SIN1 Relaxed Spiral

Newton's method with complex relaxation m = 1 - i applied to f(z) = sin(z) - 1. Every root is double, so the multiplier is (1 + i) / 2, modulus 1 / sqrt(2) and argument pi / 4, which shrinks and rotates each basin into a logarithmic spiral. The frame is centred on a pole of the Newton map at z = 3 pi / 2 rather than on a root. Hue mixes the root index with the smooth count along a teal to magenta ramp, and the concentric ripples are one level set per iteration.