Week 5: Patterns & Loops

Learning Objectives

Create repeating patterns
Use nested loops effectively
Generate circular and spiral patterns
Create kaleidoscope effects
Understand pattern mathematics

Introduction
Simple Repeating Patterns
Circular Patterns
Spiral Patterns
Nested Loop Patterns
Rotational Patterns
Geometric Patterns
Practice Exercises
Advanced Patterns
Mathematical Patterns
Challenge Project: Mandala Creator
Pattern Design Tips
Key Concepts Review
Common Mistakes
Week 5 Checklist
Next Week Preview
Additional Practice

Introduction

Patterns are everywhere in nature and art. This week, you'll learn to create beautiful repeating patterns using loops. By combining rotation with repetition, you can create stunning visual effects.

Simple Repeating Patterns

Line of Squares

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_square(size):
    for i in range(4):
        forward(size)
        right(90)

# Draw 5 squares in a row
for i in range(5):
    draw_square(50)
    penup()
    forward(70)
    pendown()

Alternating Colors

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

colors = ['red', 'blue']

for i in range(10):
    color(colors[i % 2])
    draw_square(40)
    penup()
    forward(50)
    pendown()

Circular Patterns

Circle of Squares

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_square(size):
    for i in range(4):
        forward(size)
        right(90)

# Draw 12 squares in a circle
for i in range(12):
    draw_square(50)
    right(360 / 12)  # 30 degrees

Circle of Triangles

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_triangle(size):
    for i in range(3):
        forward(size)
        right(120)

# Draw 12 triangles in a circle
for i in range(12):
    draw_triangle(60)
    right(30)

Spiral Patterns

Square Spiral

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

size = 10
for i in range(50):
    forward(size)
    right(90)
    size += 5  # Increase size each iteration

Colorful Spiral

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

colors = ['red', 'orange', 'yellow', 'green', 'blue', 'purple']
size = 5

for i in range(100):
    color(colors[i % len(colors)])
    forward(size)
    right(91)  # Slightly more than 90
    size += 2

Nested Loop Patterns

Grid of Squares

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_square(size):
    for i in range(4):
        forward(size)
        right(90)

# Draw 4x4 grid
square_size = 40
spacing = 50

for row in range(4):
    for col in range(4):
        draw_square(square_size)

        # Move to next column
        penup()
        forward(spacing)
        pendown()

    # Move to next row
    penup()
    backward(spacing * 4)
    right(90)
    forward(spacing)
    left(90)
    pendown()

Checkerboard Pattern

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_square(size, fill_color):
    color(fill_color)
    for i in range(4):
        forward(size)
        right(90)

size = 40
colors = ['black', 'white']

for row in range(4):
    for col in range(4):
        color_index = (row + col) % 2
        draw_square(size, colors[color_index])

        penup()
        forward(size)
        pendown()

    penup()
    backward(size * 4)
    right(90)
    forward(size)
    left(90)
    pendown()

Rotational Patterns

Flower Pattern

from ColabTurtle.Turtle import *
import math
initializeTurtle(initial_speed=13)

def draw_circle_approx(radius, steps=36):
    circumference = 2 * math.pi * radius
    step_length = circumference / steps
    step_angle = 360 / steps
    for i in range(steps):
        forward(step_length)
        right(step_angle)

# Draw 8 petals in a circle
for i in range(8):
    color('pink')
    draw_circle_approx(40)
    right(45)

# Draw center
color('yellow')
width(20)
forward(1)

Mandala Pattern

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

colors = ['red', 'orange', 'yellow', 'green', 'blue', 'purple']

# Multiple layers
for layer in range(3):
    for i in range(18):
        color(colors[i % len(colors)])
        forward(100 - layer * 20)
        backward(100 - layer * 20)
        right(20)

Geometric Patterns

Star Burst

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

# Draw many lines from center
for i in range(36):
    color('blue')
    forward(100)
    backward(100)
    right(10)

Spirograph Effect

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

colors = ['red', 'blue', 'green', 'orange', 'purple', 'cyan']

for i in range(360):
    color(colors[i % len(colors)])
    forward(i)
    right(59)  # Try different angles: 59, 91, 121, etc.

Practice Exercises

Exercise 1: Rainbow Circles

Draw 7 concentric circles, each in a different rainbow color.

from ColabTurtle.Turtle import *
import math
initializeTurtle(initial_speed=13)

colors = ['red', 'orange', 'yellow', 'green', 'blue', 'indigo', 'violet']

for i, col in enumerate(colors):
    color(col)
    radius = 20 + i * 10
    draw_circle_approx(radius)
    # Reposition for next circle

Exercise 2: Hexagon Grid

Create a honeycomb pattern with hexagons.

Exercise 3: Spiral of Squares

Create a spiral where each turn has a square instead of a line.

