Added sin() function. For the math nerds, not the complex sin function rather the real sin function on the y component. (x,y) -> (x, sin(y))
The non-affine transformation mixed in here is z -> log(z). I also mixed in some jitter.
For the mathematically curious, the non-affine function incorporated in this one is z -> 1/z.
More curves, and not my typical color choice. This is quite far from the starting point for this series. Despite that, algorithmically, it is a small variation on the basic algorithm that kicked off this series.
So, despite the obvious mathematical inconsistency, I am including this one and the next few in the Affine series.
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.