Chaotic N-Pendulum Simulation

A Python implementation of a chaotic N-pendulum simulation using Lagrangian mechanics. Extreme sensitivity of chaotic systems to initial conditions.

4_pendulum_50_instances.mp4

Installation

pip install -r requirements.txt

Note: For video export, you'll need FFmpeg installed:

• macOS: brew install ffmpeg
• Linux: sudo apt-get install ffmpeg
• Windows: Download from ffmpeg.org

Usage

python run_all.py

Config: Edit the configuration in run_all.py:

N = int             # Number of pendulum segments (2, 3, 4, ...)
T = int            # Simulation duration in seconds
M = int            # Number of pendulum instances
pertubation = float # Positional deviation from each other

Output

• func_N{N}k.pkl: Saved equations of motion
• simulation_results.npz: Simulation data (positions over time)
• {N}_pendulum_{M}_instances.mp4: Final animation video

C++ Renderer

A C++ renderer is available for high-resolution, high-instance videos. It reads the simulated trajectories from Python and streams raw RGB frames directly into FFmpeg.

Build

cd cpp_renderer
cmake -S . -B build
cmake --build build --config Release

Requirements:

• CMake ≥ 3.16 (brew install cmake on macOS, sudo apt install cmake on Debian/Ubuntu)
• A C++17-capable compiler such as clang++ or g++ (Xcode command-line tools or build-essential)
• FFmpeg available on your PATH (brew install ffmpeg, sudo apt install ffmpeg)

Use

• Toggle use_cpp_renderer = True inside run_all.py.