothed out to this scale. While that leads to a number, that number depends on the scale chosen, so it is not really meaningful.
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