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Trickier Cantor box-count

mark

Let C_2 denote the two-scale Cantor set that is the invariant set of the IFS

\left\{\frac{1}{2}x, \frac{1}{4}x + \frac{3}{4}\right\}.

Compute N_{\varepsilon}(C_2) for \varepsilon = 1,\: 1/2,\: 1/4, and 1/8.