https://github.com/wendtpiotr/procedural-lorenz-attractor

An interactive Lorenz attractor simulator in Unity, designed to explore chaos, the butterfly effect, and velocity dynamics in a visually intuitive way.
https://github.com/wendtpiotr/procedural-lorenz-attractor

chaos-theory lorenz-attractor physics-simulation rk4-algorithm unity3d

Last synced: 12 days ago
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An interactive Lorenz attractor simulator in Unity, designed to explore chaos, the butterfly effect, and velocity dynamics in a visually intuitive way.

• Host: GitHub
• URL: https://github.com/wendtpiotr/procedural-lorenz-attractor
• Owner: wendtpiotr
• License: mit
• Created: 2025-10-28T18:11:21.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2025-10-28T18:30:10.000Z (7 months ago)
• Last Synced: 2025-12-14T09:30:02.740Z (6 months ago)
• Topics: chaos-theory, lorenz-attractor, physics-simulation, rk4-algorithm, unity3d
• Language: C#
• Homepage:
• Size: 83 KB
• Stars: 1
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

          
# 🌀 Lorenz Attractor Visualizer



An interactive **Lorenz attractor simulator** in Unity 🎮, designed to explore chaos, the butterfly effect, and velocity dynamics in a visually intuitive way.

https://github.com/user-attachments/assets/76d7efe5-4e04-4267-96d2-44bbb219e8cf

https://github.com/user-attachments/assets/95d4b545-8f63-478f-89a7-17e371ebb23c

---

## 🔬 Features

- **Numerical Integration:** Uses **RK4** (Runge-Kutta 4th order) for accurate time evolution of the Lorenz system.

- **Dynamic Mesh Rendering:** The attractor trail is drawn with a **Mesh** rather than a LineRenderer for performance (even with 25k+ points).

- **Per-Point Velocity Coloring:**  

  Visualize instantaneous **velocity magnitude** along the trail using a customizable **Gradient** 🎨.

- **Butterfly Effect Mode 🦋:**  

  Slight rounding of initial conditions demonstrates **sensitive dependence on initial conditions** — chaos in action!

- **Compare Two Attractors:**  

  Spawn multiple attractors (normal vs. butterfly-effect) to observe **divergence over time**.

- **Orbit Camera:**  

  Smooth, mouse-controlled orbit camera that automatically centers on the active attractor points.  

---

## ⚙️ Usage

1. **Setup Attractor:**

   - Create a **ScriptableObject** (`LorenzAttractorSettings`) for each attractor.

   - Configure:

     - `timeStep`

     - `initialPosition`

     - `maxPoints`

     - `velocityGradient`

     - `enableButterflyEffect` ✅ to apply rounding to initial conditions.

   

2. **Add Attractor to Scene:**

   - Attach `LorenzAttractor.cs` to a GameObject.

   - Assign the corresponding `LorenzAttractorSettings`.

3. **Camera Setup:**

   - Attach `OrbitCamera.cs` to your main camera.

   - Set `target` to one of the Lorenz attractor GameObjects.

   - Enable `Use Dynamic Center` to follow the attractor trail.

4. **Visual Exploration:**

   - Drag the mouse to rotate the camera.

   - Scroll to zoom in/out.

   - Watch attractors diverge in real time, colored by velocity magnitude.

---

## 📊 Scientific Notes

- The Lorenz system is defined by:

\[

\begin{cases}

\frac{dx}{dt} = \sigma (y - x) \\

\frac{dy}{dt} = x (\rho - z) - y \\

\frac{dz}{dt} = xy - \beta z

\end{cases}

\]

with typical parameters:  

`σ = 10`, `ρ = 28`, `β = 8/3`.

- **Butterfly Effect:** Small differences in initial conditions (here via rounding) grow exponentially, illustrating chaotic dynamics.

- **Velocity Visualization:**  

  Each vertex is colored according to the **magnitude of its instantaneous derivative**, showing where the system moves faster or slower in 3D space.

---

## 🧩 Scripts

- `LorenzAttractor.cs` — Generates and updates the attractor mesh in real-time.  

- `LorenzAttractorEquationsSolver.cs` — Implements RK4 integration and derivative calculation.  

- `LorenzAttractorSettings.cs` — ScriptableObject storing parameters, including butterfly effect option.  

- `OrbitCamera.cs` — Smooth orbit camera centered on the attractor’s active points.

---

## 🚀 Demo Ideas

- Spawn two attractors:

  - One normal

  - One with butterfly effect enabled

- Observe divergence over time 🦋.

- Experiment with gradient coloring to highlight **high-velocity regions**.

- Increase `maxPoints` for high-resolution trails.

---

## 💻 Requirements

- Unity 2023+ (or compatible version)  

- Standard 3D pipeline  

- Optional: HDRP/URP for improved visuals