$ s_i*z^2+c$
s₀=0.1i, s_i+1=(0.5+0.1i)*s_i+(0.5-0.1i)
Center:2.7243-0.0262i; Zoom = 3276

Another zoom, same setup as yesterday. Sequence Fractals Part IV #31

$ s_i*z^2+c$
s₀=0.1i, s_i+1=-3.0*s_i²+0.1
Center:-2+0i; Zoom = 0.04

This one uses the a*s_i²+b sequence generator with a = -3, b = 0.1. The sequence converges quickly to a small value. The result is a large fractal. Large in the sense that the capture area extends well beyond the |c|<=2.0 that is typical with quadratic polynomials. The horizontal range of this image is (-25,+25).

$ s_i*z^2+c$
s₀=0.1i, s_i+1=-3.0*s_i²+0.1
Center:-15.61563-0.37619i; Zoom = 13107

Here is a deep zoom on the left side of yesterday's picture, Sequence Fractals Part IV #33. Just a little above the center line, the real axis.

$ z^2+s_i*z+c$
s₀=0.5, s_i+1=-2.0*s_i²+0.7006
Center:-0.891+0i; Zoom = 256

Another sequence fractal formula variation. A z term is added and it is multiplied by the sequence value. The constant sequence 0 would give rise to the usual quadratic / Mandelbrot situation.

I tried several different sequences, and a few zooms on each. I found nothing that stood out as distinctly different from the other formula variations presented so far.

This is the first of two zooms along the negative real axis. Here, the sequence slowly converges to a 32 cycle. Tomorrow's image, Sequence Fractals Part IV #36 is the same location with a small increase in the adder.

$ z^2+s_i*z+c$
s₀=0.5, s_i+1=-2.0*s_i²+0.7007
Center:-0.891+0i; Zoom = 256

The sequence adder is increased by 0.0001 compared to yesterday's image, Sequence Fractals Part IV #35. The capture set is gone. Gone at least in this area, and as far as I can tell, everywhere else.

The high density in both of these images is probably a result of choosing a sequence so close to the capture/no capture boundary.