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Turtle Art Patterns

Turtle Art – Mathematical Patterns Using Code and 3D Printing

Introduction

Turtle Art is a visual and mathematical way of learning where geometry is created through simple movement and rotation commands. Instead of drawing shapes directly, learners program a turtle to move forward and turn, allowing mathematics to emerge naturally through code.

In this project, mathematical patterns are created using block-based Turtle Art, exported as digital images, converted into vector graphics, and finally transformed into 3D-printed objects. The process connects math, programming, and fabrication, helping learners understand how abstract rules generate complex and beautiful forms.

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Project Objective

The objective of this project is to explore mathematical patterns, symmetry, and angles through Turtle Art coding, and to convert algorithmically generated drawings into physical artifacts using 3D printing.

Specific objectives include:

  • Creating geometric patterns using Turtle Art block coding

  • Understanding angles, rotation, and repetition through movement commands

  • Exploring nested loops and their role in pattern generation

  • Converting raster images (PNG) into vector graphics (SVG)

  • Importing SVG files into Tinkercad for 3D modeling

  • Producing a 3D-printed mathematical pattern using slicing software

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Concept Overview

The pattern is generated in a Turtle Art environment, where a turtle follows instructions such as forward and right turn. The complexity of the final design comes from repetition and rotation, not from drawing complex shapes directly.

Core Coding Logic

  • Inner Loop (repeat 6)

    • Draws a hexagon-like structure

    • Each step moves forward by a fixed length

    • Turtle turns 60 degrees after each step

    • Mathematical basis:

      • Exterior angle = 360° ÷ 6 = 60°

  • Outer Loop (repeat 36)

    • Rotates the entire hexagonal shape slightly

    • Turtle turns 40 degrees after completing each hexagon

    • Repeating this creates a radial, flower-like pattern

This shows how simple rules, when repeated, generate complex geometry.

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Mathematics Behind the Pattern

This Turtle Art project demonstrates:

  • Angles and turning as fundamental geometric operations

  • Regular polygons formed through equal rotations

  • Rotational symmetry created by repeated angular offsets

  • Algorithmic thinking, where structure emerges from rules

By changing values such as:

  • Step length

  • Number of sides

  • Turn angle

  • Number of repetitions

students can experiment and immediately observe new mathematical patterns.

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Digital Fabrication Workflow

  1. Pattern Creation

    • Pattern created using Turtle Art block coding

    • Output saved as a PNG image

  2. Vector Conversion

    • PNG converted into SVG format to preserve geometry

  3. 3D Modeling

    • SVG imported into Tinkercad

    • Lines extruded to create thickness

    • Model scaled and adjusted for printability

Logo3D design Turtle Art Patterns - TinkercadTinkercadchevron-right

  1. Slicing & Printing

    • Model exported as STL

    • Sliced using Creality slicing software

    • Printed using PLA filament on an FDM 3D printer

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Educational Significance

This project helps learners:

  • Understand geometry through motion

  • See how code controls shape formation

  • Experience mathematics as a creative and visual subject

  • Connect coding with real-world fabrication

  • Build intuition before formal formulas are introduced

Turtle Art is especially powerful for K–12 education, as it lowers the barrier to coding while strengthening mathematical reasoning.

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Design Tools and Materials

Software & Platforms:

  • Turtle Art (block-based turtle coding environment)

  • PNG to SVG conversion tool

  • Tinkercad – for extrusion and 3D modeling

  • Creality slicing software

Hardware & Materials:

  • FDM 3D printer

  • PLA filament

  • Standard nozzle (0.4 mm recommended)

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Expected Outcome

  • A Turtle Art–generated mathematical pattern

  • A clean SVG vector file suitable for fabrication

  • A 3D-printed geometric pattern artifact

  • A reusable coding template for pattern exploration

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Broader Impact

This project shows that Turtle Art is more than drawing—it is a gateway to:

  • Geometry

  • Computational thinking

  • Digital fabrication

  • STEAM learning

By transforming Turtle Art drawings into physical objects, learners realize that code can create real things, not just images on a screen.

PreviousExperimental Works

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