Spiral Text

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

• Use turtle.write() to place text at computed positions
• Place characters along a spiral path using polar coordinates
• Understand how setheading() makes each character face the right direction

Each character of a message is placed along an outward spiral, rotated to face tangentially along the curve. The result is text that winds around the center like a snail shell.

Welcome to Spiral Text!

turtle.write() can place any text at the turtle's current position. This lab combines that with spiral math to spell out a message in a spiral! Let's code it together!

How It Works

Place characters of a message one at a time. For character i, the spiral radius grows with i and the angle advances by a fixed step. setheading() aligns each character tangentially to the spiral direction.

Sample Code

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

message = "PYTHON IS FUN! " * 3
angle_step = 20
r_start = 20
r_step = 2.2

for i, ch in enumerate(message):
    angle = math.radians(i * angle_step)
    r = r_start + i * r_step
    x = r * math.cos(angle)
    y = r * math.sin(angle)
    monty.goto(x, y)
    heading = (i * angle_step + 90) % 360
    monty.setheading(heading)
    monty.pencolor('royalblue')
    monty.write(ch, font=('Arial', 10, 'bold'))

What Do You Think Will Happen?

Each character is placed at increasing radius and rotated to face the spiral direction. Will the characters look like a readable spiral, or just scattered letters? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

The message spirals outward — each character faces tangentially to the spiral curve. Were you right?

How It Works

heading = (i * angle_step + 90) % 360 adds 90° to the radial direction because setheading(0) points right (radial direction). Adding 90° makes the turtle face tangentially (along the spiral). math.cos(angle), math.sin(angle) converts polar to Cartesian for positioning.

Explanation Table

Line	What it does
enumerate(message)	Gives both index i and character ch
r = r_start + i * r_step	Radius grows linearly — Archimedean spiral
heading = (i * angle_step + 90) % 360	Tangential direction — perpendicular to radius
monty.write(ch, font=...)	Place single character at turtle's position

Learning Check

Your Turn — Change the Message

Change the message to your name repeated several times. Predict: will the spiral look different with a shorter or longer message?

▶ Run ↻ Reset

Rainbow-colored spiral text — each character gets a cycling color for a more festive effect.

Experiments

1. Tighter spiral. Decrease angle_step to 10. You'll know it worked when more revolutions of the spiral fit in the canvas.

2. Larger font. Change font=('Arial', 10, 'bold') to font=('Arial', 14, 'bold') and increase r_step = 4. You'll know it worked when larger letters appear.

3. Logarithmic spiral. Replace r = r_start + i * r_step with r = 10 * math.exp(0.06 * i). You'll know it worked when the characters space out faster near the outside.

4. Reverse the spiral. Change angle_step to negative. You'll know it worked when the spiral winds clockwise instead of counter-clockwise.

Typography in Motion!

You combined polar coordinates with turtle.write() to create spiral text! This technique is used in logo design and artistic typography. Up next: Seven-Segment Display — digital numbers from line segments.