module ThueMorse where
tms1 :: [Int]
tms1 = buildtms1 [0] 1
	where buildtms1 x n	
		|(n `rem` 2 == 0) = buildtms1 (x++[(x !! (n `div` 2))]) (n+1)
		|(n `rem` 2 == 1) = buildtms1 (x++[1- (x !! ((n-1) `div` 2))]) (n+1)
		
custinv [] 	= []
custinv x 	= (1-head x):(custinv (tail x))

tms3 :: [Int]
tms3 = buildtms3 [0] 1
	where buildtms3 x n = buildtms3 (x++(custinv x)) (n*2)
		
intToBinary :: Int -> [Bool]
intToBinary n 	| (n==0) = []
				| (n `rem` 2 ==0) = intToBinary (n `div` 2) ++ [False]
				| (n `rem` 2 ==1) = intToBinary (n `div` 2) ++ [True]
				
amountTrue :: [Bool] -> Int
amountTrue [] = 0
amountTrue (x:xs) 	| (x==True) = 1+amountTrue(xs)
					| (x==False) = amountTrue(xs)

tms4 :: [Int]
tms4= buildtms4 0
	where buildtms4 n
		|(amountTrue (intToBinary n) `rem` 2 ==0) = 0:(buildtms4 (n+1))
		|(amountTrue (intToBinary n) `rem` 2 ==1) = 1:(buildtms4 (n+1))