https://github.com/ychaaby/octrees-barnes-hut-algorithm-simulation
Octree data structure implimentation using python, 3D simulation with Matplotlib
https://github.com/ychaaby/octrees-barnes-hut-algorithm-simulation
data-structures-and-algorithms matplotlib octtree oop python
Last synced: 4 months ago
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Octree data structure implimentation using python, 3D simulation with Matplotlib
- Host: GitHub
- URL: https://github.com/ychaaby/octrees-barnes-hut-algorithm-simulation
- Owner: yChaaby
- Created: 2023-11-23T21:30:27.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2025-01-21T23:23:21.000Z (over 1 year ago)
- Last Synced: 2025-11-09T20:39:35.922Z (7 months ago)
- Topics: data-structures-and-algorithms, matplotlib, octtree, oop, python
- Language: Python
- Homepage:
- Size: 48.8 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
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README
# Octree Simulation with Barnes-Hut Algorithm
## Overview
This project implements the **Barnes-Hut algorithm** for simulating gravitational interactions in a system of stars using an **octree** data structure. The algorithm efficiently calculates the gravitational forces between particles by approximating distant interactions, reducing the computational complexity from **O(N^2)** to **O(N log N)**.
This simulation calculates accelerations and gravitational forces and visualizes the system in 3D using **Matplotlib**. The Barnes-Hut algorithm is widely used in astrophysics and particle simulations for its scalability and efficiency when dealing with large systems.
### 3D Simulation Demo
## Features
- **Octree** data structure to partition space and optimize calculations.
- **Barnes-Hut algorithm** to calculate gravitational forces and accelerations efficiently.
- **3D visualization** of the simulation using Matplotlib.
## Mathematical Formulas
The simulation uses fundamental principles of gravitational forces and accelerations to model the motion of stars.
### 1. Gravitational Force
The gravitational force between two stars is given by **Newton's law of universal gravitation**:
`F = G * (m_1 * m_2) / r^2`
Where:
- `F` is the gravitational force between two stars.
- `G` is the gravitational constant.
- `m_1` and `m_2` are the masses of the two stars.
- `r` is the distance between the two stars.
### 2. Acceleration Due to Gravity
The acceleration `a` experienced by a star due to gravitational force is calculated using Newton's second law:
`a = F / m`
Where:
- `F` is the gravitational force calculated above.
- `m` is the mass of the star.
### 3. Barnes-Hut Approximation
The Barnes-Hut algorithm approximates the gravitational interaction between distant stars using a single "center of mass" for groups of stars. The force calculation is simplified based on a **theta** parameter, which controls the threshold for approximating distant interactions:
`theta = s / d`
Where:
- `s` is the size of the octant (or group of stars).
- `d` is the distance between the center of mass of the octant and the star.
If `theta` is smaller than a given threshold, the octant is approximated as a single mass, and the force is calculated directly. Otherwise, the interaction is recursively computed with the children of the octree.
## Usage
To run the simulation, simply execute the Python script:
## Requirements
- Python 3
- OPP Concepts
- Matplotlib
- NumPy
## Installation
1. Clone the repository:
```shell
git clone https://github.com/yChaaby/Octrees_Similation.git
```
2. Install required dependencies:
```fish
pip install matplotlib numpy
```
## Usage
1. To run the simulation:
```powershell
python simulation.py
```
2. The simulation will display a 3D visualization of the stars and their interactions.
## License
None ... it's all yours