E8 Studio

An interactive WebGL studio for exploring the E8 root system,
cut-and-project quasicrystals, root systems, Coxeter multigrid tilings, Dynkin diagrams, Platonic solids, and regular four-dimensional polytopes.

Launch E8 Studio · Explore features · Mathematical visualization · Release notes · Issues

Explore E8 Studio

Click Launch E8 Studio and start exploring immediately. The hosted Studio runs entirely in the browser: no installation, account, sign-in, or upload is required. Your settings and learning progress stay in your browser.

On a first visit, Start here offers three routes: a short geometry tour, a beginner lesson, or a curated visual. Choosing a route is optional and does not change the scene until you act.

Nine interactive views

View	What it offers
Bloom	Watch a Platonic source shape pass through 600-cell-inspired stages and bloom into the E8 Coxeter projection. Animate the transformation and combine it with palettes, depth, and effects.
Platonic	Explore the five Platonic solids and four Kepler–Poinsot star polyhedra. Switch between wireframe and solid treatments, compare duals, and apply live twist, spike, and jitter deformations.
E8 Coxeter	Examine all 240 E8 roots in the Coxeter plane. Reveal the eight rings, edges, Petrie orbit, coordinate axes, Weyl mirrors, Cartan neighbors, projection modes, and mathematical color groupings.
E8 Quasicrystal	Cut the E8 lattice from eight dimensions into a two-dimensional quasiperiodic patch. Move its six-dimensional acceptance window and open a linked comparison of the visible pattern, a two-coordinate view of hidden space, and finite-patch diffraction peaks. The comparison marks points entering or leaving the selection.
4D Polytope	Move through all six convex regular 4-polytopes—from the 5-cell through the 600-cell to the 120-cell. Rotate across six independent 4D planes and control the fourth-dimensional perspective depth.
E8 SDF	See the roots as a raymarched, illuminated structure with smooth-union geometry, edge connections, ambient occlusion, reflections, and the animated “Living E8” extrusion effect.
Root Lab	Generate the A₂, B₂, G₂, and H₂/I₂(5) rank-2 root systems from two simple roots. Reveal reflection mirrors, reflection chambers, root lengths, Cartan data, and a Coxeter orbit.
Tiling Lab	Turn A₂, B₂, G₂, and H₂ root directions into dual rhombus tilings. Reveal the generating multigrid and compare periodic lattices with fivefold quasiperiodic order.
Dynkin	Compare the E₆, E₇, and E₈ Dynkin diagrams and inspect how their simple roots connect. This focused mathematical reference remains manually selected instead of joining the Auto Model visual showcase.

Shape the visual experience

E8 Studio is both an explorer and a generative visual instrument. You can:

• Choose from dozens of curated color palettes, including mathematically driven E8 color modes.
• Place the geometry in white clouds, galactic star fields, engraved gold mandalas, flowing neon plasma, sampled hydrogen probability clouds, ocean surf, white hurricanes, amber eclipses, and other procedural backgrounds. Tide and Ember replace Grid and Barset; saved scenes migrate automatically. The traced ocean uses High quality on desktop; Mobile Low keeps a simpler animated sea.
• Use the focused Visuals workspace for the complete palette, color-shift, background, effect, lighting, quick-look, and theme controls. Open Tools → Export for downloadable files.
• Apply view-aware shader effects: point and mesh views expose the full compatible catalog, while E8 SDF provides native Glow, Pulse, Heat, Iridescent, Hologram, and X-ray surface treatments.
• Animate individual sliders, extrusion, rotations, morphs, palette shifts, and camera movement.
• Spin the model itself, move the camera independently with Orbit, Dive, or Spiral, or take direct control with drag, scroll, and touch gestures.
• Start from gallery presets, move through them with previous/next controls, or use Surprise to discover unexpected combinations.
• Enter full-screen or minimal presentation mode for a clean art display.
• Use adaptive quality and reduced-motion safeguards on less powerful hardware.

Capture, share, and export

The Studio is designed to produce work you can keep or use elsewhere:

• Snapshot saves the current render as a PNG exactly as it appears.
• High-resolution PNG captures a larger render; Transparent PNG removes the background for compositing.
• Share copies a versioned scene link that restores the selected geometry, visual settings, and camera, including Tiling Lab controls. Personal and device preferences stay local.
• Video records an animated WebM clip while the geometry, camera, palettes, and effects continue moving.
• Postcard Studio creates a vertical 9:16 composition with an editable caption for social sharing or presentation.
• Tools → Export opens one panel for every model; mobile has Share and tools → Export.
• SVG saves an editable XY diagram; E8 and Dynkin retain their specialized desktop diagrams.
• OBJ and PLY save geometry for modeling tools. CSV saves the corresponding XYZ coordinate table.
• JSON exports original geometry and metadata, retaining native 4D and 8D coordinates.
• STL and 3MF turn Platonic solids and 4D projections into sized print meshes. Choose a solid convex hull for regular Platonic solids or joined struts for a frame. 3MF stores millimeter units; import STL as millimeters. Check supports and thin features in your slicer.

Geometry files describe the mathematical model; shader effects belong in PNG. See the format and printing guide for per-model details and limitations.

Exports are generated locally. The hosted Studio does not require an account or send your render to a server.

