Coloring of grids in tikz

Question

Each block in each grid need to have a tone color from the (white - black) color scheme. Hence, there will be 25 different tones of gray in each grid.

The grid below the arrows will be an exact copy of the directly grid above the arrow.

(Am still new to tikz so any help will be higly appreciated) My code is as follow:

  \documentclass{article}

  \usepackage{tikz}
  \usetikzlibrary{positioning,calc,math}
  \usepackage{graphicx}


 \begin{document}
 \begin{figure}


\begin{tikzpicture}[
GRID/.pic={\draw (0,0) grid[step=0.2] (1,1);}]
\path[use as bounding box,draw] (12,18) rectangle (0,0);

\foreach \x in {1,3,5,9}
\pic at (\x,16) {GRID};

\pic at (5,14) {GRID};

\node[yshift = 17.4cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 17.4cm,xshift = 3.5cm] () {Cost = 122};
\node[yshift = 17.4cm,xshift = 5.5cm] () {Cost = 111};
\node[yshift = 17.4cm,xshift = 9.5cm] () {Cost = 101};

\draw[->] (3.5,15.5) -- (3.5,13.5) node [midway,text width=3cm,xshift = -1.0cm] {Biased chosen template $P_1$};
\draw[->] (9.5,15.5) -- (9.5,13.5) node [midway,text width=3cm,xshift = 1.6cm] {Biased chosen template $P_2$};

\node[yshift = 14.5cm,xshift = 7.6cm] () {Binary template};

\foreach \x in {3,5,7,9}
\pic at (\x,12) {GRID}; %binary


\node[yshift = 11.5cm,xshift = 6.5cm] () {$P_1 \cdot T + (1-T) \cdot P_2 $};

\draw[->] (6.5,11.0) -- (6.5,10.5) node [midway,xshift = 1cm] {Offspring};

\pic at (6,9)  {GRID};
\draw[->] (6.5,8.5) -- (6.5,7.5) node [midway,xshift = 2cm] {Exponential mutated};
\pic at (6,6)  {GRID};

\draw[-] (6.5,5.5) -- (6.5,5);
\draw[-] (3.5,5) -- (6.5,5); 
\draw[->] (3.5 , 5) -- ( 3.5 , 4.5);


\foreach \x in {1,3,5,9}
\pic at (\x,3) {GRID};

\node[yshift = 2.5cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 2.5cm,xshift = 3.5cm] () {Cost = 141};
\node[yshift = 2.5cm,xshift = 5.5cm] () {Cost = 122};
\node[yshift = 2.5cm,xshift = 9.5cm] () {Cost = 111};
\end{tikzpicture}
\end{figure}
\end{document}

Answer 1

You can achieve this by adding lines to your pic, which are drawn in different tones of gray. Properly positioned, they will appear in each square. With two \foreach loops and some calculation, this is done in three lines.

The gray tones are set with black!<mix>. To change their range, the pic has three parameters. The <mix> is calculated as #1 + <x> * #2 + <y> * #3. The parameters have to be integer numbers. Care must be taken to keep the result in a range from 0 to 100. Parameters #2 and #3 can also be negative.

Every \pic at (...) {GRID}; has to be changed to \pic at (...) {GRID={<#1>/<#2>/<#3>}};.

Here the code:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{positioning,calc,math}
\usepackage{graphicx}

\begin{document}
\begin{figure}
\tikzset{
  pics/GRID/.style args={#1/#2/#3}{%
    code={%
      \foreach \gx in {0,1,2,3,4}{%
        \foreach \gy in {0,1,2,3,4}{%
          \pgfmathparse{#1+\gx*#2+\gy*#3}
          \draw[black!\pgfmathresult,line width=2mm] ($(0.2*\gx,0.2*\gy+0.1)$) -- ($(0.2*\gx+0.2,0.2*\gy+0.1)$);
        }
      }
      \draw (0,0) grid[step=0.2] (1,1);
    }
  }
}
\begin{tikzpicture}
\path[use as bounding box,draw] (12,18) rectangle (0,0);

\foreach \x in {1,3,5,9}
\pic at (\x,16) {GRID={0/4/20}};

\pic at (5,14) {GRID={20/10/-2}};

