Topological synchronization of chaotic systems
Apr 2022, phys.org
Topological Synchronization, the Zipper Effect, and Chaos Coupling:
As chaotic systems are being coupled, the fractal structures of the different systems will start to assimilate with each other, taking the same form, causing the systems to synchronize.
And to say another way, fractals emerge from chaos, and at the same time, they provide structure to the chaos, which allows it to snap into a higher order of complexity with other chaoses (I do hear someone saying this is a legit scrabble word).
Chaos is random and unpredictable. Scientists hate it. You have no way of knowing what the system is going to do. Like the three-body problem of three stars orbiting each other, one will eventually get kicked out, but you have no way of knowing how it will happen, you can only measure the probability.
They do follow the "strange attractor" pattern though, where if given enough time, a pattern will emerge, not exact, but a shape recognizable enough that you can make a better prediction. Pendulums do this, and the famous water wheel analogy does too, except that each time you do it, the pattern will be different, unique to the pre-existing conditions of that moment alone -- the pendulum will make a new attractor pattern every time you run it.
But within that pattern are fractals, and it's the fractals of all the attractor patterns of all the chaotic systems out there that act as the bridge to synch them up.
They showed that as chaotic systems are being coupled, the fractal structures start to assimilate each other causing the systems to synchronize. If the systems are strongly coupled, the fractal structures of the two systems will eventually become identical, causing a complete synchronization between the systems.
They termed this phenomenon Topological Synchronization.
Above image credit: Cell Division - Pixabay - 2022
Cut to the David Byrne experiment, where he's trying to find backup dancers:
Noemie began with an exercise I’ve never forgotten. It consisted of four simple rules:
- Improvise moving to the music and come up with an eight-count phrase. (In dance, a phrase is a short series of moves that can be repeated.)
- When you find a phrase you like, loop (repeat) it.
- When you see someone else with a stronger phrase, copy it.
- When everyone is doing the same phrase the exercise is over.
It was like watching evolution on fast-forward, or an emergent lifeform coming into being. At first the room was chaos, writhing bodies everywhere. Then one could see that folks had chosen their phrases, and almost immediately one could see a pocket of dancers who had all adopted the same phrase. The copying had begun already, albeit just in one area. This pocket of copying began to expand, to go viral, while yet another one now emerged on the other side of the room. One clump grew faster than the other, and within four minutes the whole room was filled with dancers moving in perfect unison.-How Music Works, David Byrne, 2012 (p67-68)
And back again:
"When the two chaotic systems are weakly coupled, the process usually starts with only particular fractal structures becoming identical. These are sets of sparse fractals that rarely will emerge from the activity of the chaotic system.Synchronization starts when these rare fractals take a similar form in both systems. To get complete synchronization there must be a strong coupling between the systems. Only then will dominant fractals, that emerge most of the time from the system's activity, also become the same.
They called this process the Zipper Effect.
But does David Byre approve?
via Bar-Ilan University, Israel: Nir Lahav et al, Topological synchronization of chaotic systems, Scientific Reports (2022). DOI: 10.1038/s41598-022-06262-z
Post Script:
Think about how the complexity of neuron-firing in the brain is a chaotic system, and how fractals are at play here.
Fractal brain networks support complex thought
Oct 2021, phys.org
via Dartmouth College: High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns, Nature Communications (2021). DOI: 10.1038/s41467-021-25876-x
Can consciousness be explained by quantum physics? Research is closer to finding out
Jul 2021, phys.org
via Cristiane de Morais Smith and Xian-Min Jin at Shanghai Jiaotong University: Xu, XY., Wang, XW., Chen, DY. et al. Quantum transport in fractal networks. Nat. Photon. (2021).
And you know Isaac Asimov already got us there:
Isaac Asimov's Robot Dreams -- a robot named Elvex (LVX-1) is updated with "fractal geometry" because the offending young scientist though it would "produce a brain pattern with more complexity, possibly closer to that of a human". The robot begins to dream about self-preservation, in direct opposition to the Laws of Robots, and is subsequently killed ("killed").
No comments:
Post a Comment