create a USA flag with different numbers of stars. Based on https://pythoncircle.com/post/661/python-script-11-drawing-flag-of-united-states-of-america-using-python-turtle/

USAflag.py

#
# Python script to create USA flag using turtle.
# Author - https://www.pythoncircle.com
# Original Author - https://www.codesters.com/preview/6fe8df0ccc45b1460ab24e5553497c5684987fb5/

import turtle
import time
from PIL import Image
import math

# create a screen
screen = turtle.getscreen()
# set background color of screen
screen.bgcolor("white")
# set tile of screen
screen.title("USA Flag - https://www.pythoncircle.com")
# "Yesterday is history, tomorrow is a mystery, 
# but today is a gift. That is why it is called the present.”
# — Oogway to Po, under the peach tree, Kung Fu Panda Movie
oogway = turtle.Turtle()
# set the cursor/turtle speed. Higher value, faster is the turtle
oogway.speed(100)
oogway.penup()
# decide the shape of cursor/turtle
oogway.shape("turtle")

# flag height to width ratio is 1:1.9
flag_height = 250
flag_width = 475

# starting points
# start from the first quardant, half of flag width and half of flag height
start_x = -237
start_y = 125

# For red and white stripes (total 13 stripes in flag), each strip width will be flag_height/13 = 19.2 approx
stripe_height = flag_height/13
stripe_width = flag_width

# length of one arm of star
star_size = 6


def draw_fill_rectangle(x, y, height, width, color):
    oogway.goto(x,y)
    oogway.pendown()
    oogway.color(color)
    oogway.begin_fill()
    oogway.forward(width)
    oogway.right(90)
    oogway.forward(height)
    oogway.right(90)
    oogway.forward(width)
    oogway.right(90)
    oogway.forward(height)
    oogway.right(90)
    oogway.end_fill()
    oogway.penup()




def draw_star(x, y, color, radius):
    # Generate points for a 5-pointed star centered at (x, y)
    points = []
    for i in range(10):
        angle_deg = 90 + i * 36  # Start from top (90°)
        angle_rad = math.radians(angle_deg)
        r = radius if i % 2 == 0 else radius * 0.382  # inner radius ≈ golden ratio
        px = x + r * math.cos(angle_rad)
        py = y + r * math.sin(angle_rad)
        points.append((px, py))

    oogway.penup()
    oogway.goto(points[0])
    oogway.color(color, color)
    oogway.begin_fill()
    oogway.pendown()
    for px, py in points[1:] + [points[0]]:
        oogway.goto(px, py)
    oogway.end_fill()
    oogway.penup()

# this function is used to create 13 red and white stripes of flag
def draw_stripes():
    x = start_x
    y = start_y
    # we need to draw total 13 stripes, 7 red and 6 white
    # so we first create, 6 red and 6 white stripes alternatively    
    for stripe in range(0,6):
        for color in ["red", "white"]:
            draw_fill_rectangle(x, y, stripe_height, stripe_width, color)
            # decrease value of y by stripe_height
            y = y - stripe_height            

    # create last red stripe
    draw_fill_rectangle(x, y, stripe_height, stripe_width, 'red')
    y = y - stripe_height


# this function create navy color square
# height = 7/13 of flag_height
# width = 0.76 * flag_height
# check references section for these values
def draw_square():
    square_height = (7/13) * flag_height
    square_width = (0.76) * flag_height
    draw_fill_rectangle(start_x, start_y, square_height, square_width, 'navy')


def draw_six_stars_rows():
    gap_between_stars = 30
    gap_between_lines = stripe_height + 6
    y = 112
    # create 5 rows of stars
    for row in range(0,5) :
        x = -222
        # create 6 stars in each row
        for star in range (0,6) :
            draw_star(x, y, 'white', star_size)
            x = x + gap_between_stars
        y = y - gap_between_lines

def draw_star_field_51():
    union_height = (7/13) * flag_height
    union_width = 0.76 * flag_height

    #layout = [6, 5, 6, 5, 6, 5, 6, 6, 6]  # total 51 stars
    #layout = [6, 5, 6, 5, 6, 6, 6, 5, 6]
    #layout = [7, 6, 7, 6, 7, 6, 7, 6] #52
    layout = [10, 10, 10, 10, 10, 10, 10, 10] #60
    rows = len(layout)
    max_cols = max(layout)

    horiz_gap = union_width / (max_cols + 1)
    vert_gap = union_height / (rows + 1)
    star_radius = min(horiz_gap, vert_gap) * 0.3

    for row_index, stars_in_row in enumerate(layout):
        y = start_y - vert_gap * (row_index + 1)
        for col in range(stars_in_row):
            x = start_x + horiz_gap * (col + 1)
            if stars_in_row < max_cols:
                x += horiz_gap / 2  # center the shorter rows
            draw_star(x, y, 'white', star_radius)


def draw_star_field():
    union_height = (7/13) * flag_height
    union_width = 0.76 * flag_height

    rows = 9
    max_cols = 6

    #  Compute true horizontal and vertical spacing
    horiz_gap = union_width / (max_cols + 1)
    vert_gap = union_height / (rows + 1)

    # Reuse the same radius scaling, now spaced correctly
    star_radius = min(horiz_gap, vert_gap) * 0.3
    #star_radius = 0.0308 * flag_height  # diameter = 0.0616

    rows = 9
    for row in range(rows):
        stars_in_row = 6 if row % 2 == 0 else 5
        y = start_y - vert_gap * (row + 1) + (vert_gap / 2)
        for col in range(stars_in_row):
            x = start_x + horiz_gap * (col + 1)
            if stars_in_row == 5:
                x += horiz_gap / 2  # center the shorter rows
            draw_star(x, y, 'white', star_radius)


def draw_five_stars_rows():
    gap_between_stars = 30
    gap_between_lines = stripe_height + 6
    y = 100
    # create 4 rows of stars
    for row in range(0,4) :
        x = -206
        # create 5 stars in each row
        for star in range (0,5) :
            draw_star(x, y, 'white', star_size)
            x = x + gap_between_stars
        y = y - gap_between_lines

# start after 5 seconds.
time.sleep(5)
# draw 13 stripes
draw_stripes()
draw_square()
#draw_star_field()
draw_star_field_51()
# draw 30 stars, 6 * 5
#draw_six_stars_rows()
# draw 20 stars, 5 * 4. total 50 stars representing 50 states of USA
#draw_five_stars_rows()
# hide the cursor/turtle
oogway.hideturtle()

# Save the canvas to a PostScript file
ts = turtle.getcanvas()
ts.postscript(file="us_flag.eps")

# Now convert to PNG using Pillow
img = Image.open("us_flag.eps")
img.save("us_flag60.png")
# keep holding the screen until closed manually
screen.mainloop()