Entangled Rotating Branes
In my last post “The Donut-Brane Particle” I presented a teaser version of a particle a particle comprising of branes. In the post I showed a rather complicated helical torus model of several particles both vibrating, but primarily rotating around two axes, forming a closed loop of moving particles.
But I said in the post that it wasn’t the true model. In the true model I would need to present the interactions that would cause this rotational motion. As I was writing the post I already knew what to do, but I also knew it wouldn’t be super easy. Most of all because I would need to build a huge geometry node model in Blender to accomplish this.
For the past four days I’ve been building the model, piece by piece. Before consulting ChatGPT for geometry nodes I had already generated the basic model using curves and modifiers, so I didn’t need to rely on ChatGPT to get things right. The only thing it needed to do was to replicate the model I had already created, but only with geometry nodes. The reason for using these is that the old way was like painting a single artwork, whereas using geometry nodes was like taking the artwork, downloading it and making digital copies of it. And most importantly, animating it. While animation is theoretically possible without geometry nodes, it’s practically impossible with a model as complicated as mine.
Creating accurate geometry nodes is hard. Whenever I consulted ChatGPT, I had to be 100 % sure that I requested exactly the right thing, as any errors would be replicated as well. But even after asking the right thing, the most common outcome would be something that didn’t work on the first try. However, just being patient and asking a lot of very specific questions, I was able to build the model.
So here it is: a model of entangled rotating branes:
What you see is two toroidal branes ‘trying’ to occupy the same space but being offset from the center by the minor radius of the toroidal brane. The combination of linear motion and vibration result in two rotations: one around the major radius of the torus and the other around the minor radius. And at each intersection of the two toruses there are two circular arrays of spheres rotating in opposite directions.
The above entangled helix of helices looks very convoluted, as I’ve made the two toroidal branes entangle around each other three times. If I change the number of entangled rotations in the model from 3 to 1, I get two donuts in the same general motion:
Here the only question is, why would the donuts be so compressed against each other, whereas with more entangled rotations the two entangled branes are truly locked in place.
You might ask: why are the spheres two branes moving in the opposite directions: why not move in the same direction? Well, I tried this, but the branes are like cogs in a mechanism. If they move in the same direction, they also rotate in the same direction. And anyone who knows anything about gear mechanisms knows that neighboring gears must always rotate in the opposite direction: otherwise, they screech to a halt.
Next, I need to formalize this shape. I already have an intuition that the ratio of the minor and major radius is crucially important, as are the number of rotations in the entangled helical branes. At the moment the shape is structured that if I change one variable, the general shape is retained, but the size of the spheres and the distance between them become incorrect. Also, the node tree looks like this:
I no longer find individual nodes easily (even on my relatively large 4K screen), so it takes forever to change the shape.
I already know that there are some nice surprises waiting once I get everything sorted out. Some of these are surprises only to you, dear reader, but they are known to me. But I’m sure I will learn surprising things as well, even though I don’t know what. Hence the surprises.
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