= Finite similarity iterated function system
{title2=$\mathcal T(K)=\bigcup_{i=1}^mS_i(K)$}
For finitely many <contracting Euclidean similarities>, the map $\mathcal T$ on nonempty compact subsets of $\mathbb R^n$ is a contraction in the <Hausdorff metric>, with contraction constant $\max_i c_i<1$. The <contraction mapping theorem> gives a unique nonempty compact invariant set. If the <open set condition> holds, its <Hausdorff dimension> is the unique $s$ satisfying $\sum_i c_i^s=1$.
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