A couple of changes mean that only an R or r will roll. Any other character will quit

import random

while True:
    print('Your score so far is {}.'.format(myScore))
    print("Would you like to roll or quit?")
    ans = input("Roll...")
    if ans.lower() == 'r':
        R = np.random.randint(1, 8)
        print("You rolled a {}.".format(R))
        myScore = R + myScore
    else:
        print("Now I'll see if I can break your score...")
        break

just indent your code correctly:

def determine_period(universe_array):
    period=0
    tmp=universe_array
    while True:
        tmp=apply_rules(tmp)#aplly_rules is a another function
        period+=1
        if numpy.array_equal(tmp,universe_array) is True:
            return period
        if period>12:  #i wrote this line to stop it..but seems its doesnt work....help..
            return 0
        else:   
            return period

You need to understand that the break statement in your example will exit the infinite loop you've created with while True. So when the break condition is True, the program will quit the infinite loop and continue to the next indented block. Since there is no following block in your code, the function ends and don't return anything. So I've fixed your code by replacing the break statement by a return statement.

Following your idea to use an infinite loop, this is the best way to write it:

def determine_period(universe_array):
    period=0
    tmp=universe_array
    while True:
        tmp=apply_rules(tmp)#aplly_rules is a another function
        period+=1
        if numpy.array_equal(tmp,universe_array) is True:
            break
        if period>12:  #i wrote this line to stop it..but seems its doesnt work....help..
            period = 0
            break

    return period

You could always use a function and return from it:

import logging

def func():
    for i, x in enumerate(x):
        logging.info("Processing `x` n.%s...", i)
        y = do_something(x)
        if y == A:
            logging.info("Doing something else...")
            do_something_else(x)
        elif y == B:
            logging.info("Done.")
            return # Exit the function and stop the loop in the process.
func()

Although using break is more elegant in my opinion because it makes your intent clearer.