How to draw uniform rectangle in a matrix of math nodes?

Question

I made a matrix of math nodes. I am able to draw a rectangle around desired nodes. But every node has content of different size, which deforms the shape of the rectangles.

I tried using x and y shift, and played with sep (row, column, inner) also, but could not get it done.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, decorations.pathreplacing}

\begin{document}

\section{Introduction}
$\widetilde{G}{\;=\;}$
   \begin{tikzpicture}[baseline=0ex]
   \matrix (G) [
       matrix of nodes, nodes in empty cells,
       left delimiter={[},right delimiter={]},
       every node/.style={font=\footnotesize}, inner sep=2.5pt,
       row sep=3.0pt,
       nodes={%
         execute at begin node=$,%
         execute at end node=$%
       }%
     ]
      {
1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0\\
0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1\\
0&\alpha^2&\alpha&\alpha^2&\alpha^2&\alpha^2&1&1&0&\alpha&1&0&\alpha^2&0&\alpha&1&\alpha^2&1&0&1&\alpha&0&1&\alpha&\alpha^2&\alpha&\alpha&\alpha&1&\alpha^2\\
\alpha^2&\alpha^2&\alpha^2&1&\alpha^2&0&1&0&\alpha&\alpha&0&1&0&\alpha^2&1&\alpha^2&1&\alpha&1&1&0&\alpha&\alpha&\alpha^2&\alpha&1&\alpha&0&\alpha^2&\alpha\\
\alpha^2&\alpha&0&\alpha&1&\alpha&\alpha^2&1&1&\alpha^2&1&0&\alpha&0&1&1&0&1&\alpha&1&\alpha^2&0&0&\alpha^2&\alpha^2&\alpha^2&\alpha&\alpha^2&\alpha&\alpha\\
\alpha&1&\alpha&\alpha&\alpha&\alpha^2&1&\alpha&\alpha^2&\alpha&0&1&0&\alpha&1&0&1&1&1&\alpha^2&0&\alpha^2&\alpha^2&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&0\\
\alpha&\alpha^2&\alpha&\alpha&1&\alpha^2&1&\alpha^2&\alpha&\alpha^2&1&0&1&0&0&\alpha&\alpha&\alpha&\alpha&\alpha^2&1&0&\alpha&\alpha&0&\alpha&1&\alpha^2&0&\alpha\\
\alpha^2&1&\alpha&0&\alpha^2&\alpha&\alpha^2&\alpha&\alpha^2&1&0&1&0&1&\alpha&\alpha&\alpha&0&\alpha^2&1&0&1&\alpha&0&\alpha&\alpha&\alpha^2&\alpha&\alpha&\alpha\\
\alpha^2&\alpha^2&1&\alpha^2&0&\alpha^2&0&1&\alpha&\alpha&1&0&\alpha^2&0&\alpha^2&1&\alpha&1&1&1&\alpha&0&\alpha^2&\alpha&1&\alpha&0&\alpha&\alpha&\alpha^2\\
\alpha^2&0&\alpha^2&\alpha&\alpha^2&\alpha^2&1&1&\alpha&0&0&1&0&\alpha^2&1&\alpha&1&\alpha^2&1&0&0&\alpha&\alpha&1&\alpha&\alpha^2&\alpha&\alpha&\alpha^2&1\\
