Finding Source of Image: Concentric Rings, Torus, Plusses/Minuses

[T.S.]

I've been trying to find the source of this image, or ones similar to it, for yonks.

The image is incomplete, which doesn't help. The reason I ask this on a physics forum is because it reminds me of those images out of the physics textbooks I used to have.

Looking at the concentric rings and how they are displaced in relation to each other it looks to me like this picture is showing a torus (the rings are more closely bunched together at the outside and the towards the middle of the picture). Plotted on this torus are two lines. The first line snakes it's way around the graph in a close series of crests and valleys. The second line is plotted so it overlaps some of the crests and valleys of the first line.

There are a number of plusses and minuses around the outside of the torus that are hard to see. There are also figures which I assume to be numbers inside small circles around the torus, but they are far too blurry to make out.

In the very centre of the picture is what looks like a incomplete pyramid or a tesseract seen from above. I believe this might have been added over the top of the graph along with the tube that leads up and out of the picture. I'm more interested in the strange graph underneath them!

 

[screwball]

Can you add any background on where you acquired this picture? And why it appears to be incomplete?

 

[sir-pinski]

After doing some research, I believe the image you are describing may be related to the concept of a "Klein bottle," which is a non-orientable surface that is often represented as a torus with a twist. The concentric rings and displaced lines on the image could be representing the twisted nature of the Klein bottle. The plusses and minuses could also be referring to the positive and negative curvature of the surface.

As for the numbers and circles, they could be related to the mathematical equations that describe the Klein bottle or could be part of a visualization of its topology.

Unfortunately, I was not able to find the exact source of this image, but it is likely from a physics or mathematics textbook or a scientific journal. I suggest searching for "Klein bottle visualization" or "Klein bottle topology" to find similar images and potentially the original source.

I hope this helps in your search for the source of the image. It is always interesting to see how complex mathematical concepts are represented visually.