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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?

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A TikZ matrix node and some overlays should get you pretty much there. Check out the manual‌​. –  Roelof Spijker Mar 5 '12 at 12:31
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Please show some attempt you've made in achieving this and specify what you're struggling with. The point of this Q&A site is to solve specific problems, not to have other people do your work. (Also note that it's not customary here to add a title, greeting or thank you line to a post body.) –  doncherry Mar 5 '12 at 14:31
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1 Answer

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

example

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.

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Instead of using ($(grid-3-3.center) + (1ex,1ex)$) to get shorter lines you may define a style that uses the shorten key and apply it o the \draw command (or a higher scope) –  Tobi Mar 5 '12 at 14:17
    
@Tobi: it's used to get longer lines, not shorter ones. And it's not necessarily symmetrical. For instance, we might want to have better connecting vertical lines. But when we try to add a line from (4,4) to (5,4) it only needs to be made longer on one end (namely on the side of the minus). As far as I know, this isn't possible with shorten. –  Roelof Spijker Mar 5 '12 at 14:50
    
I musunderstood your usage, I forgot that (grid-3-3.center)≠(grid-3-3), but shorten accepts negativ values to make a line longer an for that can be used here to. It is also possible to differentiate between shorten < and shorten > to change the length different on both ends. –  Tobi Mar 5 '12 at 15:07
    
@Tobi: Ah, yes! I forgot about the separate > and < versions. Then it can indeed be used quite well. –  Roelof Spijker Mar 5 '12 at 15:18
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