\node[yshift = 17.4cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 17.4cm,xshift = 3.5cm] () {Cost = 122};
\node[yshift = 17.4cm,xshift = 5.5cm] () {Cost = 111};
\node[yshift = 17.4cm,xshift = 9.5cm] () {Cost = 101};

\draw[->] (3.5,15.5) -- (3.5,13.5) node [midway,text width=3cm,xshift = -1.0cm] {Biased chosen template $P_1$};
\draw[->] (9.5,15.5) -- (9.5,13.5) node [midway,text width=3cm,xshift = 1.6cm] {Biased chosen template $P_2$};

\node[yshift = 14.5cm,xshift = 7.6cm] () {Binary template};

\foreach \x in {3,5,7,9}
\pic at (\x,12) {GRID={0/4/20}}; %binary


\node[yshift = 11.5cm,xshift = 6.5cm] () {$P_1 \cdot T + (1-T) \cdot P_2 $};

\draw[->] (6.5,11.0) -- (6.5,10.5) node [midway,xshift = 1cm] {Offspring};

\pic at (6,9)  {GRID={0/20/4}};
\draw[->] (6.5,8.5) -- (6.5,7.5) node [midway,xshift = 2cm] {Exponential mutated};
\pic at (6,6)  {GRID={100/-4/-20}};

\draw[-] (6.5,5.5) -- (6.5,5);
\draw[-] (3.5,5) -- (6.5,5); 
\draw[->] (3.5 , 5) -- ( 3.5 , 4.5);


\foreach \x in {1,3,5,9}
\pic at (\x,3) {GRID={10/2/10}};

\node[yshift = 2.5cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 2.5cm,xshift = 3.5cm] () {Cost = 141};
\node[yshift = 2.5cm,xshift = 5.5cm] () {Cost = 122};
\node[yshift = 2.5cm,xshift = 9.5cm] () {Cost = 111};
\end{tikzpicture}
\end{figure}
\end{document}

And this is how it looks:

Edit: having random patterns and yet controll requires some coding.

The new code has some commads to define lists for the gray tones, either manually or randomly. With \DefineMixList{<listname>}{<numbers>} you have full control, but also have to enter all 25 values, seperated by ,. With \DefineRandomMixList the values are randomly defined. These lists can be reused as often as you like. They are also written to the log file, so they can be copied and reused later.

Be aware: the random lists will change with every compilation of the document.

Here every \pic at (...) {GRID}; has to be changed to \pic at (...) {GRID={<listname>}};. And in order to have control, you can't use the grids in a \foreach loop anymore.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{positioning,calc,math}
\usepackage{graphicx}

\makeatletter
% #1: name
% #2: comma seperated list of mix values
\newcommand*{\DefineMixList}[2]{%
  \expandafter\def\csname @ml@#1\endcsname{#2}%
  \typeout{new mix list '#1': \csname @ml@#1\endcsname}%
}

% #1: name
\newcommand*{\DefineRandomMixList}[1]{%
  \pgfmathrandominteger{\@ml@entry}{0}{100}%
  \expandafter\xdef\csname @ml@#1\endcsname{\@ml@entry}%
  \foreach \@ml@ in {1,2,...,24}{%
    \pgfmathrandominteger{\@ml@entry}{0}{100}%
    \expandafter\xdef\csname @ml@#1\endcsname{\csname @ml@#1\endcsname,\@ml@entry}%
  }
  \typeout{new random mix list '#1': \csname @ml@#1\endcsname}%
}

% #1: name
\newcommand*{\InitMixFromList}[1]{%
  \@ifundefined{@ml@#1}{%
    \GenericError{%
      (Mix list)\@spaces\@spaces\@spaces\@spaces
    }{%
      Mix list Error: undefined list #1
    }{%
      the list you requested wasn't defined
    }{%
      All squares in the grid affected by this will have the\MessageBreak
      default gray tone.
    }
  }{%
    % define a temporary list
    \edef\@ml@UsedList{\csname @ml@#1\endcsname}%
  }%
}

\newcommand*{\GetNextMixFromList}{%
  \expandafter\@ml@next\@ml@UsedList,\@ml@end
}

