Logz Omega Onearm

Newton's method with complex relaxation m = 1 + 0.6i applied to f(z) = Log(z) + z. The single root is the Omega constant 0.5671 and it is simple, so the linear convergence comes from the relaxation, whose multiplier -0.6i has modulus 0.6 and argument exactly -90 degrees. The arm is drawn by the Koenigs phase psi = nu - 2 theta / pi taken mod 4 rather than by the smooth count, which gives only rings. A measured 3-cycle of multiplier 0.3455 takes about 70 percent of the window.