Orbital

An HTML-based visualization of the geometry of Orbital, a new n-dimensional AMM design from the team at Paradigm.

Read the Full Paper →

• Authors: Dave White, Dan Robinson, Ciamac Moallemi (Paradigm)
• Topic: Concentrated liquidity for n-dimensional stablecoin pools
• Innovation: Capital efficiency through geometric constraints

• Hypersphere geometry: n-dimensional trading surfaces
• Virtual reserves: Free liquidity from mathematical constraints
• Tick consolidation: Efficient multi-tick trading
• Polar decomposition: Separating balance vs. imbalance components

An interactive 3D visualization of the Orbital AMM mathematical model for multi-asset stablecoin trading with concentrated liquidity.

🌐 Live Demo: https://1elbaz.github.io/orbital/

OR

1. Download the HTML file
2. Open in any modern web browser (Chrome, Firefox, Safari, Edge)
3. Interact with the 3D model using mouse and controls

No installation required! Just open the HTML file directly in your browser.

• 🟢 Green Wireframe Sphere: The AMM constant surface ||r⃗ - x⃗||² = r²
• 🔴 Colored Planes: Tick boundaries x⃗ · v⃗ = k for concentrated liquidity zones
• 🟡 Yellow Dot: Equal price point where all assets trade at $1.00
• ⚪ White Dot: Mathematical sphere center at (r, r, r)

• AMM Constant: ||r⃗ - x⃗||² = r² (defines all valid reserve states)
• Tick Boundaries: x⃗ · v⃗ = k (creates capital efficiency zones)
• Equal Price Point: q = r(1 - 1/√n) (optimal balanced state)

• Sphere Radius (r): Adjust the AMM pool size (1M-20M)
• Tick Count: Change number of concentration zones (3-12)
• Animation Speed: Control rotation speed (0-2x)

• Click + Drag: Rotate the 3D view
• Scroll Wheel: Zoom in/out
• Reset View: Button to return to default position

• Toggle Animation: Start/stop automatic rotation
• Reset View: Return to default camera position

• Inner boundaries (red): High efficiency, low risk (covers small depegs)
• Outer boundaries (blue): Low efficiency, high risk (covers extreme depegs)
• Distance from center: Determines risk/reward profile

• All trading happens on the sphere surface
• Tick boundaries slice the sphere into manageable liquidity zones
• Equal price point represents perfect $1.00 parity for all assets

• Multi-stablecoin pools: USDC, USDT, DAI, FRAX, LUSD
• Concentrated liquidity: LPs can choose their risk tolerance
• Capital efficiency: Up to 150x improvement over traditional AMMs

• Modern web browser with WebGL support
• Internet connection (for Three.js library download)
• No additional software needed

• Three.js r128: 3D graphics library (loaded from CDN)
• Pure HTML/CSS/JavaScript: No build process required

• ✅ Chrome 80+
• ✅ Firefox 70+
• ✅ Safari 12+
• ✅ Edge 80+

||r⃗ - x⃗||² = r² (r - x₁)² + (r - x₂)² + (r - x₃)² = r²

• Replaces x × y = k for n-dimensional trading
• Ensures consistent pricing across all asset pairs
• Creates bounded reserve space (0 ≤ xᵢ ≤ r)

x⃗ · v⃗ = k (x₁ + x₂ + x₃)/√3 = k

• Creates concentration zones for capital efficiency
• k_min = r(√n - 1): Closest to equal price point
• k_max = r(n-1)/√n: Covers extreme scenarios

efficiency = x_base / (x_base - x_min(k))

• x_base: Traditional capital requirement
• x_min(k): Virtual reserves from geometric constraints
• Result: 15x to 150x efficiency gains

Built with Three.js • No installation required • Open source visualization