In my last post I talked about the unexpected twist of two strings of dots twisting around each other to form an orbital. I also showed the image where this twist is visible.
However, I think this is too zoomed out to really get the full idea of why what I realized is so different to what I had before. The difference between the old and the new is actually the concept of the origami that I had already mentioned in June:
However, in the month-long process of trying to figure out the math of the above structure, I had the idea that perhaps the structure didn’t exactly look like the original origami, but rather a rather complex-looking ‘ripped’ structure:
The annoying thing is that I was almost correct. But being almost correct was what sidelined me for quite a while. But as I was polishing and polishing the manuscript, I realized that the two images above can relatively easily be combined like this:
If you look at the above image and compare it to the green origami image before, there is no geometrical difference between the two. The major difference is that the green origami was formed using vectors, cross products and dot products and the above image with transparent blue and yellow spheres was formed using helices. So, the vector image was correct to begin with, but I couldn’t get the vectors to twist, so I had to introduce helices. However, once I got the helical image correct, now I should be able to convert it back to vectors. This might take so much time that I’d be tempted to submit the manuscript without vectors and perhaps work on the vectors as the manuscript is being peer-reviewed, so I’ll have some answers to the peer-reviewers’ questions.
As I mentioned in my last post, I still need to do the corrections to the manuscript. Who knows how long it will take. It might be really fast, or then I’ll get bogged down with something else. I have a feeling that it wont take too long anymore.
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