s_{0}=0.2.36, s_{i+1}=-0.5*s_{i}^{2}+2.8

Center:-0.359+0i; Zoom = 320

Same generating sequence as the previous few pictures. With the starting point selected to speed up the convergence of the cycle. (The starting point is within 0.01 of one of the points on the 32-cycle.) As expected, the quicker convergence puts the sequence closer to a simple repeating (although somewhat long cycle) sequence, and the capture set is larger.