Manifold Visualizer

Real-time mathematical surface visualization using WebGPU compute shaders. Renders 25+ manifold types including Klein bottles, Calabi-Yau manifolds, Hopf fibrations, and exotic surfaces with GPU-accelerated post-processing.

Live: manifold.herakles.dev

Features

• 25+ manifold types — Klein bottle, Mobius strip, Boy's surface, Calabi-Yau, trefoil knot, Costa surface, Hopf fibration, and more
• WebGPU compute pipeline — WGSL shaders for parallel surface tessellation and ray marching
• Post-processing chain — Bloom, chromatic aberration, film grain, vignette, tone mapping
• Audio reactivity — Real-time audio analysis driving surface deformation and color mapping
• Preset system — Curated visual presets with smooth parameter interpolation

Architecture

lambda/
  manifolds.py       # 25+ parametric surface equations (the math engine)
  gpu_renderer.py    # Server-side GPU rendering pipeline
  server.py          # WebSocket server for remote GPU compute
  presets.py         # Preset management
static/
  js/
    engine.js        # WebGPU initialization and render loop
    fractals.js      # Fractal generation (Mandelbrot, Julia sets)
    fractals-wgsl.js # WGSL compute shader source
app.py               # Flask backend serving the application

Tech Stack

Python, Flask, WebGPU, WGSL, GLSL, JavaScript, HTML Canvas

Manifold Types

Algebraic surfaces, minimal surfaces (Costa, Enneper), fiber bundles (Hopf fibration), topological objects (Klein bottle, Boy's surface, cross-cap), knots (trefoil, torus knots), higher-dimensional projections (Calabi-Yau), and fractal surfaces.

Running Locally

pip install -r requirements.txt
python app.py
# Open http://localhost:5000

WebGPU requires Chrome 113+ or Firefox Nightly with dom.webgpu.enabled.

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Built by D. Michael Piscitelli | herakles.dev