Consider the following update function for conway's game of life: from collections import Counter def update(live: Set[Tuple[Integer, Integer]]): counts = Counter.fromkeys(live, 0) + Counter(itertools.chain(neighbors(* cell) for cell in live)) flip = {cell for cell, count in counts.items() if (cell in live and not 1<count<4) or (cell not in live and count==3)} live ^= flip around = frozenset(filter(any, itertools.product(range(-1,2), range(-1,2)))) def neighbors(r: Integer, c: Integer): return (((r+dr)%height, (c+dc)%width) for dr, dc in around) The problem is, Count.fromkeys isn't implemented. I propose that it work exactly as it does for dict, otherwise it's difficult to add items to a Counter when you want them to start off at zero or some other count. The best solution I came up with is to, more confusingly, count live cells once extra and adjust the rules accordingly: def update(live: Set[Tuple[Integer, Integer]]): counts = Counter(itertools.chain(live, *(neighbors(*cell) for cell in live))) flip = {cell for cell, count in counts.items() if (cell in live and not 2<count<5) or (cell not in live and count==3)} live ^= flip around = frozenset(filter(any, itertools.product(range(-1,2), range(-1,2)))) def neighbors(r: Integer, c: Integer): return (((r+dr)%height, (c+dc)%width) for dr, dc in around)