\alpha^2&0&1&0&\alpha^2&0&\alpha&0&1&0&1&0&\alpha&0&\alpha^2&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha&0&1&0&1&0\\
0&\alpha^2&0&1&0&\alpha^2&0&\alpha&0&1&0&1&0&\alpha&0&\alpha^2&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha&0&1&0&1\\
0&\alpha&\alpha&\alpha^2&\alpha&\alpha&\alpha&\alpha&0&\alpha&1&0&1&0&1&\alpha^2&\alpha&\alpha^2&0&\alpha&1&0&\alpha&\alpha^2&1&\alpha^2&\alpha&\alpha&1&\alpha^2\\
\alpha&\alpha&\alpha^2&1&\alpha&0&\alpha&0&\alpha&\alpha&0&1&0&1&\alpha^2&\alpha&\alpha^2&1&\alpha&\alpha&0&1&\alpha^2&1&\alpha^2&\alpha&\alpha&0&\alpha^2&\alpha\\
\alpha&1&0&\alpha&\alpha^2&1&1&\alpha&1&\alpha^2&1&0&\alpha^2&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha&\alpha&0&0&1&1&1&\alpha&\alpha^2&\alpha&\alpha\\
1&\alpha^2&\alpha&\alpha&1&\alpha&\alpha&\alpha^2&\alpha^2&\alpha&0&1&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha&1&0&\alpha&1&1&1&0&\alpha^2&1&\alpha&0\\
1&\alpha&\alpha&\alpha&\alpha^2&\alpha&\alpha&1&\alpha&\alpha^2&1&0&\alpha&0&0&1&1&1&\alpha^2&1&\alpha^2&0&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha^2&0&\alpha\\
\alpha&\alpha^2&\alpha&0&\alpha&1&1&\alpha^2&\alpha^2&1&0&1&0&\alpha&1&1&1&0&1&\alpha&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha^2&\alpha&\alpha&\alpha\\
\alpha&\alpha&1&\alpha^2&0&\alpha&0&\alpha&\alpha&\alpha&1&0&1&0&\alpha&\alpha^2&1&\alpha^2&\alpha&\alpha&1&0&1&\alpha^2&\alpha&\alpha^2&0&\alpha&\alpha&\alpha^2\\
\alpha&0&\alpha^2&\alpha&\alpha&\alpha&\alpha&\alpha&\alpha&0&0&1&0&1&\alpha^2&1&\alpha^2&\alpha&\alpha&0&0&1&\alpha^2&\alpha&\alpha^2&1&\alpha&\alpha&\alpha^2&1\\
\alpha&0&1&0&\alpha&0&\alpha^2&0&1&0&1&0&\alpha^2&0&\alpha&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha^2&0&1&0&1&0\\
0&\alpha&0&1&0&\alpha&0&\alpha^2&0&1&0&1&0&\alpha^2&0&\alpha&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha^2&0&1&0&1\\
0&1&\alpha&\alpha^2&1&1&\alpha^2&\alpha^2&0&\alpha&1&0&\alpha&0&\alpha^2&\alpha&1&\alpha&0&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&1&\alpha&\alpha&1&\alpha^2\\
1&1&\alpha^2&1&1&0&\alpha^2&0&\alpha&\alpha&0&1&0&\alpha&\alpha&1&\alpha&\alpha^2&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&1&\alpha^2&\alpha&0&\alpha^2&\alpha\\
