Recursive fractal built from the Descartes Circle Theorem
Apollonian circle packing: given three mutually tangent circles, Descartes' theorem gives the curvature k₄ = k₁+k₂+k₃ ± 2√(k₁k₂+k₂k₃+k₃k₁) of the two tangent circles fitting in each gap. Iterating fills all space. The resulting fractal has Hausdorff dimension ≈ 1.3057 and encodes deep number theory — if the initial curvatures are integers, all subsequent curvatures are integers.