Crystal Ladder

Newton's method applied to f(z) = (z^4 - 1) sin(z), windowed on exactly one period of the ladder, Re z from -pi to pi. The step is evaluated as 1 / (4z^3 / (z^4 - 1) + cot z), the same map written so the exponential growth of sin never overflows. Two root families split the palette, sapphire for the quartet at 1, i, -1 and -i and a gold to bronze ramp indexed by |k| for the roots at k pi. Lace brightness follows the gradient of the step count rather than the count itself.