s_{0}=0.1i, s_{i+1}=(0.5+0.1i)*s_{i}+(0.5-0.1i)

Center:-1.312+0.069i; Zoom = 256

This sequence starts at 0.1i and converges to a value close to 1.0. The convergence is quick, but not a straight line.

Again, since the sequence converges quickly, the image looks almost like a regular fractal.