I am currently investigating the fractal dimension of the coastline of the island the Palm Jumeirah, including the crescent. Using the Hausdorff method I have reached an answer of 0.879. This is less than 1 and i thought the range of the value was between 1 and 2 (closer to 2 = more complex coastline). Can someone please tell me what this means or whether I have probably made an error?
2026-02-24 00:52:10.1771894330
Can the fractal dimension of a coastline be less than 1?
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The algebra is correct, but the data is wrong.
In your diagrams, the rulers - especially the long ones - stick out past the edge of the Palm Jumeriah into the sea. The overestimation of L for large G is stronger than any fractal properties the coastline has, which means that L decreases with G. To get a more accurate dimension, make sure that every ruler starts and ends on the coastline.
Being man-made, the coastline itself is very smooth so probably has an actual Hausdorff dimension close to (but greater than) 1.