1&\alpha^2&0&\alpha&\alpha&\alpha^2&\alpha&\alpha^2&1&\alpha^2&1&0&1&0&\alpha&\alpha&0&\alpha&1&\alpha^2&1&0&0&\alpha&\alpha&\alpha&\alpha&\alpha^2&\alpha&\alpha\\
\alpha^2&\alpha&\alpha&\alpha&\alpha^2&1&\alpha^2&1&\alpha^2&\alpha&0&1&0&1&\alpha&0&\alpha&\alpha&\alpha^2&\alpha&0&1&\alpha&\alpha&\alpha&0&\alpha^2&1&\alpha&0\\
\alpha^2&1&\alpha&\alpha&\alpha&1&\alpha^2&\alpha&\alpha&\alpha^2&1&0&\alpha^2&0&0&\alpha^2&\alpha^2&\alpha^2&1&\alpha&\alpha&0&1&1&0&1&1&\alpha^2&0&\alpha\\
1&\alpha&\alpha&0&1&\alpha^2&\alpha&1&\alpha^2&1&0&1&0&\alpha^2&\alpha^2&\alpha^2&\alpha^2&0&\alpha&\alpha^2&0&\alpha&1&0&1&1&\alpha^2&\alpha&\alpha&\alpha\\
1&1&1&\alpha^2&0&1&0&\alpha^2&\alpha&\alpha&1&0&\alpha&0&1&\alpha&\alpha^2&\alpha&\alpha^2&\alpha^2&\alpha^2&0&\alpha&1&\alpha^2&1&0&\alpha&\alpha&\alpha^2\\
1&0&\alpha^2&\alpha&1&1&\alpha^2&\alpha^2&\alpha&0&0&1&0&\alpha&\alpha&\alpha^2&\alpha&1&\alpha^2&0&0&\alpha^2&1&\alpha^2&1&\alpha&\alpha&\alpha&\alpha^2&1\\
     };
      \def\bshrink{0.1}
      \def\rshrink{0.08}
       \def\xshrink{.1}
        \def\yshrink{.08}
      \pgfmathtruncatemacro{\nrows}{14}
      \pgfmathtruncatemacro{\ncols}{14}
      \pgfmathtruncatemacro{\m}{2}
       \foreach \x in {0, ..., \nrows} {
       \pgfmathtruncatemacro{\tempa}{\m*\x+1}
       \pgfmathtruncatemacro{\tempb}{\m*\x+\m}
       \pgfmathtruncatemacro{\tempe}{\m*\x+2}
       \foreach \y in {0, ...,\ncols} {
         \pgfmathtruncatemacro{\tempc}{\m*\y+1}
         \pgfmathtruncatemacro{\tempd}{\m*\y+\m}
         \draw[dotted, blue]
           ([xshift=-\xshrink ex, yshift=\yshrink ex] 
G-\tempc-\tempa.north west) --
           ([xshift=\xshrink ex, yshift=\yshrink ex] 
G-\tempc-\tempb.north east) --
           ([xshift=\xshrink ex, yshift=-\yshrink ex] 
G-\tempd-\tempb.south east) --
           ([xshift=-\xshrink ex, yshift=-\yshrink ex] 
G-\tempd-\tempa.south west) --
           cycle;
        \draw[red]
           ([xshift=-\bshrink ex, yshift=\rshrink ex] 
G-\tempc-\tempe.north west) --
           ([xshift=\bshrink ex, yshift=\rshrink ex] 
G-\tempc-\tempb.north east) --
           ([xshift=\bshrink ex, yshift=-\rshrink ex] 
G-\tempd-\tempb.south east) --
           ([xshift=-\bshrink ex, yshift=-\rshrink ex] 
G-\tempd-\tempe.south west) --
           cycle;
           }
           }
    \end{tikzpicture}
\end{document}

