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The answer is 2.

Besicovitch and Ursell, Sets of fractional dimensions (V): On dimensional numbers of some continuous curves. ProcJ. London Math. Soc. 12 (1937) 18-2518–25. doi:10.1112/jlms/s1-12.45.18

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The answer is 2.

Besicovitch and Ursell, Sets of fractional dimensions (V): On dimensional numbers of some continuous curves. Proc. London Math. Soc. 12 (1937) 18-25.