Apollonian Gasket
Infinite circle packing via Descartes' theorem: (k₁+k₂+k₃+k₄)² = 2(k₁²+k₂²+k₃²+k₄²)
All curvatures (k=1/r) are integers if the initial four are — an integer Apollonian gasket.
Hausdorff dimension ≈ 1.3057 (computed numerically). Every interstice is tangent to exactly 3 circles.