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} $$