\newcommand*{\@ml@next}{}
\def\@ml@next#1,#2\@ml@end{%
  \def\@ml@temp{#1}\ifx\@ml@temp\@empty
    \def\CurrentMix{50}% default, if there are not enough numbers
  \else
    \def\CurrentMix{#1}%
  \fi
  \xdef\@ml@UsedList{#2}% removes just used element from tempoary list
}

\newcommand*{\CurrentMix}{}
\makeatother

% defining the list
\DefineRandomMixList{cost154}
\DefineRandomMixList{cost122}
\DefineRandomMixList{cost111}
\DefineRandomMixList{cost101}
\DefineRandomMixList{cost141}
\DefineRandomMixList{cost154}
\DefineRandomMixList{cost222}
\DefineRandomMixList{cost333}
\DefineRandomMixList{cost444}
\DefineMixList{cost555}{12,57,43,68,75,91,3,36,47,58,64,33,78,82,29,44,50,63,77,46,21,95,21,8,10}

\begin{document}
\begin{figure}
\tikzset{
  pics/GRID/.style={%
    code={%
      \InitMixFromList{#1}%
      \foreach \gx in {0,1,2,3,4}{%
        \foreach \gy in {0,1,2,3,4}{%
          \GetNextMixFromList
          \draw[black!\CurrentMix,line width=2mm] ($(0.2*\gx,0.2*\gy+0.1)$) -- ($(0.2*\gx+0.2,0.2*\gy+0.1)$);
        }
      }
      \draw (0,0) grid[step=0.2] (1,1);
    }
  }
}
\begin{tikzpicture}
\path[use as bounding box,draw] (12,18) rectangle (0,0);

\pic at (1,16) {GRID={cost154}};
\pic at (3,16) {GRID={cost122}};
\pic at (5,16) {GRID={cost111}};
\pic at (9,16) {GRID={cost101}};

\pic at (5,14) {GRID={cost222}};

\node[yshift = 17.4cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 17.4cm,xshift = 3.5cm] () {Cost = 122};
\node[yshift = 17.4cm,xshift = 5.5cm] () {Cost = 111};
\node[yshift = 17.4cm,xshift = 9.5cm] () {Cost = 101};

\draw[->] (3.5,15.5) -- (3.5,13.5) node [midway,text width=3cm,xshift = -1.0cm] {Biased chosen template $P_1$};
\draw[->] (9.5,15.5) -- (9.5,13.5) node [midway,text width=3cm,xshift = 1.6cm] {Biased chosen template $P_2$};

\node[yshift = 14.5cm,xshift = 7.6cm] () {Binary template};

\pic at (3,12) {GRID={cost122}}; %binary
\pic at (5,12) {GRID={cost333}}; %binary
\pic at (7,12) {GRID={cost444}}; %binary
\pic at (9,12) {GRID={cost101}}; %binary


\node[yshift = 11.5cm,xshift = 6.5cm] () {$P_1 \cdot T + (1-T) \cdot P_2 $};

\draw[->] (6.5,11.0) -- (6.5,10.5) node [midway,xshift = 1cm] {Offspring};

\pic at (6,9)  {GRID={cost555}};
\draw[->] (6.5,8.5) -- (6.5,7.5) node [midway,xshift = 2cm] {Exponential mutated};
\pic at (6,6)  {GRID={cost555}};

\draw[-] (6.5,5.5) -- (6.5,5);
\draw[-] (3.5,5) -- (6.5,5); 
\draw[->] (3.5 , 5) -- ( 3.5 , 4.5);


\pic at (1,3) {GRID={cost154}};
\pic at (3,3) {GRID={cost141}};
\pic at (5,3) {GRID={cost122}};
\pic at (9,3) {GRID={cost111}};

\node[yshift = 2.5cm,xshift = 1.5cm] () {Cost = 154};
\node[yshift = 2.5cm,xshift = 3.5cm] () {Cost = 141};
\node[yshift = 2.5cm,xshift = 5.5cm] () {Cost = 122};
\node[yshift = 2.5cm,xshift = 9.5cm] () {Cost = 111};
\end{tikzpicture}
\end{figure}
\end{document}

And now it looks like this: