Sierpinski Figures

A Python implementation for generating and visualizing Sierpinski triangles in 2D and 3D spaces. This project was developed as part of the Mathematical Modeling course.

Quick Start

1. Clone the repository:

git clone https://github.com/yourusername/sierpinski-figures.git
cd sierpinski-figures

2. Install Poetry (if not already installed):

curl -sSL https://install.python-poetry.org | python3 -

Or

pip install poetry

3. Activate the virtual environment:

poetry shell

4. Install project dependencies:

poetry install

5. Admire the beauty of Sierpinski figures:

python '.\src\Sierpinski triangle.py'

python '.\src\Sierpinski pyramid.py'

Overview

This project provides tools for creating and visualizing various Sierpinski fractals, including:

Sierpinski Triangle (2D)

• Interactive visualization
• Configurable iterations
• Color mapping options

Sierpinski Pyramid (3D)

• Full 3D rotation
• Zoom and pan controls
• Interactive vertex highlighting

Features

• Generation of Sierpinski fractals
• 2D visualization using matplotlib
• 3D rendering with interactive rotation and zoom capabilities
• Efficient recursive implementation
• Support for saving generated figures as images

Requirements

• Python 3.12+
• Poetry (Python package manager)

How to Execute the Project

To execute the project and generate the Sierpinski figures, follow these steps:

1. Ensure you have installed all dependencies as described in the Installation section.
2. Activate the virtual environment:

poetry shell

3. Run the Python scripts to generate the figures:

python '.\src\Sierpinski triangle.py'

python '.\src\Sierpinski pyramid.py'

Project Dependencies

Main dependencies managed by Poetry:

• numpy: Mathematical operations and array handling
• plotly: Interactive visualization of 2D and 3D figures
• pandas: Data manipulation and structuring
• matplotlib: 2D triangle visualization
• Sphinx: Documentation

Usage

2D Sierpinski Triangle

from sierpinski.shapes_2d import SierpinskiTriangle

# Create a triangle with 6 iterations
triangle = SierpinskiTriangle(iterations=6)
fig = triangle.plot()
fig.show()  # Opens in browser or notebook
fig.write_html("triangle.html")  # Save as interactive HTML

3D Sierpinski Pyramid

from sierpinski.shapes_3d import SierpinskiPyramid

# Create a pyramid with 4 iterations
pyramid = SierpinskiPyramid(iterations=4)
fig = pyramid.plot_3d()
fig.show()  # Opens interactive 3D visualization
fig.write_html("pyramid.html")  # Save as interactive HTML

Features of Visualization

• Interactive 2D or 3D rotation and zoom

• Hover information showing coordinates

• Screenshot capabilities

Project Structure

sierpinski-figures/
├──  docs/            # Documentation files
    ├── index.md
    ├── sierpinski_pyramid.md    
    ├── sierpinski_triangle.md
    ├── theory.md
    └── usage.md
├── examples/
    ├── chaos_game.py
    ├── convergence_visualizer.py
    └── converage_analyzer.py
├── src/
    ├── Sierpinski pyramid.md
    ├── Sierpinski triangle orgin.py
    └── Sierpinski triangle.py
├── LICNESE.md    
├── pyproject.toml    # Poetry configuration and dependencies
├── poetry.lock      # Lock file for reproducible 
└──  README.md

    

Mathematical Background

The Sierpinski figures are fractal sets that exhibit self-similarity at different scales. The project implements these mathematical concepts:

• Recursive subdivision of geometric shapes
• Iterative geometric transformations

Contributing

This is a semester project for the Mathematical Modeling course. Feel free to use this code for educational purposes.

License

This project is licensed under the MIT License - see the LICENSE.md file for details.

Authors

Kacper Smyrak Magdalena Śnietura

Mathematical Modeling Course Silesian University of Science Faculty of Applied Mathematics