Triangular Spiral

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

• Use right(120) to create a triangular spiral with sharp equilateral corners
• Color each third of the spiral a different warm color using integer division
• Understand how i // n groups segments into color bands rather than cycling segment-by-segment

Three warm color bands — red, orange, and gold — sweep outward along the arms of a tight triangular spiral. Change one number and the entire character of the shape changes.

Welcome to the Triangular Spiral!

We've seen square spirals (90°) and hexagonal spirals (60°). Now push the angle further — 120° gives the sharpest corners yet. Let's code it together!

How It Works

An equilateral triangle has interior angles of 60° and exterior angles of 120° (360° ÷ 3 = 120°). Turning 120° at every step gives the spiral triangular corners.

For coloring, (i // 60) % 3 divides the 180-step loop into three equal thirds and picks a color for each third. Integer division (//) groups segments together instead of cycling one-by-one.

Sample Code

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

colors = ['crimson', 'darkorange', 'gold']
step = 2

for i in range(180):
    monty.color(colors[(i // 60) % 3])
    monty.forward(step)
    monty.right(120)
    step += 1.5

What Do You Think Will Happen?

The square spiral had 4 sides per revolution and the hexagonal had 6. How many sides per revolution does the triangular spiral have? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

3 sides per revolution — one per 120° turn. The spiral makes crisp triangular corners. Were you right?

How It Works

(i // 60) % 3 works like this: for the first 60 steps, i // 60 = 0, so color 0 (crimson). For steps 60–119, i // 60 = 1, so color 1 (orange). For steps 120–179, color 2 (gold). This creates solid bands along the spiral arms rather than segment-by-segment flickering.

Explanation Table

Line	What it does
colors = [...]	Three warm hues — one per third of the loop
(i // 60) % 3	Groups 60 segments into each color band
monty.right(120)	Triangular corner — 360° ÷ 3 = 120°
step += 1.5	Grow the step each segment
range(180)	180 steps = 60 full "triangles" (3 sides each)

Learning Check

Your Turn — Switch to Per-Segment Colors

Change (i // 60) % 3 to i % 3. Now each individual segment cycles through the three colors. Predict how it will look different — then run it to check!

▶ Run ↻ Reset

With i % 3, each side of each tiny triangle gets its own color — creating a striped, segment-by-segment pattern. The i // 60 version gives broader color bands across entire spiral arms.

Experiments

1. Try 4 colors with i // 45. Use ['red','orange','gold','yellow'] and (i // 45) % 4. You'll know it worked when the spiral has four distinct color regions.

2. Make it spin the other way. Change right(120) to left(120). You'll know it worked when the spiral winds in the opposite direction.

3. Double the growth speed. Change step += 1.5 to step += 3. The gaps between arms widen dramatically. You'll know it worked when only 2–3 revolutions fit on screen.

4. Start from a large step. Change step = 2 to step = 40. The spiral begins already expanded. You'll know it worked when the first few loops are already wide.

Sharp Thinking!

You discovered two ways to color a spiral: i % n for segment-by-segment patterns, and i // n for broad color bands. The same trick works in any loop! Up next: Inward Collapsing Spiral — spiraling to a point instead of growing outward.