Statistics in multidigit numbers

from random import randrange
from matplotlib import pyplot as plt

# Auxiliary Functions
# 1. Find unique digits of a number
def unique(number):
    a = str(number)
    b = [int(element) for element in a]
    digits = sorted(b)
    un = list()
    for digit in digits:
        if digit not in un:
            un.append(digit)
    return len(un)

# 2. Simulate for different numbers with fixed length = num of digits
def simulate_fixed_length(sims, num_digits):
    # This list will be a list with len = 10.
    # Element in index 0 is the total number of cases our randomly created
    # numbers had only 1 digit, index 2 for a 2-unique-digit number and
    # index 9 if all the digits are different (10).
    counter = [0 for i in range(10)]
    start = 10 ** (num_digits - 1)
    stop = 10 ** num_digits
    for i in range(sims):
        r = randrange(start, stop)
        UN = unique(r)
        counter[UN - 1] += 1
        # if UN == 1:
            # print(r)
    return counter

# 3. Simulate for different lengths
def simulate(sims, num_digits_list):
    counters = list()
    for num_digit in num_digits_list:
        print("******************************************************")
        print("For " + str(num_digit) + "-digit numbers:")
        counter = simulate_fixed_length(sims, num_digit)
        counters.append(counter)
        print(counter)
        print()
    return counters

# MAIN FUNCTION
sims = 10**5
num_digits_list = range(2, 15)
counters = simulate(sims, num_digits_list)
# Plotting
x = range(1, 11)
plt.figure()
for i in range(len(counters)):
    y = counters[i]
    print(y)
    plt.plot(x, y)

plt.title("Simulations = " + str(sims))
titles = [str(i) + "-digit numbers" for i in num_digits_list]
plt.legend(titles)
plt.show()