3x3 Grid Path Visualizer

Overview

This repository contains a Jupyter Notebook (3grid.ipynb) designed to generate and visualize all possible paths on a 3x3 grid, where each path is at least four nodes long. In each path, every node of the grid is visited exactly once, showcasing unique traversals across the grid.

Project Structure

• 3grid.ipynb: The Jupyter Notebook containing the Python code for generating paths and visualizing them.
• grid_paths/: Directory containing the generated path visualizations (created after running the notebook).

Requirements

• Python 3.x
• Jupyter Notebook
• Matplotlib

You can install the required Python packages using the following command:

pip install notebook matplotlib

Usage

1. Clone this repository to your local machine.

2. Ensure you have the required dependencies installed.

3. Open the Jupyter Notebook:

   jupyter notebook 3grid.ipynb

4. Run the cells in the notebook to generate the visualizations.

5. The grid_paths directory will be created and populated with images, each representing a unique path on the 3x3 grid.

How It Works

• The notebook creates a graph representing the 3x3 grid.
• It uses a recursive approach to find all possible paths that are at least 4 nodes long without revisiting any node.
• Each path is visualized using Matplotlib, indicating the sequence of moves across the grid.
• The generated images are saved in the grid_paths directory.

Visualizations

Each image in the grid_paths directory illustrates a unique path across the 3x3 grid. The nodes are represented as blue dots, and the paths are indicated by red lines connecting these dots in the order they are visited.