After writing the previous post, I realized what I had described was a double helix. You know, the double helix of the DNA fame (see below). But unlike with DNA, in the electron, there is nothingin between the strands, causing the strands to be absolutely compact.
I've managed to plot the arrangement of the dots/pearls in the double helical orbital in excel, but yet with rather 'ugly' maths. However, one can already see that if the number of periods (number of waves from peak to peak) is odd (1, 3, 5 etc.), one can cut the wave in half (with a bit of mathematical magic). In the below image a green wave runs 7.5 periods in a 360 degree turn and the yellow wave continues for the next 360 degrees, until it ends at the beginning of the green wave.
I'll have to make the mathematics a bit prettier to publish, but this is the main idea. There is a possibility that the amplitude of the wave is so big that in the end the electron no longer looks like a donut, but rather a ball. This would explain why the electron has always been considered not to have any particular shape. To figure out whether this is the case, I need a bit more time.
I could just say that the double helical nature of the electron is a cool coincidence, but I don't think so. I think this shows that the double helix is a fundamental structure relating to many more structure and phenomena found in nature.
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