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🌪️ Lorenz Attractor in 3D | Chaotic System Visualization

This project uses Manim and SciPy to simulate and animate the Lorenz Attractor, a classic example of deterministic chaos in a 3D system. It highlights how tiny differences in initial conditions can lead to wildly divergent outcomes — the hallmark of chaos theory.

Watch here!

📈 What is the Lorenz Attractor?

The Lorenz system is a set of differential equations originally developed to model atmospheric convection. It’s defined as:

dx/dt = σ(y - x) dy/dt = x(ρ - z) - y dz/dt = xy - βz

Typical parameters:

• σ (sigma) = 10
• ρ (rho) = 28
• β (beta) = 8/3

🌀 Features of the Animation

• Two nearly identical initial conditions: [0, 1, 1.05] and [0, 1, 1.06]
• 3D axes for spatial reference
• Color-coded trajectories (green vs. red)
• Smooth VMobject curve drawing over time
• Continuous ambient camera rotation
• Explanatory text overlay

🛠️ Requirements

• Python 3.8+
• Manim Community Edition
• SciPy
• NumPy

pip install manim numpy scipy

▶️ How to Run

manim -pql Lorenz_attractor.py LorenzAttractorAnimation

Use -qh for high-quality rendering. 📁 Files

Lorenz_attractor.py — Main script
README.md — Project description

🎓 Educational Use

Perfect for:

Demonstrating chaos theory and sensitivity to initial conditions
Teaching dynamical systems and nonlinear math
Visualizing strange attractors and 3D flows

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🤝 Support Generative Math Animation

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