sidenote

The other day I thought about that it would be nice to program Conway’s Game of Life in LaTeX and create an animated PDF output. You could say that implementing the Game of Life is pretty easy. It is. But not in LaTeX, at least not for me. After using LaTeX for years I still find it hard to understand some codes and especially writing programs in “pure LaTeX”.

Since I use PGF/TikZ fairly often I decided to use pgfmath for the implementation. Pretty soon I got stuck, I needed to assign values to array elements, and I didn’t know how to overcome this problem in LaTeX. So I decided to ask a question on TeX.SX. This is the point that things get interesting.

I asked a question with the title “Assign value to array element (PGF/TikZ)”, I also wrote that my aim was to program Conway’s Game of Life in LaTeX, and posted my initial code. Before long two answers came, and the question was renamed to “Programming Conway’s Game of Life in LaTeX”. The first answer implemented the Game of Life in LaTeX, the second implemented it in LuaTeX. I was stunned. Especially from the LaTeX implementation. I didn’t – and still don’t – understand the code. :) At the end I decided I should get acquainted with LuaTeX, and write my own solution in it:

Glider

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\documentclass{article}
\usepackage[a0paper]{geometry}

\usepackage{luacode}
\usepackage{animate}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage[active, tightpage]{preview}
\PreviewEnvironment{animateinline
}
%\PreviewEnvironment{tikzpicture}

\tikzset{%
    cellframe/.style={%
        minimum size=5mm,%
        draw,%
        fill=white,%
        fill opacity=0%
    }%
}

\tikzset{%
    alivecell/.style={%
        circle,%
        inner sep=0pt,%
        minimum size=4mm,%
        fill=black%
    }%
}

\setlength{\PreviewBorder}{5mm}

\begin{document}

\begin{luacode*}
    iterations = 36
   
    grid = {{0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 1, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 1, 0, 0, 0},
        {0, 0, 0, 1, 1, 1, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0}}
\end{luacode*}

\begin{luacode*}
    function evolve(grid)
        local temp = {}
        local gridsize = #grid
       
        for i = 1, gridsize do
            temp[i] = {}
            for j = 1, gridsize do
                temp[i][j] = 0
            end
        end
       
        for i = 1, gridsize do
            for j = 1, gridsize do
               
                iminus = i - 1
                iplus = i + 1
                jminus = j - 1
                jplus = j + 1
               
                if iminus == 0 then
                    iminus = gridsize
                end
               
                if iplus == gridsize + 1 then
                    iplus = 1
                end
               
                if jminus == 0 then
                    jminus = gridsize
                end
               
                if jplus == gridsize + 1 then
                    jplus = 1
                end
               
                neighbourcount = grid[iminus][jminus] +
                    grid[iminus][j] +
                    grid[iminus][jplus] +
                    grid[i][jminus] +
                    grid[i][jplus] +
                    grid[iplus][jminus] +
                    grid[iplus][j] +
                    grid[iplus][jplus]
               
                if (grid[i][j] == 1 and (neighbourcount == 2 or neighbourcount == 3)) or (grid[i][j] == 0 and neighbourcount == 3) then
                    temp[i][j] = 1
                else
                    temp[i][j] = 0
                end
            end
        end
       
        return temp
    end
   
    function display(grid)
        local gridsize = #grid
       
       
        for i = 1, gridsize do
            for j = 1, gridsize do
                tex.sprint([[\node[cellframe] at (]])
                tex.sprint((i - 1) * 5)
                tex.sprint([[mm,]])
                tex.sprint(-((j - 1) * 5))
                tex.sprint([[mm){0};]])
               
                if grid[j][i] == 1 then
                    tex.sprint([[\node[alivecell] at (]])
                    tex.sprint((i - 1) * 5)
                    tex.sprint([[mm,]])
                    tex.sprint(-((j - 1) * 5))
                    tex.sprint([[mm){1};]])
                end
            end
        end
    end
   
    function animate(grid, iterations)
        for i = 1, iterations - 1 do
            display(grid)
            tex.sprint([[\newframe]])
            grid = evolve(grid)
        end
        display(grid)
    end
   
    function frames(grid, iterations)
        for i = 1, iterations - 1 do
            tex.sprint([[\begin{tikzpicture}]])
           
            display(grid)
            grid = evolve(grid)
           
            tex.sprint([[\end{tikzpicture}]])
            tex.sprint([[\clearpage]])
        end
       
        tex.sprint([[\begin{tikzpicture}]])
        display(grid)
        tex.sprint([[\end{tikzpicture}]])
    end
\end{luacode*}

\noindent\begin{animateinline}[autoplay,loop,
begin={\begin{tikzpicture}[scale=1
]},
end={\end{tikzpicture}}]{5}
    \luadirect{animate(grid, iterations)}
\end{animateinline
}
%\noindent\luadirect{frames(grid, iterations)}

\end{document}

Note: More information about my implementation is available in my answer on TeX.SX.

It turned out to be pretty easy to do this in LuaTeX, however I struggled with the modulus operator (%) and printing from Lua to TeX. Still it became a pretty nice solution, I think.

Last but not least I’m very grateful for the answers on my question. Here are some nice outputs of jfbu’s and JLDiaz’s answers (if you have a TeX.SX registration then please post an upvote on them because they are really great):

Gosper glider gun
Glider Glider
Gosper glider gun

Megosztás, like stb.
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