Rainbow Line Spiral

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

• Add color cycling to a growing spiral using i % len(colors)
• See how the banding interval interacts with the spiral's period
• Understand why the same modulo pattern works for both colors and shapes

The Archimedean square spiral returns — this time each segment is colored by cycling through six rainbow hues. The color bands march diagonally across the arms of the spiral.

Welcome to the Rainbow Line Spiral!

In this lab you'll add just two extra lines to the spiral from the previous lab and transform a monochrome pattern into a full rainbow. That's the power of %! Let's code it together!

How the Rainbow Works

The only additions to the Archimedean spiral are: 1. A colors list with six hues 2. monty.color(colors[i % 6]) inside the loop — one line

Because each revolution of the spiral has 4 segments and the colors cycle every 6 segments, the color boundaries cut diagonally across the spiral arms rather than aligning with corners.

Sample Code

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

colors = ['red', 'orange', 'yellow', 'green', 'blue', 'violet']
step = 2

for i in range(200):
    monty.color(colors[i % 6])
    monty.forward(step)
    monty.right(90)
    step += 1.5

What Do You Think Will Happen?

There are 6 colors and 200 segments. How many times will the full color sequence repeat? (Hint: 200 ÷ 6 = ?) Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

200 ÷ 6 = 33 full cycles with 2 segments left over — so the full rainbow appears 33 times, each one a little larger than the last. Were you right?

How It Works

colors[i % 6] maps the loop counter i to a color index: 0→red, 1→orange, 2→yellow, 3→green, 4→blue, 5→violet, 0→red again. The pattern repeats every 6 steps regardless of how high i gets.

Because the spiral has 4-sided symmetry but the color period is 6, the diagonal color stripes cross the square corners at different points on each revolution — creating a visually complex pattern from very simple math.

Explanation Table

Line	What it does
colors = [...]	Six rainbow hues
i % 6	Maps any integer to 0–5 to index the color list
monty.color(colors[i % 6])	Change color each segment
All other lines	Identical to the Archimedean spiral

Learning Check

Your Turn — Change the Color Period

What happens when the color period matches the spiral period? Change i % 6 to i % 4. With 4 colors and 4-sided corners, the colors will align with the corners. Predict what it will look like — then run it to check!

▶ Run ↻ Reset

With i % 4 and a 90° square spiral, each color occupies exactly one side per revolution — creating four clean diagonal stripes aligned with the spiral arms.

Experiments

1. Try 2 colors. Change to ['red', 'blue'] and i % 2. You'll know it worked when the spiral alternates red and blue segment by segment.

2. Try 12 colors. Use the full 12-hue color wheel list from the Color Wheel Wedges lab. You'll know it worked when tighter, more varied rainbow bands appear.

3. Change to a triangular spiral. Keep the rainbow colors and change right(90) to right(120). You'll know it worked when the spiral has triangular corners with diagonal rainbow bands.

4. Color by revolution. Replace i % 6 with (i // 4) % 6. Now all four segments of each revolution share the same color. You'll know it worked when solid-color square rings appear.

Fantastic Work!

You discovered that i % n and i // n give you two different ways to map time to color — segment-by-segment vs revolution-by-revolution. Same spiral, completely different look! Up next: Hexagonal Spiral — changing one angle transforms the whole shape.