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

LINE_LENGTH  = 5 # Try changing the line length by a little.
ANGLE = 90 # Try changing the turning angle by a few degrees.
LEVELS = 6  # Try changing the recursive level by a little.
DRAW_SOLID = False
#turtle.setheading(20) # Uncomment this line to draw the curve at an angle.

def hilbertCurveQuadrant(level, angle):
    if level == 0:
        # BASE CASE
        return
    else:
        # RECURSIVE CASE
        turtle.right(angle)
        hilbertCurveQuadrant(level - 1, -angle)
        turtle.forward(LINE_LENGTH)
        turtle.left(angle)
        hilbertCurveQuadrant(level - 1, angle)
        turtle.forward(LINE_LENGTH)
        hilbertCurveQuadrant(level - 1, angle)
        turtle.left(angle)
        turtle.forward(LINE_LENGTH)
        hilbertCurveQuadrant(level - 1, -angle)
        turtle.right(angle)
        return

def hilbertCurve(startingPosition):
    # Move to starting position.
    turtle.penup()
    turtle.goto(startingPosition)
    turtle.pendown()
    if DRAW_SOLID:
        turtle.begin_fill()

    hilbertCurveQuadrant(LEVELS, ANGLE) # Draw lower left quadrant.
    turtle.forward(LINE_LENGTH)

    hilbertCurveQuadrant(LEVELS, ANGLE) # Draw lower right quadrant.
    turtle.left(ANGLE)
    turtle.forward(LINE_LENGTH)
    turtle.left(ANGLE)

    hilbertCurveQuadrant(LEVELS, ANGLE) # Draw upper right quadrant.
    turtle.forward(LINE_LENGTH)

    hilbertCurveQuadrant(LEVELS, ANGLE) # Draw upper left quadrant.

    turtle.left(ANGLE)
    turtle.forward(LINE_LENGTH)
    turtle.left(ANGLE)
    if DRAW_SOLID:
        turtle.end_fill()

hilbertCurve((30, 350))
turtle.exitonclick()