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src=\"https://github.com/user-attachments/assets/b2cd418b-2098-4cd0-b806-a124954ef51d\" /\u003e\n\nAn interactive **Lorenz attractor simulator** in Unity 🎮, designed to explore chaos, the butterfly effect, and velocity dynamics in a visually intuitive way.\n\n\n\nhttps://github.com/user-attachments/assets/76d7efe5-4e04-4267-96d2-44bbb219e8cf\n\n\n\nhttps://github.com/user-attachments/assets/95d4b545-8f63-478f-89a7-17e371ebb23c\n\n\n---\n\n## 🔬 Features\n\n- **Numerical Integration:** Uses **RK4** (Runge-Kutta 4th order) for accurate time evolution of the Lorenz system.\n- **Dynamic Mesh Rendering:** The attractor trail is drawn with a **Mesh** rather than a LineRenderer for performance (even with 25k+ points).\n- **Per-Point Velocity Coloring:**  \n  Visualize instantaneous **velocity magnitude** along the trail using a customizable **Gradient** 🎨.\n- **Butterfly Effect Mode 🦋:**  \n  Slight rounding of initial conditions demonstrates **sensitive dependence on initial conditions** — chaos in action!\n- **Compare Two Attractors:**  \n  Spawn multiple attractors (normal vs. butterfly-effect) to observe **divergence over time**.\n- **Orbit Camera:**  \n  Smooth, mouse-controlled orbit camera that automatically centers on the active attractor points.  \n\n---\n\n## ⚙️ Usage\n\n1. **Setup Attractor:**\n   - Create a **ScriptableObject** (`LorenzAttractorSettings`) for each attractor.\n   - Configure:\n     - `timeStep`\n     - `initialPosition`\n     - `maxPoints`\n     - `velocityGradient`\n     - `enableButterflyEffect` ✅ to apply rounding to initial conditions.\n   \n2. **Add Attractor to Scene:**\n   - Attach `LorenzAttractor.cs` to a GameObject.\n   - Assign the corresponding `LorenzAttractorSettings`.\n\n3. **Camera Setup:**\n   - Attach `OrbitCamera.cs` to your main camera.\n   - Set `target` to one of the Lorenz attractor GameObjects.\n   - Enable `Use Dynamic Center` to follow the attractor trail.\n\n4. **Visual Exploration:**\n   - Drag the mouse to rotate the camera.\n   - Scroll to zoom in/out.\n   - Watch attractors diverge in real time, colored by velocity magnitude.\n\n---\n\n## 📊 Scientific Notes\n\n- The Lorenz system is defined by:\n\n\\[\n\\begin{cases}\n\\frac{dx}{dt} = \\sigma (y - x) \\\\\n\\frac{dy}{dt} = x (\\rho - z) - y \\\\\n\\frac{dz}{dt} = xy - \\beta z\n\\end{cases}\n\\]\n\nwith typical parameters:  \n`σ = 10`, `ρ = 28`, `β = 8/3`.\n\n- **Butterfly Effect:** Small differences in initial conditions (here via rounding) grow exponentially, illustrating chaotic dynamics.\n- **Velocity Visualization:**  \n  Each vertex is colored according to the **magnitude of its instantaneous derivative**, showing where the system moves faster or slower in 3D space.\n\n---\n\n## 🧩 Scripts\n\n- `LorenzAttractor.cs` — Generates and updates the attractor mesh in real-time.  \n- `LorenzAttractorEquationsSolver.cs` — Implements RK4 integration and derivative calculation.  \n- `LorenzAttractorSettings.cs` — ScriptableObject storing parameters, including butterfly effect option.  \n- `OrbitCamera.cs` — Smooth orbit camera centered on the attractor’s active points.\n\n---\n\n## 🚀 Demo Ideas\n\n- Spawn two attractors:\n  - One normal\n  - One with butterfly effect enabled\n- Observe divergence over time 🦋.\n- Experiment with gradient coloring to highlight **high-velocity regions**.\n- Increase `maxPoints` for high-resolution trails.\n\n---\n\n## 💻 Requirements\n\n- Unity 2023+ (or compatible version)  \n- Standard 3D pipeline  \n- Optional: HDRP/URP for improved visuals  \n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fwendtpiotr%2Fprocedural-lorenz-attractor","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fwendtpiotr%2Fprocedural-lorenz-attractor","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fwendtpiotr%2Fprocedural-lorenz-attractor/lists"}