map length (tiers :: [[ Int->Int->Int ]])  =  [1,1,5,13,...]

length (list :: [ Int->Int->Int ])  =  Infinity

allUnique (list :: [ Int->Int->Int ])  =  True

ratioRepetitions (list :: [ Int->Int->Int ])  =  0 % 1

tiers :: [Int->Int->Int]  =
  [ [ \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 0
                (0,-1) -> 0
                (1,1) -> 0
                (-1,0) -> 0
                (0,2) -> 0
                (1,-1) -> 0
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 1
                (0,-1) -> 1
                (1,1) -> 1
                (-1,0) -> 1
                (0,2) -> 1
                (1,-1) -> 1
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 0
                (0,-1) -> 1
                (1,1) -> 0
                (-1,0) -> 0
                (0,2) -> 1
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,-1) -> 0
                (1,1) -> 1
                (-1,0) -> 1
                (0,2) -> 0
                (1,-1) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 1
                (0,-1) -> 0
                (1,1) -> 0
                (-1,0) -> 1
                (0,2) -> 0
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,-1) -> 1
                (1,1) -> 1
                (-1,0) -> 0
                (0,2) -> 1
                (1,-1) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> -1
                (0,1) -> -1
                (1,0) -> -1
                (0,-1) -> -1
                (1,1) -> -1
                (-1,0) -> -1
                (0,2) -> -1
                (1,-1) -> -1
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 0
                (0,-1) -> 0
                (1,1) -> 0
                (-1,0) -> 0
                (0,2) -> 0
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,-1) -> 1
                (1,1) -> 0
                (-1,0) -> 0
                (0,2) -> 1
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> -1
                (0,1) -> -1
                (1,0) -> 0
                (0,-1) -> -1
                (1,1) -> 0
                (-1,0) -> 0
                (0,2) -> -1
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,-1) -> 0
                (1,1) -> 1
                (-1,0) -> 0
                (0,2) -> 0
                (1,-1) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 0
                (0,-1) -> 1
                (1,1) -> 0
                (-1,0) -> 1
                (0,2) -> 1
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,-1) -> 0
                (1,1) -> 0
                (-1,0) -> 1
                (0,2) -> 0
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 0
                (0,-1) -> 0
                (1,1) -> 1
                (-1,0) -> 0
                (0,2) -> 0
                (1,-1) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> -1
                (0,-1) -> 0
                (1,1) -> -1
                (-1,0) -> -1
                (0,2) -> 0
                (1,-1) -> -1
                ...
    , \x y -> case (x,y) of
                (0,0) -> -1
                (0,1) -> 0
                (1,0) -> -1
                (0,-1) -> 0
                (1,1) -> 0
                (-1,0) -> -1
                (0,2) -> 0
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,-1) -> 0
                (1,1) -> 1
                (-1,0) -> 0
                (0,2) -> 0
                (1,-1) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 1
                (0,-1) -> 1
                (1,1) -> 0
                (-1,0) -> 1
                (0,2) -> 1
                (1,-1) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> -1
                (1,0) -> 0
                (0,-1) -> -1
                (1,1) -> -1
                (-1,0) -> 0
                (0,2) -> -1
                (1,-1) -> -1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 2
                (0,1) -> 2
                (1,0) -> 2
                (0,-1) -> 2
                (1,1) -> 2
                (-1,0) -> 2
                (0,2) -> 2
                (1,-1) -> 2
                ...
    ]
  , ...
  ]