Please suggest which parameters should I change.

Answer 1

i would rewrote your matrix as follows:

• in matrix's options would use matrix of math nodes
• for nodes in matrix would use matrix's options and not define as every node/.style (by this nodes' contents are in math node)
• red and blue dotted lines would draw as nodes border. these nodes would place by use of the fit library in one double loop

complete mwe:

\documentclass{article}
\usepackage{geometry}
\usepackage{tikz}
\usetikzlibrary{fit, matrix}

\begin{document}

\section{Introduction}
$\widetilde{G}{\;=\;}$
   \begin{tikzpicture}[baseline]
   \matrix (G) [
       matrix of math nodes, 
       nodes={font=\footnotesize,
              text height=0.6em, minimum size=1em,
              anchor=base,inner sep=0pt},
       left delimiter={[},right delimiter={]},
       every even column/.style={column sep=2pt},
       row sep= \ifodd\pgfmatrixcurrentrow% as sugested @marmot in his answer on question
                                          % https://tex.stackexchange.com/questions/469954/
                    -\pgflinewidth%
                \else%
                    3pt%
                \fi,
     ]
      {
1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0\\
0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1&0&1\\
0&\alpha^2&\alpha&\alpha^2&\alpha^2&\alpha^2&1&1&0&\alpha&1&0&\alpha^2&0&\alpha&1&\alpha^2&1&0&1&\alpha&0&1&\alpha&\alpha^2&\alpha&\alpha&\alpha&1&\alpha^2\\
\alpha^2&\alpha^2&\alpha^2&1&\alpha^2&0&1&0&\alpha&\alpha&0&1&0&\alpha^2&1&\alpha^2&1&\alpha&1&1&0&\alpha&\alpha&\alpha^2&\alpha&1&\alpha&0&\alpha^2&\alpha\\
\alpha^2&\alpha&0&\alpha&1&\alpha&\alpha^2&1&1&\alpha^2&1&0&\alpha&0&1&1&0&1&\alpha&1&\alpha^2&0&0&\alpha^2&\alpha^2&\alpha^2&\alpha&\alpha^2&\alpha&\alpha\\
\alpha&1&\alpha&\alpha&\alpha&\alpha^2&1&\alpha&\alpha^2&\alpha&0&1&0&\alpha&1&0&1&1&1&\alpha^2&0&\alpha^2&\alpha^2&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&0\\
\alpha&\alpha^2&\alpha&\alpha&1&\alpha^2&1&\alpha^2&\alpha&\alpha^2&1&0&1&0&0&\alpha&\alpha&\alpha&\alpha&\alpha^2&1&0&\alpha&\alpha&0&\alpha&1&\alpha^2&0&\alpha\\
\alpha^2&1&\alpha&0&\alpha^2&\alpha&\alpha^2&\alpha&\alpha^2&1&0&1&0&1&\alpha&\alpha&\alpha&0&\alpha^2&1&0&1&\alpha&0&\alpha&\alpha&\alpha^2&\alpha&\alpha&\alpha\\
\alpha^2&\alpha^2&1&\alpha^2&0&\alpha^2&0&1&\alpha&\alpha&1&0&\alpha^2&0&\alpha^2&1&\alpha&1&1&1&\alpha&0&\alpha^2&\alpha&1&\alpha&0&\alpha&\alpha&\alpha^2\\
\alpha^2&0&\alpha^2&\alpha&\alpha^2&\alpha^2&1&1&\alpha&0&0&1&0&\alpha^2&1&\alpha&1&\alpha^2&1&0&0&\alpha&\alpha&1&\alpha&\alpha^2&\alpha&\alpha&\alpha^2&1\\
\alpha^2&0&1&0&\alpha^2&0&\alpha&0&1&0&1&0&\alpha&0&\alpha^2&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha&0&1&0&1&0\\
0&\alpha^2&0&1&0&\alpha^2&0&\alpha&0&1&0&1&0&\alpha&0&\alpha^2&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha&0&1&0&1\\
0&\alpha&\alpha&\alpha^2&\alpha&\alpha&\alpha&\alpha&0&\alpha&1&0&1&0&1&\alpha^2&\alpha&\alpha^2&0&\alpha&1&0&\alpha&\alpha^2&1&\alpha^2&\alpha&\alpha&1&\alpha^2\\
