Hausdorff–Besicovitch dimension of the graph of one continuous nowhere-differentiable function - O., B. Panasenko (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We investigate fractal properties of the graph of the function y = f(x) = ∑^∞_k−1β_k2^k ≡ Δ^2_β_1β_2…β_k…, where β_1 = cases 0 & if α_1(x) = 0, 1 & if α_1(x) eq 0, cases β_k = cases β_k−1 & if α_k(x) = α_k-1(x), 1 - β_k−1 & if α_k(x) eq α_k-1(x), cases 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) = _2(1 +2^_32 dimension and cell dimension α_K (Г_f) = 2-_32.