User:TachyonJack/Sandbox 3.1

$F(n)\equiv \;\;\left.{\begin{matrix}&\underbrace {n{\mbox{ layers}}\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;\vdots \qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.{\Bigg \{}\cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.} \\&\underbrace {n{\mbox{ layers}}\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;\vdots \qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.{\Bigg \{}\cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.} \\&\underbrace {\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad {\begin{matrix}\vdots \\\vdots \\\vdots \end{matrix}}\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad } \\&\underbrace {n{\mbox{ layers}}\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;\vdots \qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.{\Bigg \{}\cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.} \\&\underbrace {n{\mbox{ layers}}\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;\vdots \qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.\left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.{\Bigg \{}\cdots \cdots \cdots \cdots \left\{{\begin{matrix}&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \cdots \cdots \rightarrow n} \\&\underbrace {\qquad \;\;{\begin{matrix}\vdots \\\vdots \\\vdots \end{matrix}}\qquad \;\;} \\&\underbrace {n\rightarrow n\rightarrow \cdots \cdots \rightarrow n} \\&\underbrace {n\rightarrow n\rightarrow \cdots \rightarrow n} \\&n{\mbox{ copies of }}n\end{matrix}}\right.} \\&{\begin{matrix}n{\mbox{ towers}}\end{matrix}}\end{matrix}}\right\}n{\mbox{ Super-Layers}}$