Grid customized

Question

I would like to build a grid such as the figure shown below where each grid point is surrounded by some of the two curves that describe below.

First curve: an outline around the point forming a drawing of the symbol plus "+". See the figure below.

Second curve: an outline around a drawing point forming the symbol minus "-". See the figure below.

Question 1: How do I build a grid like the picture where I have a command to choose which of the above curves surrounds the grid point?

Question 2: How do I assign color curves and points to the Grid?

Question 3 How to connect a point in the Grid to a point up, down, left, right or in any diagornal? See figure below.

Question 4 How to make a curve that surrounds many grids as shown below?

Answer 1

As an example of how you could implement my comment. You could consider the following code.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,calc}
\def\tminus{\node[minimum height=1.33cm]{\tikz\draw plot[smooth cycle, tension=0.25] coordinates{(-.5cm,-.5ex) (.5cm,-.5ex) (.5cm,.5ex) (-.5cm,.5ex)};};}
\def\tplus{\node[minimum height=1.33cm] {\tikz\draw plot[smooth cycle, tension=0.25] coordinates{(-.5ex,0) (-.5ex,-.5cm+.5ex) (-.5cm, -.5cm+.5ex) (-.5cm, -.5cm-.5ex) (-.5ex, -.5cm-.5ex) (-.5ex, -1cm) (.5ex,-1cm) (.5ex, -.5cm-.5ex) (.5cm, -.5cm-.5ex) (.5cm, -.5cm+.5ex) (.5ex, -.5cm+.5ex) (.5ex,0)};};}
\begin{document}
  \begin{tikzpicture}[every node/.style={anchor=center, minimum height=1cm, minimum width=1cm}]
    \matrix (grid) [matrix of nodes,column sep=10pt,row sep=10pt] {
      \tplus  & \tminus & \tplus  & \tplus  & \tminus\\
      \tplus  & \tplus  & \tminus & \tplus  & \tminus\\
      \tplus  & \tplus  & \tplus  & \tminus & \tminus\\
      \tplus  & \tminus & \tminus & \tplus  & \tminus\\
      \tplus  & \tplus  & \tplus  & \tminus & \tplus\\
    };
    \draw (grid-1-4) -- (grid-1-5);
    \draw (grid-1-4) -- (grid-2-4);
    \draw (grid-1-5) -- (grid-2-5);
    \draw (grid-2-5) -- (grid-3-5);
    \draw (grid-3-5) -- (grid-4-4);
    \draw (grid-4-4) -- (grid-4-3);
    \draw (grid-4-3) -- (grid-4-2);
    \draw (grid-4-2) -- (grid-4-1);
    \draw (grid-4-1) -- (grid-3-1);
    \draw (grid-3-1) -- (grid-3-2);
    \draw (grid-3-2) -- (grid-3-3);
    \draw ($(grid-3-3.center) + (1ex,1ex)$) -- ($(grid-2-4.center) - (1ex,1ex)$);

    \draw[rounded corners] (grid-1-1.north west) -- (grid-2-1.south west) -- (grid-2-2.south west) -- (grid-3-2.south west) -- (grid-3-2.south east) -- (grid-1-2.north east) -- cycle;
  \end{tikzpicture}
\end{document}

Which leads to

Note that the connecting is not entirely straightforward. The nodes have bounding boxes and if you want to get "good-looking" edges between two diagonal pluses you have to put in some manual work, like I showed in the last draw diagonal.

Furthermore drawing a curve around a set of symbols has to be done manually as well. It may be possible to automate these things, but it will certainly not be straightforward or easy.