Rainbow Square Spiral

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

• Use a for loop to repeat a drawing step many times
• Cycle through a list of colors using the % (modulo) operator
• See how adding a tiny rotation each time creates a dramatic spiral effect

Draw a square, turn a little, draw a slightly larger square — and repeat. After 36 squares you get a glowing color tunnel that spins right off the screen.

Welcome to the Rainbow Square Spiral!

In this lab you'll use a loop to draw 36 squares, rotating a little each time. Tiny changes — just 10 degrees and 8 pixels — add up to something spectacular. Let's code it together!

How the Spiral Works

Each time through the loop, Monty draws one square and then:

1. Rotates 10 degrees to the right (so the next square is slightly turned)
2. Grows the side length by 8 pixels (so the next square is slightly larger)

After 36 repetitions, those tiny changes stack into a full 360-degree rotation and a square that is nearly 300 pixels wide — starting from just 20.

Sample Code

import turtle
monty = turtle.Turtle()
monty.speed(0)
monty.shape('turtle')

colors = ['red', 'orange', 'yellow', 'green', 'blue', 'violet']
side = 20

for i in range(36):
    monty.color(colors[i % len(colors)])
    for j in range(4):
        monty.forward(side)
        monty.right(90)
    monty.right(10)
    side += 8

monty.hideturtle()

What Do You Think Will Happen?

The outer loop runs 36 times and there are 6 colors in the list. How many times will each color appear in the finished spiral? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

Each color appears exactly 6 times — because 36 ÷ 6 = 6, and i % 6 cycles through 0 → 1 → 2 → 3 → 4 → 5 → 0 → 1 → … Were you right?

How It Works

The program uses two nested loops. The outer loop (for i in range(36)) runs once per square. The inner loop (for j in range(4)) draws the four sides of each square: forward, turn 90°, forward, turn 90°, and so on.

After the inner loop finishes one square, the outer loop does two more things before starting the next square:

• monty.right(10) — turns Monty 10 degrees, so the next square is slightly rotated
• side += 8 — makes the next square 8 pixels wider on each side

The color is chosen with colors[i % len(colors)]. The % operator gives the remainder after dividing, so i % 6 always produces a number from 0 to 5, cycling the list no matter how big i gets.

Explanation Table

Line	What it does
monty.speed(0)	Maximum speed — no animation delay
colors = [...]	A list of 6 color names to cycle through
side = 20	Starting side length of the first (smallest) square
for i in range(36)	Repeat the square-drawing block 36 times
colors[i % len(colors)]	Pick the color at position i mod 6, cycling the list
for j in range(4)	Draw 4 sides to make one square
monty.right(90)	Turn at each corner of the square
monty.right(10)	Rotate 10° before the next square — creates the spiral
side += 8	Grow the square by 8 pixels each iteration

What Is Modulo?

The % operator gives you the remainder of division. 7 % 3 is 1 (7 ÷ 3 = 2 remainder 1). It's the perfect tool for cycling through a list — the index always stays in bounds!

Learning Check

Your Turn — Complete the Spiral

The program below draws the squares but all in the same color — boring! Add one line inside the outer loop to make each square use the next color in the list. Hint: look at how colors and i are used in the sample above.

▶ Run ↻ Reset

The missing line is monty.color(colors[i % len(colors)]) — place it right after the for i line.

Experiments

Try these changes in the Try It Now editor above:

1. Change the number of squares. Replace range(36) with range(72). How does the spiral change? You'll know it worked when the spiral wraps around twice as far.

2. Change the rotation angle. Replace monty.right(10) with monty.right(5). Now 36 squares only cover 180 degrees. What happens to the shape? You'll know it worked when the spiral opens into a fan instead of a closed tunnel.

3. Change the growth rate. Replace side += 8 with side += 4. The spiral gets tighter. What does side += 16 do? You'll know it worked when the squares expand much more quickly to the edges of the canvas.

4. Reverse the spiral direction. Change monty.right(10) to monty.left(10). You'll know it worked when the spiral winds in the opposite direction.

5. Add more colors. Add 'pink' and 'brown' to the colors list. With 8 colors and 36 squares, each color appears only 4–5 times. Does the spiral look different with more stripes? You'll know it worked when you can count more than 6 distinct color bands.

Spectacular Work!

You just used nested loops, a color list, the modulo operator, and a growing variable to produce a dazzling rainbow tunnel — all in under 20 lines of code! Up next: try the Pinwheel of Triangles to see how the same rotation idea works with a completely different shape.