Six-Fold Mandala

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

• Draw one section of a mandala and stamp it six times rotating 60° between each
• Build complex symmetric patterns from a simple repeated unit
• Understand how 360 / 6 = 60° rotation creates six-fold symmetry

Twelve concentric rings of petals, arcs, and diamonds — all generated by drawing one sixth of the design and rotating it six times. Change one detail and all six sections update instantly.

Welcome to the Six-Fold Mandala!

Mandalas are ancient art forms based on radial symmetry. In this lab you'll code one from scratch using a single repeated function! Let's code it together!

How It Works

mandala_section() draws one sixth of the design from the center outward — a petal, then an arc, then a diamond shape. The outer loop calls it six times, rotating 60° each time.

Sample Code

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

def petal(size, color):
    monty.color(color)
    monty.begin_fill()
    monty.circle(size, 60)
    monty.left(120)
    monty.circle(size, 60)
    monty.left(120)
    monty.end_fill()

def mandala_section():
    for i, r in enumerate([30, 50, 70, 90]):
        color = ['crimson', 'darkorange', 'gold', 'royalblue'][i]
        petal(r, color)
        monty.penup()
        monty.goto(0, 0)
        monty.setheading(monty.heading())
        monty.pendown()

for i in range(6):
    monty.penup()
    monty.goto(0, 0)
    monty.setheading(i * 60)
    monty.pendown()
    mandala_section()

What Do You Think Will Happen?

We draw 4 petals per section and 6 sections — how many petals total? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

4 × 6 = 24 petals — arranged in four concentric rings of six, each ring a different color. Were you right?

How It Works

petal(size, color) draws a lens shape by drawing two 60° arcs. The turtle starts and ends at the center each time because goto(0, 0) repositions after each petal. setheading(i * 60) before each section rotation ensures all sections start from the same angle offset.

Explanation Table

Line	What it does
monty.circle(size, 60)	Draw a 60° arc — one side of the petal lens
monty.left(120)	Turn 120° to draw the return arc
monty.goto(0, 0)	Return to center between petals
setheading(i * 60)	Rotate 60° before each section

Learning Check

Your Turn — Change to 8-Fold

Change range(6) to range(8) and i * 60 to i * 45. Eight-fold symmetry appears in Islamic tile work and snowflakes. Predict how the mandala will change — then run it!

▶ Run ↻ Reset

Eight-fold symmetry produces 4 × 8 = 32 petals — the sections are narrower and pack more tightly around the center.

Experiments

1. Change petal colors. Replace the color list with ['navy', 'royalblue', 'deepskyblue', 'lightcyan']. You'll know it worked when the mandala turns blue.

2. Larger outer ring. Change [30, 50, 70, 90] to [30, 55, 85, 120]. You'll know it worked when the outermost petals are larger.

3. Add a center dot. After the loop, add monty.penup(); monty.goto(0, -15); monty.dot(30, 'gold'). You'll know it worked when a gold circle fills the center.

4. Try 12-fold. Change to range(12) and i * 30. You'll know it worked when 12 sections appear, making a very dense mandala.

Mandala Complete!

You created a mandala from one function repeated 6 times! Any change to mandala_section() automatically updates all six sections. Up next: Mirror Butterfly — bilateral symmetry via coordinate negation.