A fractal packing of circles built from Descartes' Circle Theorem: for four mutually tangent circles with curvatures ki=1/ri (sign negative for the enclosing circle), (k1+k2+k3+k4)2=2(k12+k22+k32+k42),
which solves to k4=k1+k2+k3±2k1k2+k2k3+k1k3. The same identity holds in complex centers via bi=kizi, so every triple of touching circles admits a unique inscribed companion. Starting from three equal mutually tangent inner circles inside an outer enclosure, the gasket grows depth-by-depth — each new ring colored by recursion depth — until the disc is densely packed by infinitely many tangent circles whose limit set has Hausdorff dimension ≈1.3057.