[derefr]

Neither this, nor the post it's inspired by, is as interesting to me as a question with a much simpler-to-calculate answer: what's the smoothest (i.e. lowest fractal-dimension, smallest surface-area-to-volume ratio) country?

At the top would be some country with artificially-defined borders that have not since been reshaped by war or treaty. At the bottom would likely be the most "historied" country.

(Then again, at the bottom might just be Canada or Russia, since they have so much jagged coast to count. Perhaps, for the parts of a country that abut international waters instead of another country, we could use the political boundaries of the country's coastal waters surrounding that coast, rather than the boundaries of its landmass.)

[9NRtKyP4]

Mandelbrot on the "fractal dimension" of coastlines:

http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastO...

The figure under "The Richardson Effect" on this page has some examples of how measured length of coastlines scales with the the scale of measurement:

http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/worksh...

[f_allwein]

Would be interesting as even natural borders are very different. I remeber South Africa (very straight coastline) vs Ireland (very fractal coastline) being used as an example for complexity in nature.

[kijin]

Coastlines vary even within the same country. See South Korea (rank 51). Very smooth in the east, crazy fractals in the southwest.

[Keyframe]

At the bottom might be more defined by geography than anything else. For example, Norway.

[alanbernstein]

Right, the fractal structure is of coastlines, not borders in general.