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README.md

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-# aizawa-attractor
+# Aizawa Attractor Visualization
+
+## Overview
+This repository contains an interactive 3D web visualization of the **Aizawa attractor**, a classic chaotic system from chaos theory. The attractor is rendered with **Three.js** and features:
+
+- Smooth 3D curve generated from the Aizawa ODE system.
+- Color gradient (deep blue → cyan → magenta) that indicates the flow direction.
+- Bloom post‑processing for a glowing, energy‑field look.
+- OrbitControls for rotation, zoom, and pan.
+- Live UI controls (via `lil‑gui`) to adjust the attractor parameters `a, b, c, d, f` in real time.
+- Animation of a glowing sphere traveling along the trajectory, with a fading trail.
+- Simple explanatory side panel describing the attractor and its mathematics.
+
+The project is built with modern JavaScript (ES modules) and uses **Vite** as the development server and build tool.
+
+## Features
+- **Accurate mathematics**: Implements the continuous‑time Aizawa ODE with classic parameter values.
+- **Dynamic visualization**: Real‑time updates when parameters change.
+- **Performance‑focused**: Uses a single `BufferGeometry` and reuses materials to avoid per‑frame allocations.
+- **Responsive UI**: Sliders, randomize/reset buttons, and toggles for trail/full‑curve modes.
+- **Adjustable animation speed**.
+
+## Installation
+```bash
+# Clone the repository (if you haven't already)
+git clone https://github.com/Ramakm/aizawa-attractor.git
+cd aizawa-attractor
+
+# Install dependencies
+npm install
+```
+
+## Development
+Start the development server:
+```bash
+npm run dev
+```
+Open the URL shown in the terminal (usually `http://localhost:5173`). The visualization will load automatically.
+
+## Build for Production
+```bash
+npm run build
+```
+The built files are placed in the `dist/` directory and can be served by any static web server.
+
+## Usage
+- **OrbitControls**: Left‑drag to rotate, scroll to zoom, right‑drag to pan.
+- **Parameter sliders**: Adjust `a, b, c, d, f` to explore different chaotic shapes.
+- **Randomize**: Click the *Randomize Parameters* button for nearby values.
+- **Reset**: Restores the classic parameter set (`a=0.95, b=0.7, c=0.6, d=3.5, f=0.1`).
+- **Trail / Full Curve**: Toggle between showing only the moving point with a short trail or the entire attractor curve.
+- **Play / Pause**: Control the animation of the traveling sphere.
+- **Speed**: Choose *slow*, *normal*, or *fast* animation speed.
+
+## Math Details
+The attractor follows the continuous‑time ODE system:
+```
+dx/dt = (z - b) * x - d * y
+dy/dt = d * x + (z - b) * y
+dz/dt = c + a * z - (z³ / 3) - x² + f * z * x³
+```
+Classic parameters:
+- `a = 0.95`
+- `b = 0.7`
+- `c = 0.6`
+- `d = 3.5`
+- `f = 0.1`
+
+Initial point: `(x0, y0, z0) = (0.1, 0.0, 0.0)`
+Integration uses a fixed time step (`dt ≈ 0.01`) to generate tens of thousands of points.
+
+## Project Structure
+```
+aizawa-attractor/
+├─ index.html          # Entry HTML file
+├─ src/
+│   ├─ main.js        # Entry point, wires everything together
+│   ├─ scene.js       # Three.js scene, camera, renderer, post‑processing
+│   ├─ math.js        # ODE integration logic
+│   ├─ attractor.js   # Geometry creation, animation, color gradient
+│   ├─ ui.js          # lil‑gui controls and UI handling
+│   └─ style.css      # Global styling
+├─ package.json        # npm scripts and dependencies
+└─ README.md           # This document
+```
+
+## Contributing
+Feel free to open issues or submit pull requests for improvements, bug fixes, or new features (e.g., alternative attractors, additional visual effects, etc.).
+
+## License
+This project is licensed under the ISC license.