s0=0.1i, si+1=(0.5+0.1i)*si+(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.