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Function Visualizer

A real-time mathematical function visualizer that creates beautiful, animated patterns using complex mathematical operations. The application supports GPU acceleration and includes advanced features for performance monitoring, saving/loading, and customization.

2025-08-08.13-17-48.mp4

Features

🎨 Visualization

  • 15 Mathematical Operations: Sine/cosine waves, XOR patterns, cellular automata, domain warping, polar transformations, noise generation, SDF tiling, Gabor noise, and more
  • Normalized Composition: Each function is normalized to [0,1] range before combining, with individual strength controls
  • Real-time Animation: Smooth, time-based parameter evolution
  • GPU Acceleration: CuPy support for faster computation when available
  • Visual Fidelity Control: Adjustable resolution scaling for performance optimization
  • Color Evolution: Sophisticated color mapping with harmonic layers and temperature variations

💾 Save/Load System

  • Parameter Saving: Save your favorite visualizations with timestamps
  • Preset System: Export and import parameter presets with metadata

📊 Performance Monitoring

  • Real-time FPS Display: Monitor frame rate and performance
  • Auto-optimization: Automatic fidelity adjustment based on performance
  • Performance Warnings: Alerts for low FPS or high memory usage
  • Optimization History: Track performance optimizations made

⚙️ Configuration

  • JSON Configuration: Centralized settings management
  • Customizable UI: Show/hide performance display, toolbar
  • Hardware Detection: Automatic GPU/CPU selection
  • Logging System: Comprehensive logging with file output

Installation

  1. Clone the repository:

    git clone <repository-url>
cd function-visualizer

  2. Install dependencies:

    pip install -r requirements.txt

  3. Optional GPU acceleration:

    pip install cupy-cuda11x  # Replace with your CUDA version

Usage

Basic Usage

python visualizer.py

Controls

  • R: Randomize parameters (new pattern)
  • S: Save current state
  • L: Load saved state
  • F: Toggle fullscreen
  • H: Toggle toolbar visibility
  • P: Toggle performance display

Sliders

  • Step: Animation speed (0.0-0.2)
  • Scale: Visual fidelity/performance (5-100%)

Configuration

The application uses config.json for settings. Key configuration options:

{
  "window": {
    "width": 800,
    "height": 600,
    "title": "Function Visualizer"
  },
  "visualization": {
    "default_time_step": 0.05,
    "default_visual_fidelity": 100.0,
    "frame_rate": 20
  },
  "performance": {
    "enable_gpu": true,
    "auto_adjust_fidelity": true
  },
  "saving": {
    "auto_save_interval": 0,
    "save_directory": "saves"
  }
}

Project Structure

function-visualizer/
├── visualizer.py          # Main application
├── core/                  # Core computation and rendering
│   ├── nd.py              # NumPy/CuPy selection and helpers
│   ├── params.py          # Parameter randomization and defaults
│   ├── color/
│   │   ├── palettes.py    # Palettes and sampling
│   │   ├── space.py       # RGB/HSV utilities and vibrance
│   │   └── tone.py        # Contrast/gamma/brightness
│   ├── feedback/
│   │   ├── state.py       # Feedback state singleton
│   │   └── compute.py     # Feedback signal computation
│   ├── patterns/          # Individual pattern operators
│   │   ├── sin_cos.py
│   │   ├── xor.py
│   │   ├── cellular.py
│   │   ├── domain_warp.py
│   │   ├── polar.py
│   │   ├── noise.py
│   │   ├── gabor_noise.py
│   │   ├── abs_transform.py
│   │   ├── power.py
│   │   ├── voronoi.py
│   │   ├── sdf_shapes.py
│   │   ├── reaction_diffusion.py
│   │   └── sinusoidal_field.py
│   ├── compute/
│   │   ├── compose.py     # Orchestrates ops and color mapping
│   │   └── registry.py    # Maps op keys to functions
│   └── rendering/
│       └── image.py       # Image generation from functions
├── config.py              # Configuration management
├── requirements.txt       # Dependencies
├── README.md              # This file
├── ui/
│   └── visualizer_ui.py   # User interface
├── utils/
│   ├── hardware.py        # GPU/CPU detection
│   ├── logger.py          # Logging system
│   ├── save_manager.py    # Save/load functionality
│   └── performance.py     # Performance monitoring
└── saves/                 # Saved files (auto-created)
    ├── parameters/        # Saved parameters
    ├── images/            # Exported images
    └── videos/            # Video frames

Mathematical Operations

The visualizer supports 15 different mathematical operations:

  1. Sine Waves (use_sin): Basic sine wave patterns
  2. Cosine Waves (use_cos): Basic cosine wave patterns
  3. XOR Patterns (use_xor): Bitwise XOR with morphing
  4. Cellular Automata (use_cellular): Grid-based patterns
  5. Domain Warping (use_domain_warp): Coordinate transformation
  6. Polar Transformations (use_polar): Radial coordinate patterns
  7. Noise Generation (use_noise): Multi-octave pseudo-noise
  8. Absolute Value (use_abs): Absolute value transformations
  9. Power Functions (use_power): Exponential transformations
  10. Feedback Loops (use_feedback): Frame-to-frame feedback
  11. Voronoi Diagrams (use_voronoi): Distance field patterns
  12. Reaction-Diffusion (use_reaction_diffusion): Gray-Scott model
  13. Sinusoidal Fields (use_sinusoidal_field): Complex 2D field patterns
  14. SDF Shapes/Tiles (use_sdf_shapes): Tileable signed distance fields with circle/rounded-box mixing and smooth edges
  15. Gabor Noise (use_gabor_noise): Oriented, band-limited noise with Gaussian envelope and time animation

Performance Tips

  • GPU Acceleration: Install CuPy for significant performance improvement
  • Visual Fidelity: Lower the scale slider for better performance
  • Auto-optimization: Enable auto-adjust fidelity in config
  • Memory Monitoring: Install psutil for memory tracking

Troubleshooting

Common Issues

  1. Low FPS: Reduce visual fidelity or enable auto-optimization
  2. GPU Not Detected: Ensure CuPy is properly installed for your CUDA version
  3. Save/Load Errors: Check file permissions in saves directory

Logging

The application logs to both console and file (visualizer.log). Check logs for detailed error information.

Development

Adding New Mathematical Operations

  1. Create a new operator in core/patterns/your_op.py exporting:
    • apply(x, y, time_val, params) → returns an array contribution (same shape as x).
  2. Register the operator in core/compute/registry.py by mapping a key (e.g., 'use_your_op') to your function.
  3. Add any parameters and ranges to core/params.py and include your op key in the randomized operations set if desired.
  4. (Optional) Extend color behavior in core/color/* if your op needs custom color handling.
  5. Run visualizer.py and test.

Extending the UI

  1. Modify ui/visualizer_ui.py for new controls
  2. Update the main visualizer class for new callbacks
  3. Add configuration options in config.py

License

This project is open source. Feel free to contribute improvements!

Contributing

  1. Fork the repository
  2. Create a feature branch
  3. Make your changes
  4. Add tests if applicable
  5. Submit a pull request

Acknowledgments

  • PIL/Pillow for image processing
  • NumPy for array operations
  • CuPy for GPU acceleration
  • Tkinter for the user interface