s0=0.4, si+1=(0.28+0.96i)*si
Center:-0.5677-0.5371i; Zoom = 10
This is one of my favorites. There is a lot going on.
The white area is a true capture area. Typically, with the non-convergent sequences, the bouncing around is enough to knock an otherwise convergent orbit into the escape region. Here, for some values of c, the basin of attraction is big enough that the orbits can be disturbed by a displacement of 0.4 without escaping. These orbits would not converge to a point or finite cycle, but they would remain bounded.
But, since some points are captured and some escape, there is a boundary between those two sets where interesting things happen. Typically, each iteration step removes a thin layer around the capture set, revealing a little more detail. There is a smooth color transition. That is happening here. In addition, the sequence gives the orbit an extra kick. That causes larger chunks to be kicked out to the escape set. You can see this in areas that look almost like a puzzle. Interconnecting pieces of distinctly different colors.