Learn while exploring

The educational system is integrated with the visual controls instead of being a separate textbook:

• Contextual essays explain the object or view currently on screen.
• Selection notes cover every Platonic solid, regular star polyhedron, and convex regular 4-polytope.
• Guided learning paths connect geometry, symmetry, E8 roots, the McKay correspondence, and signed-distance rendering.
• Every lesson includes a three-stage Studio experiment with model-aware setups, observation prompts, revealed takeaways, prerequisite context, and links to related ideas.
• Quizzes provide explanations rather than only marking an answer right or wrong.
• A searchable glossary defines the mathematical language used throughout the Studio.
• Root picking reveals 8D coordinates, opposite roots, and Cartan-neighbor structure.
• The Learning Center opens on a question-led home with four paths and a clear beginner starting point. Its searchable reader covers 13 lessons with worked examples, vocabulary, evidence tables, self-checks, and guided experiments. Test the angle rule with the interactive regular-solid corner calculator.
• Jump between understanding, experiments, quizzes, and resources; return from a quiz to its lesson and continue the next unfinished experiment step.
• Daily facts, biographies, a historical timeline, badges, and locally saved lesson and experiment progress reward deeper exploration.
• Source links and claim labels distinguish established mathematics, historical context, interpretation, and app-designed visualization.

Getting around

• First visit: use Start here to choose a geometry tour, a beginner lesson, or a curated visual. The optional three-step tour is also available from Guided tour in the header or Tools menu.
• Mouse: drag to orbit, scroll to zoom, and click supported roots or structures for details.
• Touch: drag to orbit and pinch to zoom; the responsive control drawer keeps the render visible on smaller screens.
• Keyboard: use 1–9 for views, Space to pause, S for PNG, L for the Learning Center, G for the glossary, H for presentation mode, and Ctrl/⌘ + K for commands.
• Workspaces: use View for geometry and camera controls, Visuals for appearance, and Learn for orientation, guided paths, references, progress, and interactive mathematics.
• Reset and recovery: camera and view resets stop conflicting animation drivers and return to a known pose.

Mathematical Visualization

E8 Studio separates three things:

• Established mathematics — canonical root data, element counts, coordinates, Coxeter structure, and polytope relationships.
• Interpretation — carefully qualified visual connections, including the Studio’s presentation of the McKay correspondence.
• Artistic visualization — lighting, color, Bloom transitions, signed-distance materials, and other explanatory display choices.

Automated tests verify the rank-2 reflection and multigrid constructions, E8 lattice enumeration and cut-and-project selection, 240-root E8 Weyl closure, Cartan relations, the eight-by-thirty Coxeter projection, Lie-bracket adjacency, Platonic Euler characteristics, regular 4-polytope counts, and educational-source coverage. The source ledger is maintained in src/content/sources.js.

Run locally

Most visitors only need the hosted Launch E8 Studio link. The following instructions are for contributors, offline use, and custom builds.

Requirements

• Node.js 20.19+ or 22.12+
• Python 3.12+

git clone https://github.com/agentcarlosian/e8-studio.git
cd e8-studio
npm ci
npm run dev

Vite prints the local development URL. Development source should be opened through the server rather than directly through file://.

Build targets

npm run build:web          # Desktop site and Canvas2D fallback → dist/web
npm run build:offline      # Inline PWA/Electron page → dist/index.html
npm run build:single       # Self-contained desktop HTML
npm run build:mobile       # Mobile smoke HTML + clean dist/mobile Capacitor input
npm run build:share        # Desktop and mobile standalone files
npm run electron:dist      # Desktop installers/packages
npm run release:artifacts  # Versioned bundle and checksums

Generated output is written to ignored dist/ or dist-app/ directories.

Verification

Install the browser-test dependencies once:

python -m pip install -r requirements-dev.txt
python -m playwright install chromium

Run the release checks:

python scripts/verify.py
python scripts/test_robustness.py
python scripts/test_math.py
npm run smoke:mobile-v2
npm run test:deferred-view
npm run test:quasicrystal-comparison
python scripts/test_startup_recovery.py --built
python -B scripts/test_packaging_assets.py

GitHub Actions runs release checks on Linux and core build/test contracts on Windows. Dependency updates are monitored by Dependabot.

Architecture

index.html              Desktop web entry
mobile.html             Dedicated mobile entry
src/
  views/                WebGL visualization modules
  math/                 E8 and polytope mathematics
  fx/                   Rendering effects and procedural backgrounds
  ui/                   Controls, palettes, essays, and themes
  state/                Camera, gallery, persistence, and progress
  services/             Export and recording orchestration
  mobile/               Hybrid Canvas 2D + WebGL mobile application
data/                   Canonical and precomputed geometry
scripts/                Build, verification, and release tooling
electron/               Electron shell
android/                Capacitor Android project

The hosted application is bundled with Vite. Standalone, Electron, and mobile targets use separate verified build paths. See docs/architecture/build-boundaries.md for details.

Platform support

• Modern desktop browsers with WebGL2 for the full visual Studio
• A Canvas2D Studio route in hosted web builds when WebGL cannot start
• Responsive touch-oriented desktop shell
• Dedicated hybrid mobile interface with Canvas 2D scenes and ray-marched WebGL SDF
• Electron on desktop platforms
• Android through Capacitor

Performance varies by device and GPU. The WebGL SDF automatically selects a High, Balanced, or Low shader budget from device constraints while preserving all 240 roots through the compact eight-ring representation. Changing the quality control recompiles that budget immediately. Effects declare their compatible views and approximate GPU cost, so unavailable or overly expensive combinations are not presented as active controls. Adaptive resolution, reduced-motion handling, and animation recovery provide additional fallbacks.

Contributing

Focused bug reports and improvements are welcome. Read CONTRIBUTING.md before opening a pull request. Please report vulnerabilities privately according to SECURITY.md.

• Report a bug
• Request a feature

Acknowledgments

The project draws on standard references for E8, Coxeter-plane projections, regular polytopes, the McKay correspondence, and sphere tracing. Full citations are maintained in the application’s source registry.

The generative control-panel format was inspired in part by Asobo Design’s DESIGN ≠ FORMULA. E8 Studio is an independent implementation and shares no code with that project.

License

E8 Studio is available under the MIT License. © 2026 Carlosian.