## Sequence Fractals Part IV #33

$s_i*z^2+c$
s0=0.1i, si+1=-3.0*si2+0.1
Center:-2+0i; Zoom = 0.04

This one uses the a*si2+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).

## Sequence Fractals Part IV #31

$s_i*z^2+c$
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.

## Sequence Fractals Part IV #30

$s_i*z^2+c$
s0=1.5, si+1=0.9*si+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.

## Sequence Fractals Part IV #29

$s_i*z^2+c$
si=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 si.

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.

## Sequence Fractals Part IV #28

$z^2+c*s_i$
s0=0.3, si+1=(-0.5+0.25i)*si2+(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.

## Sequence Fractals Part IV #26

$z^2+c*s_i$
s0=0.3, si+1=(-0.5+0.25i)*si2+(1.2+0.5i)
Center:0+0i; Zoom = 0.5

Some more playing around with complex parameters in the a*si2+b sequence generator.

I have not investigated the long term behavior of this sequence. Given the large capture set and Mandlebrot-like right side, I suspect it the sequence converges to very short cycle, most likely a single point.

A couple of zooms to follow.

## Sequence Fractals Part IV #24

$z^2+c*s_i$
s0=0.4, si+1=-1.5*si2+0.9
Center:0.50789+1.055828; Zoom = 10240

I have generated and discarded many images in the last few days, trying to find something unique. Most are interesting, but feel too much like “variation on a theme”. Along the way I got distracted, that happens a lot. I pulled up a palette that I was working on earlier this year for non-fractal abstract art. I tweaked it some to get a better fit for fractals, and here is the result.

As for the main theme, this is another sequence with a which converges to a long cycle. The big difference is just the new colors.