Generating the Dragon Curve with Python and Turtle Graphics

The dragon curve is a fractal that exhibits self‑similar structure at any scale, similar to the Mandelbrot set. It can be generated by repeatedly folding a strip of paper and recording the sequence of right (R) and left (L) turns.

Each iteration is built by copying the previous sequence, appending an R, and then appending the reversed previous sequence with R and L swapped. The first few iterations are:

Iteration 1: R

Iteration 2: R R L

Iteration 3: R R L R L L

Iteration 4: R R L R L R R L L R R L L

In Python, the algorithm is implemented with three functions:

<code>R = "R"
L = "L"

def iterate(sequence: str) -> str:
    sequence = sequence + R + swapLetters(sequence[::-1])
    return sequence

def swapLetters(sequence: str) -> str:
    newSequence = ""
    for letter in sequence:
        if letter == R:
            newSequence = newSequence + L
        else:
            newSequence = newSequence + R
    return newSequence

def dragon(n_iterations: int) -> str:
    initial_sequence = R
    for i in range(0, n_iterations):
        initial_sequence = iterate(initial_sequence)
    return initial_sequence
</code>

The generated sequence is then visualized using the turtle module. The drawing script imports the functions, sets up the Turtle speed, color, and screen, and iterates over the sequence, turning right for R and left for L:

<code>from dragon import dragon, R
from turtle import Turtle, Screen

# Turtle setup
 turtle = Turtle("turtle")
 turtle.hideturtle()
 turtle.speed("fastest")
 turtle.color("#ff69aa")

# Screen setup
 screen = Screen()
 screen.title("Dragon Curve")
 screen.bgcolor("black")
 screen.screensize(1920*3, 1080*3)
 screen.setup(width=1.0, height=1.0)

# Draw
 LENGTH = 10
 turtle.forward(LENGTH)
 for element in dragon(17):
     if element == R:
         turtle.right(90)
         turtle.forward(LENGTH)
     else:
         turtle.left(90)
         turtle.forward(LENGTH)

 # Exit
 turtle.color("white")
 turtle.write("click to exit", font=("Calibri", 16, "bold"))
 screen.exitonclick()
</code>

To create a smoother, circular version, replace the straight‑line moves with turtle.circle calls:

<code># Draw (circular version)
 LENGTH = 10
 for element in dragon(17):
     if element == R:
         turtle.circle(-4, 90, 36)
     else:
         turtle.circle(4, 90, 36)
</code>

The article concludes that what initially appears complex becomes simple when broken down, and readers now have a complete Python implementation to generate and visualize the impressive dragon curve fractal.