Branch & Bound Geometric Shapes

Question

I am dividing a box to two halves, and plotting it in Tikz. An example code is:

\begin{figure}[!h]
\scalebox{1.5}{
\begin{tikzpicture}
\filldraw[fill=gray!40!white, draw=black] (0,0) rectangle (4,2);
\node[black](dot) at (2,1) {\textbullet};
%\node[below=0cm of dot]  {\small{$x_a$}};
\draw[dashed] (1,-1) -- (3,3) ;
\node[] at (1,1.5) {\small{$r^\top x_a \geq r^\top x$}};
\node[] at (3,0.5) {\small{$r^\top x_a \leq r^\top x$}};
\node[] at (3.2,3.3) {\small{$r^\top x_a$}};
\end{tikzpicture}
}
\end{figure} 

This produces:

Now I will calculate some mathematical stuff in the two halves, and again divide each half, and so on. Therefore, I need to use some Branch & Bound structure, but each element should be a geometric shape as the one above. I just need to have a tree where the elements are geometric shapes which will be inserted by me (thanks @marmot)

Any template or example link will be really appreciated.

Answer 1

Here is a proposal.

\documentclass{article}
\usepackage{forest}
\usepackage{mathrsfs}
\begin{document}
\begin{forest}
for tree={s sep+=3em,l sep+=1em}
 [$\mathscr{Z}$,minimum width=3cm,minimum height=1.2cm,draw,label=right:$x_2$,
    alias=n1
  [$\mathscr{Z}_{11}$,minimum width=1.2cm,minimum height=1.2cm,draw,trapezium,
    trapezium left angle=90, trapezium right angle=60,label=right:$x_2^{(1,1)}$,
    alias=n11]
  [$\mathscr{Z}_{12}$,minimum width=1.2cm,minimum height=1.2cm,draw,,draw,trapezium,
  trapezium left angle=120, trapezium right angle=90,label=right:$x_2^{(1,1)}$,
    alias=n12]
 ]
\path (n1.south)  -- (n11.north) coordinate[midway] (aux);
\draw[dashed] (current bounding box.west|-aux)--
 (current bounding box.east|-aux);
\end{forest}
\end{document}

Answer 2

Here is another proposal.

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
\def\initialrectangle{
\draw[fill=gray!40!white] (0,0) rectangle (4,2)
(1,1.5) node{Tom} (3,0.5) node{Jerry};
}

\initialrectangle
\draw[dashed] (1,-1)--(3,3) node[above]{separator};

\begin{scope}[shift={(-100:3.5)}]
\clip (1,-1)--(3,3)-|(0,0);
\initialrectangle
\end{scope}

\begin{scope}[shift={(-80:3.5)}]
\clip (3,3)--(1,-1)-|(4,2);
\initialrectangle
\end{scope}

\end{tikzpicture}
\end{document}