Islamic Geometric Star Pattern

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

• Construct an 8-pointed star using only straight lines and 45° angles
• Tile the star pattern across a grid using translation (offset by fixed amounts)
• Understand how Islamic geometric art uses exact angle rules

A repeating pattern of 8-pointed stars and cross shapes — the kind found in mosque tile work and Persian manuscripts — built entirely from straight line segments at 45° angles.

Welcome to the Islamic Star!

Islamic geometric art uses only ruler and compass — no freehand curves. This lab builds one of the most common patterns: the 8-pointed star grid! Let's code it together!

How It Works

An 8-pointed star is drawn as two overlapping squares rotated 45° from each other, both centered on the same point. A function star8(cx, cy, size, color) draws one star at a given center. The outer loop tiles the stars in a grid, offsetting each star by a fixed spacing.

Sample Code

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

def star8(cx, cy, size, color):
    monty.pencolor(color)
    for angle_offset in [0, 45]:
        monty.penup()
        monty.goto(cx, cy)
        monty.setheading(angle_offset - 135)
        monty.forward(size)
        monty.setheading(angle_offset)
        monty.pendown()
        for _ in range(4):
            monty.forward(size * 1.4)
            monty.left(90)

spacing = 90
colors = ['navy', 'royalblue']
for row in range(-2, 3):
    for col in range(-2, 3):
        cx = col * spacing
        cy = row * spacing
        color = colors[(row + col) % 2]
        star8(cx, cy, 30, color)

What Do You Think Will Happen?

Two squares rotated 45° from each other form an 8-pointed star. Will the tiled stars connect at their points, or will there be gaps? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

The stars form a repeating grid pattern — like Islamic tile work. Were you right about the gaps?

How It Works

An 8-pointed star is two squares rotated 45° from each other, sharing the same center. The for angle_offset in [0, 45] loop draws each square in sequence. Before drawing, the turtle walks from the center (cx, cy) out to the square's starting corner: setheading(angle_offset - 135) points it toward the corner, and forward(size) steps out to it. Because both squares are positioned from the same center, their overlap forms a symmetric 8-pointed star.

Explanation Table

Line	What it does
for angle_offset in [0, 45]	Draw two squares — one rotated 45° from the other
setheading(angle_offset - 135) then forward(size)	Walk from the star's center to the square's starting corner
size * 1.4	Side length adjusted so the two squares create points
spacing = 90	Distance between star centers
(row + col) % 2	Alternate colors in checkerboard pattern

Learning Check

Your Turn — Change Spacing

Change spacing = 90 to spacing = 60. Will the stars overlap, spread apart, or touch perfectly? Predict, then run it to find out!

▶ Run ↻ Reset

At spacing = 60 the stars touch perfectly at their points, and the leftover space between them forms the cross shapes seen in real Islamic tile work.

Experiments

1. Fill the stars. Add begin_fill() before and end_fill() after the inner loop. You'll know it worked when the star outlines are filled in.

2. Use gold and navy. Change the color list to ['navy', 'gold']. You'll know it worked when the checkerboard alternates navy and gold stars.

3. Bigger stars. Change size = 30 to size = 40. You'll know it worked when the stars are larger and the spacing between them decreases.

4. Try a single centered star. Remove the outer loops and call star8(0, 0, 80, 'darkred'). You'll know it worked when one large 8-pointed star fills the screen.

Pattern Complete!

You recreated a 1000-year-old pattern used in mosques and palaces! Geometric art proves that math and beauty are not opposites — they're the same thing. Up next: Category 6 — Nature and Science patterns!