dots 0 = [ [ 0, 0, 0 ] ]
dots generation = let
     	axis = case mod generation 4 of
	 0 -> [ 1,1,1 ]
	 1 -> [ 1,1,-1 ]
	 2 -> [ 1,1,-1 ]
	 3 -> [ 1,-1,-1 ]
   	indots = dots (-1+generation)
    	aboves = [ zipWith(+) xyz axis | xyz <- indots ]
     	belows = [ zipWith(-) xyz axis | xyz <- indots ]
    	diffx m w | null w = m | null m = w
     	diffx m w = case head m `compare` head w of
     	 EQ -> tail m `diffx` tail w
	 LT -> head m : diffx (tail m) w
	 GT -> head w : diffx m (tail w)
     	in belows `diffx` indots `diffx` aboves

main = sequence_ [ writeFile (show generation ++ ".pgm") ("P5 900 900 1\n" ++
       	           [ if [ -7 + div j 60,
		     	  -7 + div k 60,
			  -7 + div (min (min (mod j 60) (60 - mod j 60))
			       	   	(min (mod k 60) (60 - mod k 60))
			      	   ) 2
		   	] `elem` lights then '\1' else '\0'
		      | j <- [0..899], k <- [0..899] ])
		      | generation <- [0..19], let lights = dots generation ]