1.3.1 Flags (Array Slicing)

Overview

Flags are structured patterns made of rectangular colour blocks. Creating them teaches you one of NumPy’s most powerful features: array slicing. You will learn to select and modify rectangular regions of images using simple slice notation, building the foundation for complex compositions and transformations.

Learning objectives

1. Use NumPy slice notation [start:stop] to select array regions.
2. Apply multi-dimensional slicing to RGB images [rows, cols, channels].
3. Create structured compositions by manipulating rectangular regions.
4. Transfer slicing knowledge to tiling and pattern generation tasks.

Quick start — create your first flag

Let’s create the flag of France using vertical colour bands. Run this code:

import numpy as np
from PIL import Image

# Create blank canvas (standard 2:3 flag ratio)
height, width = 300, 450
flag = np.zeros((height, width, 3), dtype=np.uint8)

# Blue stripe (left third: columns 0-149)
flag[:, 0:150, 0] = 0    # Red channel
flag[:, 0:150, 1] = 85   # Green channel
flag[:, 0:150, 2] = 164  # Blue channel

# White stripe (middle third: columns 150-299)
flag[:, 150:300, :] = 255

# Red stripe (right third: columns 300-449)
flag[:, 300:450, 0] = 239
flag[:, 300:450, 1] = 65
flag[:, 300:450, 2] = 53

# Save the flag
result = Image.fromarray(flag, mode='RGB')
result.save('france_flag.png')

What you just did: You used NumPy array slicing to select vertical columns. The notation [:, 0:150] means “all rows, columns 0 to 149”. The colon : selects all rows, while 0:150 specifies which columns to modify.

Core concepts

Concept 1 — Array slicing syntax

Array slicing lets you select rectangular regions from arrays using the colon operator. For 2D images, the basic pattern is:

image[row_start:row_stop, col_start:col_stop]

The fundamental rules:

• start is inclusive, stop is exclusive: [0:100] selects indices 0 through 99.
• Omitting values: : alone means “all”, :10 means “0 to 10”, 10: means “10 to end”.
• Negative indices: -1 is the last element, -10: selects the last 10 elements.

import numpy as np

# Create 200x300 image
img = np.zeros((200, 300, 3), dtype=np.uint8)

# Top half (rows 0-99)
img[0:100, :] = [255, 0, 0]  # Red

# Bottom half (rows 100-199)
img[100:200, :] = [0, 0, 255]  # Blue

# Right quarter (all rows, last 75 columns)
img[:, 225:] = [0, 255, 0]  # Green (overwrites part of each half)

Concept 2 — Multi-dimensional slicing

RGB images are 3D arrays with shape (height, width, 3). The third dimension holds colour channels. You can slice across all three dimensions simultaneously:

import numpy as np

img = np.zeros((200, 300, 3), dtype=np.uint8)

# Select a rectangular region, all channels
img[0:100, 0:100, :] = [255, 0, 0]  # Top-left square, red

# Select entire red channel only
red_channel = img[:, :, 0]

# Select a single row across all channels (horizontal line)
horizontal_line = img[50, :, :]

# Select a single column across all channels (vertical line)
vertical_line = img[:, 100, :]

Broadcasting shortcut: NumPy automatically expands (broadcasts) values to match array dimensions. This means you can assign a single value or a short list to a multi-dimensional slice:

# These are equivalent:
img[0:100, 0:100, 0] = 255
img[0:100, 0:100, 1] = 0
img[0:100, 0:100, 2] = 0

# Can be written as (NumPy broadcasts the list):
img[0:100, 0:100] = [255, 0, 0]

Exercises

Three progressively challenging exercises, each building on the previous using the Execute, Modify, Create approach.

# Top stripe (rows 0-99)
flag[0:100, :] = [0, 85, 164]  # Blue

# Middle stripe (rows 100-199)
flag[100:200, :] = [255, 255, 255]  # White

# Bottom stripe (rows 200-299)
flag[200:300, :] = [239, 65, 53]  # Red

MODIFY II.

Create the German flag

Modify the France flag code to create the flag of Germany (horizontal stripes: black on top, red in middle, gold on bottom).

Goals

1. Switch orientation — change from vertical stripes to horizontal stripes.

What to expect

The key difference is which dimension you slice. Vertical stripes use [:, start:stop] (all rows, specific columns). Horizontal stripes use [start:stop, :] (specific rows, all columns).

2. Divide into three equal bands — calculate the row boundaries.

What to expect

Divide the height into thirds. For height=300: rows 0-99, 100-199, 200-299. You can also calculate dynamically with height // 3 and 2 * height // 3.

3. Apply the official German colours — Black [0, 0, 0], Red [221, 0, 0], Gold [255, 206, 0].

What to expect

Each stripe gets a single colour assignment using broadcasting: flag[0:100, :, :] = [0, 0, 0] for the black band, and so on.