\alpha&\alpha&\alpha^2&1&\alpha&0&\alpha&0&\alpha&\alpha&0&1&0&1&\alpha^2&\alpha&\alpha^2&1&\alpha&\alpha&0&1&\alpha^2&1&\alpha^2&\alpha&\alpha&0&\alpha^2&\alpha\\
\alpha&1&0&\alpha&\alpha^2&1&1&\alpha&1&\alpha^2&1&0&\alpha^2&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha&\alpha&0&0&1&1&1&\alpha&\alpha^2&\alpha&\alpha\\
1&\alpha^2&\alpha&\alpha&1&\alpha&\alpha&\alpha^2&\alpha^2&\alpha&0&1&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha&1&0&\alpha&1&1&1&0&\alpha^2&1&\alpha&0\\
1&\alpha&\alpha&\alpha&\alpha^2&\alpha&\alpha&1&\alpha&\alpha^2&1&0&\alpha&0&0&1&1&1&\alpha^2&1&\alpha^2&0&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha^2&0&\alpha\\
\alpha&\alpha^2&\alpha&0&\alpha&1&1&\alpha^2&\alpha^2&1&0&1&0&\alpha&1&1&1&0&1&\alpha&0&\alpha^2&\alpha^2&0&\alpha^2&\alpha^2&\alpha^2&\alpha&\alpha&\alpha\\
\alpha&\alpha&1&\alpha^2&0&\alpha&0&\alpha&\alpha&\alpha&1&0&1&0&\alpha&\alpha^2&1&\alpha^2&\alpha&\alpha&1&0&1&\alpha^2&\alpha&\alpha^2&0&\alpha&\alpha&\alpha^2\\
\alpha&0&\alpha^2&\alpha&\alpha&\alpha&\alpha&\alpha&\alpha&0&0&1&0&1&\alpha^2&1&\alpha^2&\alpha&\alpha&0&0&1&\alpha^2&\alpha&\alpha^2&1&\alpha&\alpha&\alpha^2&1\\
\alpha&0&1&0&\alpha&0&\alpha^2&0&1&0&1&0&\alpha^2&0&\alpha&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha^2&0&1&0&1&0\\
0&\alpha&0&1&0&\alpha&0&\alpha^2&0&1&0&1&0&\alpha^2&0&\alpha&0&\alpha&0&\alpha^2&0&\alpha&0&\alpha^2&0&\alpha^2&0&1&0&1\\
0&1&\alpha&\alpha^2&1&1&\alpha^2&\alpha^2&0&\alpha&1&0&\alpha&0&\alpha^2&\alpha&1&\alpha&0&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&1&\alpha&\alpha&1&\alpha^2\\
1&1&\alpha^2&1&1&0&\alpha^2&0&\alpha&\alpha&0&1&0&\alpha&\alpha&1&\alpha&\alpha^2&\alpha^2&\alpha^2&0&\alpha^2&1&\alpha&1&\alpha^2&\alpha&0&\alpha^2&\alpha\\
1&\alpha^2&0&\alpha&\alpha&\alpha^2&\alpha&\alpha^2&1&\alpha^2&1&0&1&0&\alpha&\alpha&0&\alpha&1&\alpha^2&1&0&0&\alpha&\alpha&\alpha&\alpha&\alpha^2&\alpha&\alpha\\
\alpha^2&\alpha&\alpha&\alpha&\alpha^2&1&\alpha^2&1&\alpha^2&\alpha&0&1&0&1&\alpha&0&\alpha&\alpha&\alpha^2&\alpha&0&1&\alpha&\alpha&\alpha&0&\alpha^2&1&\alpha&0\\
\alpha^2&1&\alpha&\alpha&\alpha&1&\alpha^2&\alpha&\alpha&\alpha^2&1&0&\alpha^2&0&0&\alpha^2&\alpha^2&\alpha^2&1&\alpha&\alpha&0&1&1&0&1&1&\alpha^2&0&\alpha\\
1&\alpha&\alpha&0&1&\alpha^2&\alpha&1&\alpha^2&1&0&1&0&\alpha^2&\alpha^2&\alpha^2&\alpha^2&0&\alpha&\alpha^2&0&\alpha&1&0&1&1&\alpha^2&\alpha&\alpha&\alpha\\
1&1&1&\alpha^2&0&1&0&\alpha^2&\alpha&\alpha&1&0&\alpha&0&1&\alpha&\alpha^2&\alpha&\alpha^2&\alpha^2&\alpha^2&0&\alpha&1&\alpha^2&1&0&\alpha&\alpha&\alpha^2\\
1&0&\alpha^2&\alpha&1&1&\alpha^2&\alpha^2&\alpha&0&0&1&0&\alpha&\alpha&\alpha^2&\alpha&1&\alpha^2&0&0&\alpha^2&1&\alpha^2&1&\alpha&\alpha&\alpha&\alpha^2&1\\
     };
\foreach \i in {1,3,...,29}
{
\pgfmathtruncatemacro{\m}{\i+1}
\foreach \j in {1,3,...,29}
{
\pgfmathtruncatemacro{\n}{\j+1}
\node[draw=red, inner sep=0pt, fit=(G-\i-\n)(G-\m-\n)]{};
\node[draw=blue, dotted, inner sep=0pt, fit=(G-\i-\j)(G-\m-\n)]{};
}
}
    \end{tikzpicture}
\end{document}