$ z^2+c*s_i$
s₀=0.3, s_i+1=(-0.5+0.25i)*s_i²+(1.2+0.5i)
Center:-0.82443+0.27707i; Zoom = 5120

Here is a zoom into the left side of the comb in the upper left of the previous image, Sequence Fractals Part IV #26

Are those puzzle pieces on the left?

$ z^2+c*s_i$
s₀=0.3, s_i+1=(-0.5+0.25i)*s_i²+(1.2+0.5i)
Center:-0.8244795+0.27693854i; Zoom = 102400

Here is a zoom into the top of the mountain peak in the lower center of Sequence Fractals Part IV #27.

I feel compelled to try to describe this when I should just let the image speak for itself. This has some characteristic of the jigsaw puzzle fractals. See Sequence Fractals Part III #27 and Sequence Fractals Part IV #16 for a description of "jigsaw puzzle fractals". The areas that I image as the puzzle pieces have a fractal spirals along the edges. The "drop cloth" fractals, see Sequence Fractals Part IV #22 and Sequence Fractals Part IV #23 also have fractal shapes on the edges of puzzle pieces. This one however seems much more organized than the splashed paint appearance of the others.

$ s_i*z^2+c$
s_i=1.0, 0.001 repeating
Center:-12.2+0.0i; Zoom = 3

Introducing a new variation on the sequence fractal formula. The z² part is mulplied by the sequence value s_i.

To get my footing with the new formula I started out with a simple two step repeating sequence. The "do-nothing" value of one alternates with the a very small value, 0.001. If an orbit tries to escape, every other step pulls it back. The result is that a large area around the origin is captured. Today's view is far out to the left (-12 units) on the negative real axis.

$ s_i*z^2+c$
s₀=1.5, s_i+1=0.9*s_i+0.1
Center:-0.7348+0.180i; Zoom = 128

The sequence multiplies z² again. The sequence starts at 1.5 and converges to 1.0 along the real axis.

Since the sequence converges quickly to the multiplicative identity, 1.0, the resulting images look like Mandelbrot set zooms.

$ s_i*z^2+c$
s₀=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.

$ 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.