Tikz and pgf: Grid of Dots with Text and Circles

Question

I wish to have a grid of points or dots along with the labels, and combine them into a single figure like the one below.

I tried the closest graph I can for the first grid in the top left, and here's the result of it,

\documentclass{article}   
\usepackage{tikz}
  \begin{tikzpicture}
    \foreach \x in {0,1,2,3,4,5,6}
    \foreach \y in {0,1,2,3,4,5,6}
    {
    \draw (\x,\y) circle (0.3cm);
    }
    \fill (3,4) node {\textbf{A}};
    \fill (4,3) node {\textbf{B}};
    \fill (3,3) node {\textbf{X}};
    \fill (3,2) node {\textbf{C}};
    \fill (2,3) node {\textbf{D}};
  \end{tikzpicture}
\end{document}

I would be happy if you could help me with the codes of these grids for both two and one dimension.

Thank you in advance!

Answer 1

This is not as elegant as cmhughes' answer. You can also use shifts and scopes to position the figures.

Code

%\documentclass{article}   
\documentclass[border=5,convert]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning, calc}
\tikzset{circle node/.style = {circle,inner sep=1pt,draw, fill=white},
        X node/.style = {fill=white, inner sep=1pt},
        dot node/.style = {circle, draw, inner sep=5pt}
}

\begin{document}
  \begin{tikzpicture}[scale=0.5]
    \foreach \x in {0,...,6}
    \foreach \y in {0,...,6}
    {
    \fill (\x,\y) circle (2pt);
    }
    \foreach \a/\b/\c in {3/4/A,4/3/B,3/2/C,2/3/D}
    \fill (\a,\b) node (\c) [circle node] {\textbf{\c}};
    \node [X node] at (3,3) {\textbf{X}};

    \node at (11,3) {FIRST ORDER};

    \begin{scope}[shift={(15,3)}]
    \foreach \x in {0,...,8}
        \fill (\x,0) circle (2pt);  
    \node at (4,0) [X node] {\textbf{X}};
    \foreach \x in {3,5}
        \node [dot node] at (\x,0) {};
    \end{scope}

    \begin{scope}[shift={(0,-8)}]
        \foreach \x in {0,...,6}
        \foreach \y in {0,...,6}
        {
        \fill (\x,\y) circle (2pt);
        }
        \foreach \a/\b/\c in {2/4/E,4/4/F,4/2/G,2/2/H}
        \fill (\a,\b) node [circle node] {\textbf{\c}};
        \node [X node] at (3,3) {\textbf{X}};

        \node at (11,3) {SECOND ORDER};

        \begin{scope}[shift={(15,3)}]
            \foreach \x in {0,...,8}
            \fill (\x,0) circle (2pt);  
            \node at (4,0) [X node] {\textbf{X}};
            \foreach \x in {2,6}
            \node [dot node] at (\x,0) {};
        \end{scope}
    \end{scope}
  \end{tikzpicture}
\end{document}

Output

Answer 2

Here's something to get you started

The idea is to set up nodes using the foreach command and name them as x-y. You can then circle the appropriate nodes.

The coordinate system starts at (0,0) and goes up to (8,8). You can adjust the scale as you see fit.

\documentclass{article}
\usepackage{tikz}

\tikzset{mystyle/.style={shape=circle,fill=black,scale=0.3}}
\tikzset{withtext/.style={fill=white}}

\begin{document}

\begin{figure}
    \begin{minipage}{.5\textwidth}
        \begin{tikzpicture}[scale=.5]
            % setup the nodes
            \foreach \x in {0,...,8}
            \foreach \y in {0,...,8}
            {
            \ifnum\x=4
                \ifnum\y=4
                    \node (\x-\y) at (\x,\y){X};
                \else
                    \node[mystyle] (\x-\y) at (\x,\y){};
                \fi
            \else
                \node[mystyle] (\x-\y) at (\x,\y){};
            \fi
            }
            % circle selected nodes with letters
            \foreach \mynode/\mytext in {4-3/A,3-4/B,5-4/C,4-5/D}
            {
                \draw[withtext] (\mynode) circle (0.4cm) node {\mytext};
            }
        \end{tikzpicture}
    \end{minipage}%
    \begin{minipage}{.5\textwidth}
        \begin{tikzpicture}[scale=.5]
            % setup the nodes
            \foreach \x in {0,...,8}
            {
            \ifnum\x=4
                \node (\x) at (\x,0){X};
            \else
                \node[mystyle] (\x) at (\x,0){};
            \fi
            }
            % circle selected nodes
            \foreach \mynode in {3,5}
            {
                \draw (\mynode) circle (0.3cm);
            }
        \end{tikzpicture}
    \end{minipage}%
\end{figure}

\end{document}