The original Koch Snowflake is based on triangles. Draw quadratic Koch snowflake that breaks a line into 4 smaller pieces of 1/3 of the original length as shown.

The following is drawn with 4 initial lines that forms a square.

Source Code:

import turtle

screen = turtle.Screen()
screen.title('Quadratic Koch Curve - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.setworldcoordinates(-1000,-1000,1000,1000)
screen.tracer(0,0)
turtle.speed(0)
turtle.hideturtle()
turtle.bgcolor('midnight blue')
turtle.color('white')

def koch(x1,y1,x2,y2):
    distance=((x2-x1)**2 + (y2-y1)**2)**0.5
    if distance<10:
        turtle.up()
        turtle.goto(x1,y1)
        turtle.down()
        turtle.goto(x2,y2)
        return
    turtle.up()
    turtle.goto(x1,y1)
    direction=turtle.towards(x2,y2)
    turtle.seth(direction)
    turtle.fd(distance/3)
    x3,y3 = turtle.xcor(), turtle.ycor()
    turtle.left(90)
    turtle.fd(distance/3)
    x4,y4 = turtle.xcor(), turtle.ycor()
    turtle.right(90)
    turtle.fd(distance/3)
    x5,y5 = turtle.xcor(), turtle.ycor()
    turtle.right(90)
    turtle.fd(distance/3)
    x6,y6 = turtle.xcor(), turtle.ycor()
    koch(x1,y1,x3,y3)
    koch(x3,y3,x4,y4)
    koch(x4,y4,x5,y5)
    koch(x5,y5,x6,y6)
    koch(x6,y6,x2,y2)
    

koch(-400,-400,-400,400)
koch(-400,400,400,400)
koch(400,400,400,-400)
koch(400,-400,-400,-400)
screen.update()