EXPZ2 Crossed Beams

Newton's method applied to f(z) = exp(z^2) - 1, framed 16 wide on the origin. The roots satisfy z^2 = 2 pi i k, so they string out along the two diagonals as square-root spirals and meet at the origin, which is a double root and renders as the pearl lens at the centre. Magenta runs on the diagonal carrying positive k and gold on the one carrying negative k. The imaginary axis is invariant and never converges, since the step there grows like exp(y^2) / 2y, and it is the star-dust ground.