EXPM1Z Ember Ladder

Newton's method applied to f(z) = exp(z) - 1 - z, framed on the pole of the Newton map at 2 pi i rather than on a root. The root at the origin is double, so |f| contracts by a measured 0.25 per step and the smooth count is a single log base 4. The two halves of the plane behave differently, the left collapsing toward -1 in one step and the right marching back by about z - 1 each step. The greatest real part an orbit ever reached is carried as a third colour channel and runs the right side gold.