Four-Fold Symmetric Doodle

By the end of this lab you'll be able to:

• Record turtle commands as data in a list and replay them
• Apply a 90° rotation to a list of recorded moves to create four-fold symmetry
• Understand the difference between recording commands and executing them immediately

One quadrant of a geometric doodle is recorded, then replayed three more times at 90°, 180°, and 270° rotations — automatically producing perfect four-fold rotational symmetry.

Welcome to the Four-Fold Doodle!

This lab teaches a powerful programming idea: recording actions as data. Draw once, replay four times with different rotations — instant symmetry! Let's code it together!

How It Works

We store moves as a list of tuples: ('forward', 40), ('left', 60), etc. After building the list, we replay it four times, rotating 90° between each replay. This guarantees perfect four-fold symmetry regardless of what moves are in the list.

Sample Code

import turtle
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()

moves = [
    ('forward', 50), ('left', 60), ('forward', 40), ('right', 90),
    ('forward', 30), ('left', 120), ('forward', 50), ('left', 90),
    ('forward', 40), ('right', 60), ('forward', 60),
]

colors = ['crimson', 'royalblue', 'forestgreen', 'darkorange']

for rotation in range(4):
    monty.pencolor(colors[rotation])
    monty.penup()
    monty.goto(0, 0)
    monty.setheading(rotation * 90)
    monty.pendown()
    for cmd, val in moves:
        if cmd == 'forward':
            monty.forward(val)
        elif cmd == 'left':
            monty.left(val)
        elif cmd == 'right':
            monty.right(val)

What Do You Think Will Happen?

Each of the 4 replays starts facing a different direction: 0°, 90°, 180°, 270°. Will the four colored replays look like four independent doodles, or will they form one symmetric pattern? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

One symmetric pattern — the four colored arms are rotations of each other, meeting at the center to form a cohesive design. Were you right?

How It Works

monty.setheading(rotation * 90) is the key. Before each replay, the turtle is sent to the origin facing a new direction. From the turtle's perspective, every replay feels identical — but because the starting heading rotates, the result rotates too.

Explanation Table

Line	What it does
moves = [...]	Record commands as a list of (command, value) tuples
monty.setheading(rotation * 90)	Rotate starting direction for each replay
for cmd, val in moves	Unpack each recorded move
colors[rotation]	Different color per rotation

Learning Check

Your Turn — Add More Moves

Add 3 more moves to the moves list — any combination of forward/left/right. Predict how the symmetry will change (it will stay four-fold!), then run it.

▶ Run ↻ Reset

No matter what you put in moves, the result is always four-fold symmetric — the rotation mechanism guarantees it.

Experiments

1. Six-fold symmetry. Change range(4) to range(6) and rotation * 90 to rotation * 60. You'll know it worked when 6 arms appear.

2. Monochrome. Use 'black' for all colors. You'll know it worked when all arms are the same color, making the symmetry even more obvious.

3. Draw with pen up partway. Add ('penup', 0) and ('pendown', 0) entries and handle them in the replay loop. You'll know it worked when some moves create dashes.

4. Random moves. Generate moves with random.choice and random.randint. You'll know it worked when a different symmetric pattern appears each run.

Commands as Data!

You learned a powerful idea: storing actions as data so you can replay them with transformations. This technique is used in undo/redo systems and animation! Up next: Six-Fold Mandala — extending to 6-fold symmetry.