Python Turtle Spirograph - by chatgpt; steps calculation is interesting

tutle_spirograph.py

# Set up the screen
screen = turtle.Screen()
screen.bgcolor("white")

# Set up the turtle
pen = turtle.Turtle()
pen.speed(0)  # Fastest drawing speed
pen.width(2)

def draw_spirograph(R, r, d):
    """
    Draw a spirograph using:
    R: Radius of the fixed outer circle.
    r: Radius of the rolling circle.
    d: Distance from the center of the rolling circle to the drawing point.
    """
    # Calculate the number of steps based on the greatest common divisor of R and r
    gcd_val = math.gcd(R, r)
    num_steps = int(r/gcd_val) * 360
    
    for i in range(0, num_steps, 30):
        theta = math.radians(i)
        x = (R - r) * math.cos(theta) + d * math.cos(((R - r) / r) * theta)
        y = (R - r) * math.sin(theta) - d * math.sin(((R - r) / r) * theta)
        pen.goto(x, y)
    pen.hideturtle()

# Parameters for the spirograph
R = 100  # Radius of the fixed circle
r = 87   # Radius of the rolling circle
d = 100  # Distance from the center of the rolling circle to the drawing point

pen.up()
pen.goto((R-r)+d, 0)  # Move the pen to the starting point
pen.down()

draw_spirograph(R, r, d)

# Finish up
turtle.done()