Random Number Generator example

This example investigates random number generation. You will see how to generate and display images in a Jupyter notebook using the PIL module.

A random number generator should produce evenly distributed random numbers. An array of numbers will be generated randomly and displayed graphically to investigate their randomness.

1. Bad RNG

The first RNG is a bad RNG. It contains a lot of common errors that reduce the randomness of the numbers generated:

Use of "%" operation results in unequal probability of random numbers.
Simple linear algebra leads to predictable results.
Use of the same seed leads to the same pattern.

Reference:

https://www.random.org/

http://hasard.readthedocs.org/en/latest/common_errors.html



In [1]:

    
from PIL import Image
from time import time

rand_seed = int(time())
def rng():
    """Return a pseudo-random number between 0 to 8388593.""" 
    global rand_seed
    # For these choice of numbers, see P L'Ecuyer, 
    # "Tables of linear congruential generators of different sizes 
    # and good lattice structure"
    rand_seed = (rand_seed * 653276) % 8388593
    return rand_seed

rgb = bytearray()
for i in range(512*384):
    if i%(128*96)==0:
        # Use similar seeds
        rand_seed = int(time())
    gray = rng()%256
    rgb.extend([gray,gray,gray])

image = Image.frombytes('RGB', (512,384), bytes(rgb))
image.save("/home/xilinx/jupyter_notebooks/examples/data/random_1.jpg", 'JPEG')
image









    Out[1]:

The regular patterns in the image above indicate that the random numbers are not evenly distributed.

2. A better one...

The second RNG is much better than the first one, although this would still not be sufficiently random for security protection.



In [2]:

    
from PIL import Image
from random import randint

rgb = bytearray()
for i in range(512*384):
    gray = randint(0, 255)
    rgb.extend([gray,gray,gray])

image = Image.frombytes('RGB', (512,384), bytes(rgb))
image.save("/home/xilinx/jupyter_notebooks/examples/data/random_2.jpg", 'JPEG')
image









    Out[2]: