Ztan Jade Lattice

Newton's method applied to f(z) = z tan(z) - 1. The roots are the real solutions of z tan z = 1, each just above k pi with a pole of the tangent wedged between neighbours, so the basins narrow into a ladder and the frame is turned to run the real axis down the page. The map also carries two attracting 2-cycles on the imaginary axis with multiplier 0.89165, which take about 71 percent of this window as the dark jade ground, shaded by the two-step residual ln(1 / |z_K - z_K-2|).