I’ve just finished writing an article for The Invariant Magazine (the annual Oxford Maths Society magazine which tends to actually get published once a decade) about cellular automata.
Whilst writing, I became a bit distracted, and decided to write some haskell to print 1D automata. After replacing most variables with single letters, and manually inlining some things, behold:
import Data.Bits
ns xs = zip3 (drop (l-1) xs') xs (tail xs') where xs' = cycle xs; l = length xs
s ru xs = map (\(l,c,r) -> if (2^(l*4 + c*2 + r) .&. ru) == 0 then 0 else 1) $ ns xs
ss = map (\c -> if c == 0 then ' ' else '#')
printAutomata :: Int -> Int -> [Int] -> IO () --one type sig needed
printAutomata n r xs = mapM_ putStrLn $ map ss $ take n $ iterate (s r) xs
Then in GHCI, let’s try to simulate Rule 90 starting with a single cell of state 1.
Prelude> :l ca.hs
[1 of 1] Compiling Main ( ca.hs, interpreted )
Ok, modules loaded: Main.
*Main> printAutomata 20 90 $ (replicate 20 0) ++ [1] ++ (replicate 20 0)
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
Yay Sierpinski!
