More snowcapped mountains.

New Series, Brr. Lots of white, vaguely reminiscent of snowcapped mountains.

Again, mostly pictures without words. I am not going to try to explain how I generated these. If anyone is interested, send me a message or leave a comment.

As for meaning and emotions, I leave that to the viewer to decide. Personally, I enjoy winter mountain sports. So despite the messy chaotic nature of these images, I find them optimistic. I long for the winter to come and the snow to start falling.

Leave a comment on what you see.

The previous images in this series were mostly created a month ago. The final touches, the finishing was done a week ago. As was the selecting, sorting, ordering, to put them into a series.

I have stopped describing the algorithms that generate these. I feel every one of these images deserves some words. But what is there to say? When I try to explain something, I end up just stating the obvious. So what follows is mostly just pictures without words.

If you have any questions about anything, just ask in the comments. I will explain as best I can.

I love these messy chaotic images. I know they are not for everyone's taste. But I find them fascinating. I encourage you to look closely and discover the fine details.

I mentioned that I consider these constructive. That I apply selected formulas, and colors, to achieve a desired effect. I am getting better at doing that, but often the effect comes with side effects.

Here I started with everything expanding out radially from the lower left quadrant. Then I got the color dialed in. Mostly black and white, which makes the blue pop, with a little complementary rust on the left. Then I got the details on the left side, the streaking, the contrails, the 'eye of the storm'.

After many attempts, either I gave up, or after studying it long enough I discovered it was actually perfect as it, or the universe was telling me this is the way it must be. In truth, now I have no desire to change any of it.

My program is set up to apply effects (formulas) globally. I am working on modifications to apply effect to isolated areas. It is not there yet, and I am having plenty of fun as-is.

The faux-fractal formulas of the previous series, along with some new ones, become tools of algorithmic art. They are operations to apply to create an effect.

I have stopped posting coordinates and formulas. In fact I have stopped keeping track of them. I still have the program code for all of these. If you are interested, just ask in the comments and I will try to provide information.

Today I start posting the Storm series.

In the previous series, Sequence Fractals V, I declared that any mathematical significance was gone. I continued to post formulas and images with "if you do this then that happens" type of commentary. Leaning towards the explore side of the explore/construct scale.

Now I move to the construction side of the scale and embrace the chaos. "Storm" seems like the perfect theme.

$ z^{2^{s_i}}+c$
s₀=1.0, s_i+1=(0.6+0.8i)*s_i
Center: 0+0i; Zoom = 0.5

I am going to close the Sequence Fractal series (plural) for now. I may add to it later, or start a part VI. I started the series on April 5, Sequence Fractals Introduction #1. It is time to take a break.

I have not followed up on few things in the introduction. I leave these behind with the intention to return someday. Although I have to confess that much of my "do someday" list will migrate to the "never got around to it" list. Here are a few of the things in the introduction that I will try to return to:

The above mentioned Sequence Fractals Introduction #1 directly draws a sequence.

Sequence Fractals Introduction #11 and Sequence Fractals Introduction #12 uses the sequence in the coloring algorithm on a normal fractal calculation.

Sequence Fractals Introduction #17 uses a sequence of functions rather the a sequence of numbers. (Yes in a mathematical sense there is an equivalence between numbers and functions. But the different starting points lead you down different paths.)

I said yesterday Sequence Fractals Part V #38 that I was going to continue with more artistic images derived from the formulas in this series. I will be posting them, but not calling them sequence fractals, or any other kind fractal. I am not sure what to call them, but they have certainly moved away from fractals to generative art or abstract art. I will not (usually) post the underlying formula. It is a distraction and a lot of manually copying number from one program to another for me. If you are every curious whether some was generating with a formula, and want information on it, just send me and email or ask in a comment.

To close, I reimagine Sequence Fractals Part V #18. Some small changes remove the trash in the upper right. Actually not removed, just painted over so it blends in. A nice transition from a raw fractal-like imaging to a more artistic interpretation.

$ z^{2^s_i}+c$
s₀=-0.01+i, s_i+1=(0.71+0.71i)*s_i
Center:473+.005i; Zoom = 1

This one is similar to yesterday's post, Sequence Fractals Part V #37. Same formula, a different starting point for the spiral sequence.

The upper left is a mess. Most of the rest of the image is populated with repeating, slightly morphing shapes. There seems to be a lot of potential. In fact, this is close to something that I would just say "done" and publish it.

This one is the last of the older pictures that were created with a "fractal mindset". That is, more or less raw pictures intended to give some insight into the math. I have several more queued up that I created with the "art mindset". The formulas create a background, that I use as inspiration to build a piece of abstract art. Many of those are derived from today's formula.

$ z^{2^s_i}+c$
s₀=1+2i, s_i+1=(0.71+0.71i)*s_i
Center0.310-0.023i; Zoom = 2

Like yesterday, Sequence Fractals Part V #26, the sequence is following a logarithmic spiral outward. The iteration formula has been modified, the stacked exponents are gone and now the sequence value is directly the exponent of z.

The white dots are an artifact of the coloring algorithm. As usual there is too much going on here. The left and right side are too different. Perhaps with some work, maybe a lot of work. the two sides could represent a contrasting duality. Dots vs rainbows. Of course to highlight that contrast, other aspects should be consistent throughout the frame. It is almost there, if I stare at it long enough.

$ z^{2^s_i}+c$
s₀=1, s_i+1=(0.8+0.6i)*s_i
Center:0; Zoom = 0.4

I tried to just post yesterday's image, Sequence Fractals Part V #35, and let it go. I tried and couldn't. So here is another, more artistic, interpretation of the same formula.

$ z^{2^s_i}+c$
s₀=1, s_i+1=(0.8+0.6i)*s_i
Center:0; Zoom = 0.4

Back to the older pictures. Here the sequence starts out small, then grows, following a logarithmic spiral outward.

$ z^{2^s_i}+c$
s₀=1, s_i+1=(-0.8+0.6i)*s_i
Center:-0.493-0.255; Zoom = 51

Yesterday's, Sequence Fractals Part V #33, comments work just as well for today's picture, so I will not repeat them. Same limited palette. Same lacy patterns. But more drama and a feeling on conflict in today's picture