triangle_reflection_complex/billiard_words.hs

import Data.List
import Data.Ord
import Text.Printf

main = do
  putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q/fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist, length w <= 100]

wordlist = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord p q) | p <- [0..50], q <- [1..50], p <= q]
    where
      sl ((p,q),_) = fromIntegral p / fromIntegral q

-- only allows slopes 0 <= p/q <= 1
slopeWord :: Int -> Int -> String
slopeWord p q = concat $ map word $ zipWith step list (tail list)
    where
      p_ = p `div` gcd p q
      q_ = q `div` gcd p q
      xmax = if (p_-q_) `mod` 3 == 0 then q_ else 3*q_ :: Int
      list = [(x,(x*p) `div` q) | x <- [0..xmax]]
      step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2-y1)
      word (0,0) = "bc"
      word (1,0) = "ab"
      word (2,0) = "ca"
      word (0,1) = "baca"
      word (1,1) = "acbc"
      word (2,1) = "cbab"