Four mutually tangent spheres seed a recursive 3D packing. Drag to rotate; adjust depth to add more spheres.
Descartes' Circle Theorem (1643): If four mutually tangent circles have curvatures k₁,k₂,k₃,k₄ then (k₁+k₂+k₃+k₄)²=2(k₁²+k₂²+k₃²+k₄²). This extends to spheres in 3D. Starting from four mutually tangent spheres, each interstice can be filled by a unique "Soddy sphere", and the process repeated forever. The packing has fractal dimension ≈ 2.47 in 3D.