I am also including some that did not make the final cut for our Christmas project. These have been reworked, and in some cases evolved to where the posted item bears almost no resemblance to the original. This is one of those.

The image size we needed to wrap the cups was closer to a square. I have resized the originals to fit the 16:9 ratio I use on this blog. The resizing in some combination of cropping, squeezing, stretching, and extending. But for the most part it remains true to the original.

For Christmas, my lovely and crafty wife Karen was printing images on glasses for gifts. She asked if I could create art that did not have a seam when wrapped around a glass. After giving it some thought and a lot of experimentation, we got it figured out. Only a few days past Christmas.

If you print this image, then roll it into a cylinder, the left and right edges match.

Fewer nested circles is each feature. Old 33 1/3 records?

That was fun, two more.

Larger components, with transparent glass appearance.

The next (saved) variant embraces the floating sets of concentric circles.

I liked the previous two, but I was disappointed with the variations I made. So I tried progressively more extreme experiments. The intermediate steps are not worth show, but they led to this. It looks like something nasty seen under a microscope.

This is a recent piece, inspired by the previous Janus #51.

Here is an older piece. As with some others in this collection, I wanted to publish it, but I never got back to it.

It has been 10 days. I am really slowing down. Perhaps things will pick up in the new year. Here are a couple that I had passed on earlier. I admit, they are not my best, but I need something to keep the blog active.

(Continuing from the previous post) That was forty-plus years ago. After awhile, it became been-there/done-that. Everyone was doing it, and they all start to look the same. I stuck with it longer than most. But eventually I too tired of the detailed perfection of fractals and moved on to messier, and less mathematical art.

By the way, this is an alternate coloring of the same fractal shape as the previous post.

Sometime around 1980 I saw a fractal image for the first time in an article in Scientific American. I am a computer programmer and a mathematician, and I would dabble with computer generated art in my spare time. But I never seen anything like the fractals in that article. I was hooked.