sierpinski_simple.py

from PIL import Image
from random import choice


ITERATIONS = 1_000_000
SIZE = 1000
OFFSET = 50

WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
START_POINT = (SIZE // 2, SIZE // 2)

POINTS = (
    (OFFSET, SIZE - OFFSET),
    (SIZE // 2, OFFSET),
    (SIZE - OFFSET, SIZE - OFFSET)
)

def get_point(point):
    # Randomly pick a vertex of the triangle
    p = choice(POINTS)
    # Calculate the point halfway with the provided one
    return (int((point[0] + p[0]) / 2), int((point[1] + p[1]) / 2))


def main():
    # Create an image filled with white
    image = Image.new("RGB", (SIZE, SIZE), (255, 255, 255))

    # Draw the vertexes and the starting point in black
    for p in POINTS:
        image.putpixel(p, BLACK)

    current_point = START_POINT
    image.putpixel(current_point, BLACK)
    
    # Iterate calcualting the mid point and drawing it in black
    for i in range(ITERATIONS):
        current_point = get_point(current_point)
        image.putpixel(current_point, BLACK)

    image.show()


if __name__ == '__main__':
    main()