Turtle graphics is one of those things that feels like a toy, but it's actually a fantastic way to visualize how loops and geometry interact in your code. Instead of staring at text in a console, you get to see your logic literally draw itself on the screen. Today, we're going to build a colorful, expanding geometric spiral.

Getting our canvas ready

First, we need to bring in the module and set up our "turtle"—which is really just a cursor that moves based on X and Y coordinates. I like to name my turtle t just to keep the code concise.

import turtle

t = turtle.Turtle()
t.speed(0) # This makes the turtle move as fast as possible
screen = turtle.Screen()
screen.bgcolor("black")
t.color("cyan")

The struggle with triangle angles

I want this spiral to be based on a triangle. My first instinct is usually to think, "A triangle has 60-degree angles, so I'll just turn 60 degrees." Let's see what happens when I try that in a loop.

# My first attempt (The Mistake)
for i in range(3):
    t.forward(100)
    t.right(60)

If you run that, you'll notice it doesn't actually make a triangle; it just makes a weird open zig-zag. I forgot a fundamental rule of Turtle: the turtle turns based on the exterior angle, not the interior one. To get a 60-degree interior angle, I actually need to turn 120 degrees (180 - 60 = 120). It's a common trip-up, even for experienced devs when they come back to Turtle after a few years.

Here is the corrected logic for a proper triangle:

for i in range(3):
    t.forward(100)
    t.right(120)

Turning a shape into a spiral

A simple triangle is boring. To make it a spiral, we need to do two things: increase the distance the turtle moves every time it turns, and run the loop many more times than just three. I'll use a variable for the distance and increment it inside the loop.

distance = 5
for i in range(100):
    t.forward(distance)
    t.right(120)
    distance += 3 # Every side gets slightly longer

Now we have a growing triangular spiral. It looks clean, but it's a bit monochromatic. Let's spice it up.

Adding a splash of color

To make this look professional, I'll define a list of colors and use the modulo operator (%) to cycle through them. This ensures that no matter how many times the loop runs, we never go out of bounds of our color list.

colors = ["red", "purple", "blue", "green", "orange", "yellow"]
distance = 5

for i in range(150):
    t.color(colors[i % 6]) # Cycle through the 6 colors
    t.forward(distance)
    t.right(120)
    distance += 3

turtle.done()

By changing the angle from 120 to something like 121 or 119, you'll notice the whole shape starts to rotate slightly, creating a much more complex "vortex" effect. That's the beauty of this—small tweaks to the math create massive changes in the art.

📋 Practical Task

Exercise: Building a Nested Square Mandala

Your task is to create a geometric mandala using a square as the base shape. Modify the spiral logic from the lesson to achieve the following:

• Use a square as the base (think about what the turn angle should be).
• Create a list of at least four different colors and cycle through them.
• Set the loop to run 200 times.
• Slightly offset the angle (e.g., use 91 degrees instead of 90) to create a rotating, nested effect.
• Ensure the background color is set to "black" and the turtle speed is set to 0.