LOG1PZ2 Teal Scars

Newton's method with complex relaxation m = 1 - i applied to f(z) = log(1 + z^2) on the principal branch. The only root is the double root at the origin, so convergence is linear with multiplier (1 + i) / 2, which turns every basin ripple into a logarithmic spiral. The two scars are the branch cut itself, where the principal logarithm jumps by 2 pi i along the rays z = it with |t| >= 1. The teal glow is a residence-time count in a ribbon straddling that cut, measured in the w = 1 + z^2 plane.