Programming Conway’s Game of Life in LaTeX / sidenote

Programming Conway’s Game of Life in LaTeX

2013. november 18. 10:01

alkotunk, gizmó, ismeretterjesztő, szoftver

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

sidenote

Programming Conway’s Game of Life in LaTeX

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