s0=0.4, si+1=-0.5*si2+2.8026
Center:-0.33742+0.00008i; Zoom = 2560
Now a very small change to the adder in the sequence generating formula. The capture set is gone. The big picture, zoom = 1, look very much like Sequence Fractals Part IV #18 except the main body is no longer white. It is a palette-dependent non-capturing color.
By my spreadsheet investigation, The sequence converges slowly to a 32-cycle. It may have bifurcated to a 64-cycle.
The result is on the boundary between normal swirly fractals and the jigsaw fractals. It reminds me of a paint drop cloth after a sloppy painter has used it for many projects.