= Open set condition
A finite family of contracting similarities $S_1,\ldots,S_k$ satisfies the open set condition if there is a nonempty bounded <open set> $O$ with $S_i(O)\subseteq O$ and $S_i(O)\cap S_j(O)=\varnothing$ for $i\ne j$. This permits the closures to meet. For the invariant compact set, this separation makes its <Hausdorff dimension> equal to the similarity exponent $s$ defined by $\sum_i c_i^s=1$, where $c_i$ are the contraction ratios. The level-$n$ cylinder sets supply the upper dimension bound; the separated cylinder masses with weights $c_i^s$ supply the matching mass-distribution lower bound. For the 24 maps of ratio $1/5$ retaining all but the central square, $O=(0,1)^2$ works and $s=\log24/\log5$.
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