Sneaking in some curves. Most of this is still based on affine transformations, and it has the same mood as the others. So I am going to go ahead and place this in the Affine series.

We are now two weeks into this series, so time for a quick recap. The basic idea is to use affine transformations to tilt, stretch, and shrink lines. Always straight, no curves. Then adjust colors to highlight the "top" side of the line, while leaving the other side transparent. See Affine #1 and Affine #2 for more details.

"Top" is in quotes. For example a 180 degree rotation is a affine transformation which turns top into bottom. So "top" depends on the particular transformaion details.

In the initial pictures, the transformations included rotations of many angles, generally close to 0, 45, 90 degrees. The most recent pictures had only small rotations, keeping things close to the horizontal.

This one has a bigger range of angles like the earlier ones. I have added some jitter like the recent ones to break up the straight lines.

Affine jitters, in color.

Got the jitters.

Now each affine transformation is given "the jitters". Lines are chopped up and the segments are displaced slightly. As before, the color is altered for pixels on one side of the line segment.

Turning up the colors.

It is getting crowded. Many close to horizontal lines overlapping with vertical extensions.

Dialing up the number of lines…

I am struggling with this one. It is both too messy, and not messy enough. It looks better from a distance. I have the bright blue diagonal separating regions of orange/yellow and lighter colors. But up close the lines are too straight and the clean areas are too clean.

Normally I would just set this aside and maybe return to it later. But today I decided to post it anyway as a work in process.

The shading alternates above, then below, the lines.

See the notes for yesterday's picture Affine #6. I lack that restraint and had to keep adding lines.

There is a lot of potential here. Using just a few relatively short line segments, then varying the orientation and colors. I have several more that I consider experimental. They are not published now, but they convinces me that this is an idea worth exploring further in a future series. I am officially adding that to my "maybe someday" list.

This one colors on one side of a few short line segments. I like the very minimal look. But it takes remarkable restraint to not keep adding more lines.

The introduction to the multi-part sequence fractals series earlier this year had two similar images. Sequence Fractals Introduction #17, and Sequence Fractals Introduction #18.

The other pictures in the sequence fractal series had a non-linear component. Somewhere in the generating formula there was "z^a" with a != 1, usually a=2. Just for fun, I tried building some pictures without exponents in the formula. The results were interesting and I included those two in the introduction. But I never got back to the purely linear variety in the rest of that series.

So anyway, I am exploring similar ideas now in a slightly different context.

The images are generated by creating some number of affine transformations, usually between 20 and 100. Each will take the real axis to another line in the plane. The colors of the pixels near and above the lines are altered.

In mathematics an affine transformation looks like y = ax + b. You may recognize this from high school algebra as the formula for a line. Lines and affine transformations are closely related. Hint: affine transformations move lines to lines. See the Wikipedia article for details.