We investigate fractal properties of the graph of the function
where
and α k (x) is the kth ternary digit of x: In particular, we prove that this graph is a fractal set with Hausdorff–Besicovitch α 0(Г f )=log2(1+2log 23 ) dimension and cell dimension αK(Г f )=2-log32.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1225–1239, September, 2009.
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Panasenko, O.B. Hausdorff–Besicovitch dimension of the graph of one continuous nowhere-differentiable function. Ukr Math J 61, 1448–1466 (2009). https://doi.org/10.1007/s11253-010-0288-8
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DOI: https://doi.org/10.1007/s11253-010-0288-8