Complete solution

python · germany_flag.py Copy

import numpy as np
from PIL import Image

# Create blank canvas
height, width = 300, 450
flag = np.zeros((height, width, 3), dtype=np.uint8)

# Black stripe (top third: rows 0-99)
flag[0:100, :, :] = [0, 0, 0]

# Red stripe (middle third: rows 100-199)
flag[100:200, :, :] = [221, 0, 0]

# Gold stripe (bottom third: rows 200-299)
flag[200:300, :, :] = [255, 206, 0]

# Save the flag
result = Image.fromarray(flag, mode='RGB')
result.save('germany_flag.png')

Extension challenge

Try creating the flag of the Netherlands (horizontal stripes: red, white, blue). Use official colours: Red [174, 28, 40], White [255, 255, 255], Blue [33, 70, 139].

CREATE III.

Build the Swiss flag

Create the flag of Switzerland from scratch. This flag has a red field with a white cross at its centre, requiring you to combine both horizontal and vertical slicing.

Requirements

• Square format: 300 x 300 pixels.
• Red background: [255, 0, 0].
• White cross: [255, 255, 255].
• Cross proportions: bars are 1/5 of the flag dimension, centred.

Starter code

python · switzerland_starter.py Copy

import numpy as np
from PIL import Image

# Create square flag (Switzerland uses 1:1 ratio)
size = 300
flag = np.zeros((size, size, 3), dtype=np.uint8)

# TODO Step 1: Fill entire background with red
# Hint: Use flag[:, :] = [255, 0, 0]

# TODO Step 2: Create vertical bar of cross (centred, white)
# The bar width should be size // 5 (60 pixels)
# Calculate left and right positions to centre it
# Hint: left = (size - bar_width) // 2

# TODO Step 3: Create horizontal bar of cross (centred, white)
# Same proportions as vertical bar

# Save
result = Image.fromarray(flag, mode='RGB')
result.save('switzerland_flag.png')

switzerland_starter.py — starter code

Hint 1 — Red background

To fill the entire array with red, use:

python Copy

flag[:, :] = [255, 0, 0]

This selects all rows and all columns, then broadcasts the RGB value across every pixel.

Hint 2 — Centring calculations

For a bar with width bar_width centred in dimension size:

python Copy

bar_width = size // 5  # 60 pixels for size=300
left = (size - bar_width) // 2  # (300 - 60) // 2 = 120
right = left + bar_width  # 120 + 60 = 180

So the vertical bar occupies columns 120-179 (centred).

Hint 3 — Combining horizontal and vertical bars

The cross is formed by two overlapping rectangles. The vertical bar spans all rows but only the centre columns. The horizontal bar spans all columns but only the centre rows. Where the two bars overlap, they both assign white, so the result is a clean cross.

Complete solution

python · switzerland_flag.py Copy

import numpy as np
from PIL import Image

# Create square flag (Switzerland uses 1:1 ratio)
size = 300
flag = np.zeros((size, size, 3), dtype=np.uint8)

# Step 1: Fill background with red
flag[:, :] = [255, 0, 0]

# Step 2: Create white vertical bar (centred)
bar_width = size // 5  # 60 pixels
left = (size - bar_width) // 2  # 120
right = left + bar_width  # 180
flag[:, left:right, :] = 255  # White vertical bar

# Step 3: Create white horizontal bar (centred)
bar_height = size // 5  # 60 pixels
top = (size - bar_height) // 2  # 120
bottom = top + bar_height  # 180
flag[top:bottom, :, :] = 255  # White horizontal bar

# Save
result = Image.fromarray(flag, mode='RGB')
result.save('switzerland_flag.png')

Key insight: The cross is formed by two overlapping rectangles. Where they overlap, both set the same white colour, so the result is a perfect cross.

Make it your own

Try creating the flag of the United Kingdom. This challenging project requires diagonal lines, which you can create using loops and individual pixel manipulation.

Strategy:

1. Start with a blue background: flag[:, :] = [0, 33, 71].
2. Add white diagonals using loops to set pixels along diagonal lines.
3. Add the red cross (vertical and horizontal bars, like Switzerland).
4. Add thinner red diagonals on top of the white ones.

python Copy

# Diagonal from top-left to bottom-right
for i in range(min(height, width)):
    flag[i, i, :] = [255, 255, 255]

# Diagonal from top-right to bottom-left
for i in range(min(height, width)):
    flag[i, width - i - 1, :] = [255, 255, 255]

Experiment with line thickness and colours to match the official Union Jack design.

Downloads

Summary

In 15-20 minutes, two core concepts: array slicing syntax and multi-dimensional slicing.

Common pitfalls to avoid

• Confusing row and column order: remember [row, col] not [x, y]. Rows are vertical position, columns are horizontal.
• Off-by-one errors: [0:100] selects 100 elements (0-99), not 101. The stop index is exclusive.
• Forgetting the channel dimension: img[0:100, 0:100] modifies all channels. Use img[0:100, 0:100, 0] for the red channel only.

Connection to future learning

The rectangular slicing you practised here is the foundation for:

• 1.3.2 (Repeat): tiling patterns using slicing to place repeated elements.
• 1.3.3-1.3.4: Truchet and Wang tiles (complex tiling systems).
• Module 3: image transformations and masking (selecting regions for effects).
• Module 7: image segmentation (dividing images into regions for analysis).

References