I got hold of, and looked through the paper suggested in the root of this thread "Pseudo random trees in Monte-Carlo http://portal.acm.org/citation.cfm?id=1746034", and based upon this I have thrown together a version of the binary tree based random number generator suggested. I would like to point out that I do not know very much about random number generators, the underlying mathematics or any subsequent papers on this subject, this is just a very naive implementation based upon this one paper. As a question, the following code actually generates a stream of numbers that is more random than I was expecting, if anyone can explain why I would be very interested. import System.Random data LehmerTree = LehmerTree {nextInt :: Int, leftBranch :: LehmerTree, rightBranch :: LehmerTree} instance Show LehmerTree where show g = "LehmerTree, current root = "++(show $ nextInt g) mkLehmerTree :: Int->Int->Int->Int->Int->Int->LehmerTree mkLehmerTree aL aR cL cR m x0 = innerMkTree x0 where mkLeft x = (aL * x + cL) `mod` m mkRight x = (aR * x + cR) `mod` m innerMkTree x = let l = innerMkTree (mkLeft x) r = innerMkTree (mkRight x) in LehmerTree x l r mkLehmerTreeFromRandom :: IO LehmerTree mkLehmerTreeFromRandom = do gen<-getStdGen let a:b:c:d:e:f:_ = randoms gen return $ mkLehmerTree a b c d e f instance RandomGen LehmerTree where next g = (fromIntegral.nextInt $ g, leftBranch g) split g = (leftBranch g, rightBranch g) genRange _ = (0, 2147483562) -- duplicate of stdRange test :: IO() test = do gen<-mkLehmerTreeFromRandom print gen let (g1,g2) = split gen let p = take 10 $ randoms gen :: [Int] let p' = take 10 $ randoms g1 :: [Int] -- let p'' = take 10 $ randoms g2 :: [Float] print p print p' -- print p''