http://en.wikipedia.org/wiki/Conway’s_Game_of_Life
I wrote this independently before I saw Alex’s adaptation. Change block size and sparsity with the sliders (changes will restart the simulation).
Code at the end 
Some further ideas:
• ability to control speed of simulation
• color variations (color groups randomly or even by state)
• user-selectable color
• library of interesting starting states (i.e. Gosper's Glider Gun)
• wrap-around world (edges are currently treated as dead)
• optimize calculations (only check changed areas, etc.)
• run/stop parameter slider
• tap-for-next-generation (these last 2 are features of Alex's version)
Here’s the source:
function setup()
blockSize = 12
sparsity = 10
watch("generation")
iparameter("sparsity",2,25,sparsity)
iparameter("blockSize",6,24,blockSize)
resetGrid()
end
function resetGrid()
generation = 0
oSparsity = sparsity
oBlockSize = blockSize
grid = {}
nextGrid = {}
for i = 1,HEIGHT,blockSize do
grid[i] = {}
nextGrid[i] = {}
for j = 1,WIDTH,blockSize do
-- zero is alive, non-zero is dead
grid[i][j] = math.random(0,sparsity)
nextGrid[i][j] = 1
end
end
end
function draw()
background(0,0,0)
fill(0, 255, 41, 255)
generation = generation + 1
for i = 1,HEIGHT,blockSize do
for j = 1,WIDTH,blockSize do
-- reset on parameter changes
if (oSparsity ~= sparsity) then
resetGrid()
end
if (oBlockSize ~= blockSize) then
resetGrid()
end
-- draw live cells
if (grid[i][j] == 0) then
rect(i,j,blockSize,blockSize)
end
n = 0
-- count live neighbors
for k = (i - blockSize),(i + blockSize),blockSize do
for l = (j - blockSize),(j + blockSize),blockSize do
--skip off grid coords
if (k < 0 or l < 0 or k > HEIGHT or l > WIDTH) then
--nop
--skip myself
elseif (k == i and l == j) then
--nop
else
if (grid[k][l] == 0) then
n = n + 1
end
end
end
end
-- conway's game of life rules
if (n < 2) then
nextGrid[i][j] = 1
elseif (n == 2) then
nextGrid[i][j] = grid[i][j]
elseif (n == 3) then
--print(i,j,"birth")
nextGrid[i][j] = 0
elseif (n > 3) then
nextGrid[i][j] = 1
end
end
end
grid = tableCopy(nextGrid)
end
function tableCopy(t)
if type(t) ~= 'table' then return t end
local mt = getmetatable(t)
local res = {}
for k,v in pairs(t) do
if type(v) == 'table' then
v = tableCopy(v)
end
res[k] = v
end
setmetatable(res,mt)
return res
end
