It's about Exercise 1.19, Fractals in Probability and Analysis?
Suppose $S\subset\mathbb{N}$, and we are given $E,F\subset\{0,1,2\}$. Define $B_S=\{x=\sum_{k=1}^\infty x_k2^{-k}\}$ where $x_k\in E$ if $k\in S$ and $x_k\in F$ otherwise.
The Hausdorff dimension $\dim(B_S)$ in terms of $E,F,S$ is asked to be calculated.
I learn how to calculate the Hausdorff dimension of some symmetric set, i.e if I scale or translate it, It's similar to itself such as Canton sets. But this exercise gives a different set. Could someone give me some hints/solutions?