Home▸Generative Art & Algorithmic Patterns▸Apollonian Gasket Generator

◎ The Apollonian Gasket: Packing Infinity into a Circle

Interactive fractal circle-packing generator where adjusting starting circle radii and recursion depth fills the gaps with infinitely nested tangent circles in real time.

Generative Art & Algorithmic Patterns3DModerate60 FPS

Three mutually tangent circles inside a boundary circle spawn an infinite cascade of ever-smaller tangent circles filling every remaining gap — a real fractal built live from Descartes' Circle Theorem, rendered as a receding 3D disc tunnel.

🔬 What It Demonstrates

Every curved-triangle gap between three tangent circles has an exact, computable circle that fills it, found from the circles' curvatures alone via Descartes' Circle Theorem — and repeating the rule forever never runs out of gaps.

🎮 How to Use

Adjust recursion depth and the starting radius ratio to reshape the gasket, use relief depth to turn the flat fractal into a 3D tunnel, and switch colour mode to see generation depth or circle size. Drag to orbit, scroll to zoom.

💡 Did You Know?

When the starting circles have integer curvatures, every circle in the entire infinite gasket also has an integer curvature — a surprising link between this ancient geometry problem and modern number theory.

⚙ Under the hood

Interactive 3D fractal where adjusting seed circle radii shows how the Apollonian gasket packs infinitely many tangent circles into ever-shrinking gaps.

apollonian-gasketcircle-packingfractalsgenerative-geometryrecursive-patternsgenerative-art

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install