Snowflake Arms

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

• Write an arm() function that draws one branch with side twigs
• Use a loop with left(60) to repeat the arm six times around a center
• Recognize how six-fold symmetry is built from one repeated unit

Six identical arms radiate from the center, each with two smaller side branches — a crystalline snowflake that grows from a single reusable function.

Welcome to the Snowflake Arms!

Real snowflakes have six-fold symmetry — every arm is identical. In this lab you'll draw one arm as a function and call it six times to build the whole crystal! Let's code it together!

How the Snowflake Works

The arm(length) function draws one arm: out from center, adds two small side branches, then returns to center. Calling it 6 times with left(60) between each call (6 × 60° = 360°) assembles the full snowflake.

Sample Code

import turtle
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()
monty.color('steelblue')

def arm(length):
    monty.forward(length)
    monty.left(45)
    monty.forward(length / 3)
    monty.backward(length / 3)
    monty.right(90)
    monty.forward(length / 3)
    monty.backward(length / 3)
    monty.left(45)
    monty.backward(length)

for i in range(6):
    arm(120)
    monty.left(60)

What Do You Think Will Happen?

After calling arm() and then left(60), six times, how many total degrees has Monty turned? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

6 × 60° = 360° — a full rotation, ending exactly where Monty started. Were you right?

How It Works

Inside arm(), the turtle goes out, adds side branches at ±45°, and comes back: - forward(length) — draw the main arm - left(45) then forward/backward — draw the left twig - right(90) then forward/backward — draw the right twig - left(45) then backward(length) — return to center, facing original direction

The function returns the turtle to its exact starting state — same position, same heading. This is essential for the loop to work: each call to arm() leaves Monty ready for the next left(60).

Explanation Table

Line	What it does
def arm(length)	One snowflake arm — main branch plus two side twigs
monty.left(45)	Turn 45° to draw the left twig
monty.right(90)	Turn 90° (past center) to draw the right twig
monty.left(45)	Return to original heading
monty.backward(length)	Return to center of snowflake
monty.left(60)	Rotate 60° — 6 × 60° = 360° for full snowflake

Learning Check

Your Turn — Add More Twig Levels

The arm() function below is missing the right twig — only the left twig is drawn! Add the two missing lines inside arm() to draw the matching right twig.

▶ Run ↻ Reset

Add monty.right(90) then monty.forward(length / 3) then monty.backward(length / 3) — mirroring the left twig but turning right instead.

Experiments

1. Change the twig angle. Replace left(45) and right(90) with left(30) and right(60). You'll know it worked when the twigs are narrower, making the snowflake look more spiky.

2. Make a 4-armed snowflake. Change range(6) to range(4) and left(60) to left(90). You'll know it worked when the snowflake has four arms at 90° angles like a plus sign.

3. Color each arm differently. Move monty.color(...) inside the loop, cycling through ['steelblue','white','lightblue']. You'll know it worked when each arm is a different shade.

4. Add tiny end twigs. Inside arm(), before backward(length), add smaller side branches at length / 2 position. You'll know it worked when each arm has two sets of twigs.

Beautiful Work!

You built a six-fold symmetric snowflake from a single arm function — the same principle used in all symmetric design, from logos to mandalas! Up next: Polka Dot Canvas — scattering hundreds of colorful dots with random.