future_life.py

import itertools

W, H = 4, 4

def create_matrices():
    # N -> matrix
    matrices = {}

    perm = ["".join(seq) for seq in itertools.product("01", repeat=W*H)]

    for index, p in enumerate(perm):
        i = 0
        # Initialize a new matrix
        matrix = [[0 for x in range(W)] for y in range(H)]
        for row in range(H):
            for col in range(W):
                matrix[row][col] = int(p[i]) # matrix consists of integer 0 and 1
                i += 1
        # Matrix is ready
        matrices[index] = matrix

    return matrices


def neighbors(matrix, i, j):
  total = 0
  for x in range(i-1, i+2):
    for y in range(j-1, j+2):
      if x == i and y == j: continue

      #Circular board
      """
      if x == -1: x = W-1
      if y == -1: y = H-1
      if x == W:  x = 0
      if y == H:  y = 0
      """
      if x == -1: continue
      if y == -1: continue
      if x == W:  continue
      if y == H:  continue
      
      total += matrix[x][y]
  return total


def check_future(present, future):
    for i in range(W):
        for j in range(H):
            nbrs = neighbors(future, i, j)
            if present[i][j] == 1:
                # This cell is alive; it will stay alive if in the future it has 2 or 3 neighbors
                if (nbrs == 2 or nbrs == 3) and future[i][j] == 1:
                    # good
                    continue
                # This cell is alive; it will die from loneliness or overpopulation
                elif (nbrs < 2 or nbrs > 3) and future[i][j] == 0:
                    # good
                    continue
                else:
                    return False
            else:
                # This cell is not alive; it will be born if in the future it has exactly 3 neighbors
                if nbrs == 3 and future[i][j] == 1:
                    # good
                    continue
                else:
                    return False
    return True


all_possible_futures = all_possible_presents = create_matrices()

for pkey in all_possible_presents.keys():
    present = all_possible_presents[pkey]
    # Check all candidates
    for fkey in all_possible_futures:
        future = all_possible_futures[fkey]
        if (check_future(present, future)):
            print("Possible cadidate for (" + str(pkey) + ") " +
                  str(present) + " -> (" + str(fkey) + ") " + str(future))