map length (tiers :: [[ (Int,Int) ]])  =  [1,2,3,4,5,6,7,8,9,10,11,12,...]

length (list :: [ (Int,Int) ])  =  Infinity

allUnique (list :: [ (Int,Int) ])  =  True

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

tiers :: [(Int,Int)]  =
  [ [(0,0)]
  , [ (0,1)
    , (1,0)
    ]
  , [ (0,-1)
    , (1,1)
    , (-1,0)
    ]
  , [ (0,2)
    , (1,-1)
    , (-1,1)
    , (2,0)
    ]
  , [ (0,-2)
    , (1,2)
    , (-1,-1)
    , (2,1)
    , (-2,0)
    ]
  , [ (0,3)
    , (1,-2)
    , (-1,2)
    , (2,-1)
    , (-2,1)
    , (3,0)
    ]
  , [ (0,-3)
    , (1,3)
    , (-1,-2)
    , (2,2)
    , (-2,-1)
    , (3,1)
    , (-3,0)
    ]
  , [ (0,4)
    , (1,-3)
    , (-1,3)
    , (2,-2)
    , (-2,2)
    , (3,-1)
    , (-3,1)
    , (4,0)
    ]
  , [ (0,-4)
    , (1,4)
    , (-1,-3)
    , (2,3)
    , (-2,-2)
    , (3,2)
    , (-3,-1)
    , (4,1)
    , (-4,0)
    ]
  , [ (0,5)
    , (1,-4)
    , (-1,4)
    , (2,-3)
    , (-2,3)
    , (3,-2)
    , (-3,2)
    , (4,-1)
    , (-4,1)
    , (5,0)
    ]
  , [ (0,-5)
    , (1,5)
    , (-1,-4)
    , (2,4)
    , (-2,-3)
    , (3,3)
    , (-3,-2)
    , (4,2)
    , (-4,-1)
    , (5,1)
    , (-5,0)
    ]
  , [ (0,6)
    , (1,-5)
    , (-1,5)
    , (2,-4)
    , (-2,4)
    , (3,-3)
    , (-3,3)
    , (4,-2)
    , (-4,2)
    , (5,-1)
    , (-5,1)
    , (6,0)
    ]
  , ...
  ]