If we take the Cantor set and instead of removing the interval $[1/3, 2/3]$, we remove the open interval $[x,1-x]$, with $0<x<1/2$, will the similarity dimension change? What I think is that we again get scaling factor $3$ and we get two copies of the lines, but rescaled. So the similarity dimension is $\log(2)/\log(3) = 0.63$.
2026-03-27 23:37:51.1774654671
Finding the similarity dimension of a variation of the Cantor Set.
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Yes, the similarity dimension will be different. The generalized Cantor set consists of two copies of itself, scaled by the factor of $x$. So, its dimension (similarity, Hausdorff, box/Minkowski, packing...) is $\log 2/\log(1/x)$.