Hexagonal Spiral

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

• Change one number (the turn angle) to transform a square spiral into a hexagonal one
• Color segments with a blue-to-green gradient by cycling a color list
• Understand why 60° produces hexagonal corners while 90° produces square ones

One parameter change — turning 60° instead of 90° — transforms the familiar square spiral into a graceful hexagonal one. Each segment is tinted in a cool blue-to-green gradient that cycles outward as the spiral grows.

Welcome to the Hexagonal Spiral!

In the last two labs you saw a square spiral. Now we change just ONE number and watch the whole shape transform. Let's code it together!

How It Works

A regular hexagon has six sides. At each corner, the turtle turns the exterior angle of a hexagon: 360 / 6 = 60°. Because we also grow the step length each iteration, the path spirals outward rather than closing into a hexagon.

The color list has seven hues from deep navy through cyan to green. i % len(colors) maps each segment index to a color, cycling continuously as the spiral grows.

Sample Code

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

colors = ['navy', 'blue', 'dodgerblue', 'deepskyblue',
          'cyan', 'mediumaquamarine', 'green']
step = 2

for i in range(240):
    monty.color(colors[i % len(colors)])
    monty.forward(step)
    monty.right(60)
    step += 0.8

What Do You Think Will Happen?

The square spiral used right(90). This one uses right(60). Will the corners look sharper or more rounded than the square spiral? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

The corners are less sharp — 60° turns are gentler than 90° turns, giving the spiral a rounder, more flowing appearance. Were you right?

How It Works

right(60) creates hexagonal corners because 60° is the exterior angle of a regular hexagon (360° ÷ 6 = 60°). The growing step prevents the path from closing into a hexagon — instead it spirals outward one ring at a time.

colors[i % len(colors)] uses len(colors) instead of hardcoding 7. This is good practice: if you add or remove a color, the modulo automatically adjusts.

Explanation Table

Line	What it does
colors = [...]	Seven-hue navy-to-green gradient
i % len(colors)	Maps segment index to color list — works for any list length
monty.right(60)	Hexagonal corner — 360 / 6 = 60°
step += 0.8	Grow the step — source of the spiral
range(240)	240 steps = 40 full "hexagons" (6 sides each)

Learning Check

Spot the Bug!

The program below draws the same hexagon over and over in the same place — no spiral! Find the missing line and add it so the path spirals outward.

▶ Run ↻ Reset

Add step += 0.8 as the last line inside the loop — without it, every segment is the same length and the path just traces the same hexagon repeatedly.

Experiments

1. Try a pentagon spiral. Change right(60) to right(72) (360/5). You'll know it worked when the spiral has five-sided corners instead of six.

2. Try a triangle spiral. Change right(60) to right(120) (360/3). You'll know it worked when the corners become sharp 120° turns.

3. Speed up the growth. Change step += 0.8 to step += 2. The loops spread out faster. You'll know it worked when there are fewer, more widely spaced rings.

4. Switch to warm colors. Replace the colors list with ['darkred', 'red', 'orangered', 'orange', 'gold', 'yellow', 'lightyellow']. You'll know it worked when the spiral shifts from fiery red through yellow.

Excellent Work!

You discovered that one number — the turn angle — determines the polygon shape of a spiral. Change 60° → 90° → 120° and watch the whole pattern transform! Up next: Triangular Spiral — pushing the turn angle even further.