def functionA(origin_matrix,N_times):
   #apply rule on the origin_matrix to generate another matrix which is the next sate of it.
   #apply rule on origin_matrix for N_times
   return the_final_matrix

def functionB(origin_matrix):
   #determine the period of the the origin_matrix.
   return period
	
iterations = 0;
tmp = origin_matrix;

do
    tmp = operation(tmp);
    iterations += 1;
while tmp != origin_matrix;

return iterations;
	
while True:
    tmp = operation(tmp)
    iterations += 1

    if tmp == origin_matrix:
        break  # Or you could return here.
	
matrix = origin_matrix

for i in range(N_times):
    matrix = operation(matrix)

return matrix