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I have applied the Hausdorff method to find the fractal dimension of the coastline of one of my country's islands. Is there any way for me to find the area of the islands with the fractal dimension I have calculated?

Perhaps, there is a way reverse the equation of the box-counting method to find how many areas the island has contained. Does anyone have any suggestions?

Draveenn
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  • From the dimension value: no. From the box counting method: yes. – Paul Childs Feb 17 '20 at 02:53
  • No. The dimension of the boundary really tells you nothing about the area it encloses. For a more down-to-earth example, the boundary of any disk is one dimensional (the boundary is a circle, which is a rectifiable curve). However, a disk can have any area you like---just change the radius. – Xander Henderson Feb 17 '20 at 04:30

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