import turtle
turtle.tracer(10, 0) # Increase the first argument to speed up the drawing.
turtle.setworldcoordinates(0, 0, 700, 700)
turtle.hideturtle()
turtle.pensize(2)

def drawKochCurve(startPosition, heading, length):
    if length < 1:
        # BASE CASE
        return
    else:
        # RECURSIVE CASE
        # Move to the start position.
        recursiveArgs = []
        turtle.penup()
        turtle.goto(startPosition)
        turtle.setheading(heading)
        recursiveArgs.append({'position':turtle.position(),
                              'heading':turtle.heading()})

        # Erase the middle third.
        turtle.forward(length / 3)
        turtle.pencolor('white')
        turtle.pendown()
        turtle.forward(length / 3)

        # Draw the bump.
        turtle.backward(length / 3)
        turtle.left(60)
        recursiveArgs.append({'position':turtle.position(),
                              'heading':turtle.heading()})
        turtle.pencolor('black')
        turtle.forward(length / 3)
        turtle.right(120)
        recursiveArgs.append({'position':turtle.position(),
                              'heading':turtle.heading()})
        turtle.forward(length / 3)
        turtle.left(60)
        recursiveArgs.append({'position':turtle.position(),
                              'heading':turtle.heading()})

        for i in range(4):
            drawKochCurve(recursiveArgs[i]['position'],
                     recursiveArgs[i]['heading'],
                     length / 3)
        return

def drawKochSnowflake(startPosition, heading, length):
    # A Koch snowflake is three Koch curves in a triangle.

    # Move to the starting position
    turtle.penup()
    turtle.goto(startPosition)
    turtle.setheading(heading)

    for i in range(3):
        # Record the starting position and heading.
        curveStartingPosition = turtle.position()
        curveStartingHeading = turtle.heading()
        drawKochCurve(curveStartingPosition,
                      curveStartingHeading, length)

        # Move back to the start position for this side.
        turtle.penup()
        turtle.goto(curveStartingPosition)
        turtle.setheading(curveStartingHeading)

        # Move to the start position of the next side.
        turtle.forward(length)
        turtle.right(120)

drawKochSnowflake((100, 500), 0, 500)
turtle.exitonclick()