What I call the wreath attractor isn’t a chaotic or strange attractor in the mathematical sense. But I started using the name and it kind of stuck.

I guess the most we can say is that it’s a transform:

In my implementation p0 to p4 are normal real parameters with typical ranges from –1 to +1 for p1 to p3. p0 and p4 are about 10 times larger. p5 is a special case and can take only discrete values: 0.5, 1, 1.5, 2, 2.5,…

This system of equations lends itself well to experimentation. For example, limiting the source, the possible starting positions of the tracing particles, has a profound impact on the final look. A striking example is used in the animation. 10 concentric circles serve as the source and the resulting image is what you get when the circles are iteratively transformed a hundred times.

During the animation, the parameters p1 to p3 are slightly tweaked from frame to frame. The convoluted geometry is quite sensitive so the changes are smaller than 0.001.  Each frame consists of 5 million particle iterations, taking a few seconds to render. The retro flickering effect is a result of the statistical nature of the process,  giving a slightly different exposure each frame.