Sinh Orchid Galaxies

Newton's method with complex relaxation m = 1 + i applied to f(z) = sinh(z) - i. Every root is double, so the multiplier is (1 - i) / 2, which shrinks the error by 0.707 and turns it -45 degrees each step, making every basin a logarithmic spiral. The necklaces of double-spiral knots are strung between the poles of the Newton map at z = i(3 pi / 2 + 2 k pi). Brightness is modulated by the Koenigs angle phi = arg w - 2.2662 log|w|, which is constant along an orbit.