## Steeds & Riders

In my last post I outlined a paradigm that we can use to build ‘pseudo-particles’ with properties a lot more naturalistic than those we generally find in Cellular Automata. However, as I mentioned, this paradigm comes with a price: an apparent sparsity of the kinds of interesting, emergent patterns that systems like CAs give you.

This sparsity is only to be expected. Irregular graphs of the kind I use are inherently noisier than the tidy lattices employed by CAs. That noisiness gives us enough robustness to model curved space and approximate quantum uncertainty, but means that we can’t rely on exact patterns of cell activation to represent physical phenomena. However, this isn’t to say that we can’t build interesting and exciting patterns in this paradigm–far from it. And in this post, I’m going to explain how it can be done.

The first step is to point you at the slides I used in my talk at the JOUAL conference in Italy last year. You can find them here:

http://www.alexlamb.com/science.html

This talk covered some research I did on extending Jellyfish–most notably to create pseudo-particles on three dimensional graphs that polarize and retain their orientation as they move. Just as they can fly in any direction, they can polarize in any direction too, without requiring any change to the algorithm.

The core concept that I share in the slides to achieve this couldn’t be easier: you put one Jellyfish inside another. I call this a ‘steed-rider relationship’. You advance an ordinary pseudo-particle with simple iterative steps to move it forward, (that’s the steed), but you also adjust the position of pseudo-particle the same size that’s trapped inside it, (the rider). Half of the rider’s front nodes are located in the front node set of the steed, the other half are in the back. That’s it. Voila: polarization. The particle self-organizes to give you a nice naturalistic property that’s unexpectedly robust.

What’s also interesting about this kind of particle relationship is that the steed’s update algorithm isn’t affected by the rider it carries. This means that the rider manifests as an *intrinsic property* of the steed, rather than as a physical sub-particle. You can break the steed up so that it’s in multiple locations at once and the property will be retained. This gets useful if you extend the model a little further.

By creating a rider that’s much smaller than its steed, and changing its update rule a little, you can pretty easily create a rider that moves around inside its steed as it travels. And because in three dimensions the steed always tends toward having a circular profile, the rider ends up traveling around the edge of the steed along a helical path. Voila: intrinsic angular momentum, AKA spin.

Sadly, this kind of spin isn’t quite like that we see in physical particles, because for Jellyfish instances it can only be aligned with the steed particle’s direction of motion. Nevertheless, by increasing the number of riders that the steed carries, you can build particles for which angular momentum comes in tidy discrete quantities. Use one rider and the momentum is always clockwise or anti-clockwise (-1 or 1). Use two riders and the momentum can be in one of three states, both anti-clockwise, both clockwise, or in opposite directions (-2, 0, 2). Use three and you get the following pattern: (-3, -1, 1, 3). This is the same pattern that we see for spin number in subatomic particles.

I should re-iterate a point here that I made last week. Nice though these apparent similarities between these discrete systems and physics are, they’re not illustrative of anything except *potential*. This work is still a long way from being physical science. Furthermore, the simulations are costly and still somewhat unreliable. The best video I have of particle spin is here:

http://www.youtube.com/watch?v=gsCwILrSuBM

As you can see, at this scale, the rider has a tendency to flip direction from time to time, reversing the particle’s spin. Clearly much larger simulations are needed to test what this approach is truly capable of.

Nevertheless, the doors seem to be wide open to further experimentation. For instance, by creating riders that only travel in packs of a certain size, you can build particles with flavors that obey the properties of mathematical groups. That could be useful further down the line if we get as far as trying to emulate the Standard Model. In short, there seems to be plenty of fun work to do here and I’ve barely scratched the surface.

If you’d like to see a preprint of the paper I submitted to the JOUAL proceedings, just let me know. Or, if you’d like to see some open-source code for building this kind of simulation, that can be arranged. If you’re at all intrigued by these kind of simulations, I encourage you to try them out for yourself. There’s a world of fascinating science out there waiting to happen, and a lot of it can be discovered right there in your living-room.