Squares In Binary Visual Representation

README.md

This python file shows the values of the squares of n numbers in binary visualy, which reveals an intresting pattern.
It uses green (0, 255, 0) for '1' and red (255, 0, 0) for '0' and white for spaces that are unused because the length of the binary number is short.

I would reccomend downloading the file and opening it with a program that lets you view the individual pixels. Below is a screenshot of a slice of the pattern.

binarysquaresvis.py

from PIL import Image
import math
def square_to_binary(n):
    return bin(n**2)[2:]

def binary_to_color(binary_string):
    return [(0, 255, 0) if char == '1' else (255, 0, 0) for char in binary_string]

def create_image(n):
    max_binary_length = len(square_to_binary(n))
    image = Image.new('RGB', (n, max_binary_length+1), (255, 255, 255))
    for i in range(1, n+1):
        binary_string = square_to_binary(i)
        colors = binary_to_color(binary_string)
        for j, color in enumerate(colors):
            image.putpixel((i-1, max_binary_length-len(colors)+j), color)
        blue_value = int((i-1)/(n-1)*255)
        image.putpixel((i-1, max_binary_length), (0, 0, blue_value))
    image.save('output.png')

create_image(5000)

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