Exercise 4: Rotating Triangles

Draw 12 triangles rotating around a center point, each in a different color.

Exercise 5: Complex Mandala

Create a multi-layered mandala with at least 3 different patterns.

Advanced Patterns

Fibonacci Spiral (Approximation)

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_square(size):
    for i in range(4):
        forward(size)
        right(90)

# Fibonacci sequence
a, b = 1, 1
for i in range(10):
    draw_square(b * 10)
    right(90)
    a, b = b, a + b

Kaleidoscope Pattern

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_pattern():
    colors = ['red', 'orange', 'yellow']
    for i in range(3):
        color(colors[i])
        forward(80)
        right(120)

# Repeat pattern in circle
for i in range(12):
    draw_pattern()
    right(30)

Wave Pattern

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

# Create wave effect
for i in range(20):
    forward(20)
    right(30)
    forward(20)
    left(60)
    forward(20)
    right(30)

Mathematical Patterns

Polygons Inscribed in Circle

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

def draw_polygon(sides, size):
    angle = 360 / sides
    for i in range(sides):
        forward(size)
        right(angle)

# Draw polygons from 3 to 8 sides
colors = ['red', 'orange', 'yellow', 'green', 'blue', 'purple']
for sides in range(3, 9):
    color(colors[(sides - 3) % len(colors)])
    draw_polygon(sides, 60)

Golden Spiral Approximation

from ColabTurtle.Turtle import *
initializeTurtle(initial_speed=13)

# Golden ratio approximation
size = 5
for i in range(60):
    forward(size)
    right(89)
    size += 0.618  # Golden ratio

Challenge Project: Mandala Creator

Create a function that generates customizable mandalas.

Requirements:

Function with parameters: layers, petals, colors
At least 3 different pattern types
Smooth transitions between layers
Color gradients

Example:

from ColabTurtle.Turtle import *
import math

def draw_circle_approx(radius, steps=36):
    circumference = 2 * math.pi * radius
    step_length = circumference / steps
    step_angle = 360 / steps
    for i in range(steps):
        forward(step_length)
        right(step_angle)

def draw_petal(size):
    """Draw a single petal shape"""
    for i in range(2):
        draw_circle_approx(size, 36)
        left(90)

def draw_mandala(layers=3, petals=8, colors=None):
    """
    Draw a customizable mandala

    Parameters:
    -----------
    layers : int
        Number of concentric layers
    petals : int
        Number of petals per layer
    colors : list
        List of colors to use
    """
    if colors is None:
        colors = ['red', 'orange', 'yellow', 'green', 'blue', 'purple']

    initializeTurtle(initial_speed=13)
    bgcolor('black')

    # Draw each layer
    for layer in range(layers, 0, -1):
        radius = layer * 30

        # Draw petals in circle
        for i in range(petals):
            color(colors[i % len(colors)])

            # Draw petal
            draw_circle_approx(radius, 36)

            # Rotate for next petal
            right(360 / petals)

    # Draw center
    color('yellow')
    width(20)
    forward(1)

# Create mandala
draw_mandala(4, 12, ['red', 'pink', 'orange', 'yellow', 'white'])

Pattern Design Tips

Start Simple: Begin with basic repeating shapes
Add Rotation: Rotate slightly after each iteration
Vary Size: Increase or decrease size progressively
Color Cycling: Use modulo to cycle through colors
Experiment with Angles: Small angle changes create interesting effects
Layer Patterns: Combine multiple pattern types
Use Symmetry: Repeat patterns at regular intervals

Key Concepts Review

Repetition: Use loops to repeat patterns
Rotation: Combine rotation with repetition for circular patterns
Nested Loops: Create 2D grids and complex patterns
Incremental Change: Gradually modify size, angle, or color
Modulo Operator: Cycle through arrays with i % length
Symmetry: Regular intervals create balanced designs

Common Mistakes

Mistake 1: Wrong Rotation Angle

# ❌ For 12 items in a circle
for i in range(12):
    draw_shape()
    right(12)  # Wrong! Should be 360/12 = 30

# ✅ Correct
for i in range(12):
    draw_shape()
    right(360 / 12)  # 30 degrees

Mistake 2: Not Returning to Center

# For circular patterns, make sure shape returns to center
# Or move back to center after drawing

Mistake 3: Grid Positioning Errors

# Remember to reset position after each row
# Use backward() to return to start of row

Week 5 Checklist

By the end of this week, you should be able to:

Next Week Preview

In Week 6, we'll learn to:

Navigate to specific coordinates
Use absolute positioning
Create grid-based drawings
Implement coordinate systems
Build location-aware patterns

Additional Practice

Create these patterns:

A spiral galaxy effect
A flower garden (multiple flowers arranged in pattern)
A geometric tessellation
An Islamic art-inspired pattern
Your own original mandala design

Keep creating beautiful patterns! 🌸🐢

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