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We prove that, for any finite set of minimal $r$-graph patterns, there is afinite family $\mathcal F$ of forbidden $r$-graphs such that the extremalTur\'an constructions for $\mathcal F$ are precisely the maximum $r$-graphsobtainable from mixing the given patterns in any way via blowups and recursion.This extends the result by the second author~\cite{PI14}, where the abovestatement was established for a single pattern.  We present two applications of this result. First, we construct a finitefamily $\mathcal F$ of $3$-graphs such that there are exponentially manymaximum $\mathcal F$-free $3$-graphs of each large order $n$ and, moreover, thecorresponding Tur\'an problem is not finitely stable. Second, we show thatthere exists a finite family $\mathcal{F}$ of $3$-graphs whose feasible regionfunction attains its maximum on a Cantor-type set of positive Hausdorffdimension.

Finite Hypergraph Families with Rich Extremal Tur\'an Constructions via Mixing Patterns