Fractals Are the Future

Topological synchronization of chaotic systems

Apr 2022, phys.org

https://phys.org/news/2022-04-topological-synchronization-chaotic.html

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)

https://store.mcsweeneys.net/products/how-music-works

 

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

https://dx.doi.org/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

https://medicalxpress.com/news/2021-09-fractal-brain-networks-complex-thought.html

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

http://dx.doi.org/10.1038/s41467-021-25876-x

Can consciousness be explained by quantum physics? Research is closer to finding out

Jul 2021, phys.org

https://sciencex.com/news/2021-07-consciousness-quantum-physics-closer.html

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).

https://doi.org/10.1038/s41566-021-00845-4

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").

Mandibulips and the Swarm Amplified Human

It starts out like this -- our body parts are already a swarm. We take it for granted that our body parts know where they are and what they're doing, and can talk to each other. "Stereotypical body control is taken care of by neural subsystems so that the conscious cognitive system can deal with more complex world dynamics." -link

What we don't take for granted, and what we might even find uncomfortable to imagine because it means radically redefining the human condition, is that our assemblage of body parts will one day extend to the technosphere of nanobots, controlled not by us alone but by an emergent swarm cognition consisting of all the nodes in our extended neural network, and all of this wired directly into our own big bundle of blinking neurons in our head.

But then, in the same way these "nodes" of flying, crawling, swimming bots will join with us, our body parts will disarticulate to become part of the greater network. In the beginning, we will need "humans-in-the-loop," but eventually, we will need bigger and more centralized centers of control to interact with control the decentralized swarms. There will be humans in the loop, only a bit more efficient, so that one human will control multiple body-swarm entities. Your hands will no longer be your own. We will share everything. Today, your privacy is gone, tomorrow, the body itself. 

A theoretical approach for designing a self-organizing human-swarm system

Aug 2021, phys.org

https://techxplore.com/news/2021-08-theoretical-approach-self-organizing-human-swarm.html

Bio-inspired metaphor for design, the swarm-amplified human, which essentially proposes that the swarm should self-organize itself into and act like human body parts."

The paper highlights the potential benefits of using human state classification as a control input fed to a robot swarm, rather than having a human user controlling the swarm at all times.

"Designing robot swarms that are an extension of the human body relates to integrating neural logic into robot swarms on the network level, which has received only limited attention so far," Hasbach said. "We have proposed some ideas on how robot swarms could be thought of as neural systems."

^That's just the press release for this theoretical framework. I'd like to paste a few lines from the paper itself because if I didn't tell you, you might think it came from a good scifi novel. In other words, you can't make this stuff up:

Because no holistic theory has been explicitly formulated that can inform how humans and robot swarms should interact.

Joint human–swarm loops, that is, a cybernetic system made of human, swarm and interface. 

An intelligent system that balances between centralized and decentralized control.

The robot swarm should be integrated into the human’s low-level nervous system function.

The swarm amplified human treats the swarm as an extension of the human nervous system, integrated at low-level sensory–motor behaviour

Interfacing at the low-level nervous system means essentially two things (Figure 9). First, as said before, low-level stereotypic sensory–motor control often feels automatic to the conscious mind. When walking down the street, you rarely think about walking. Therefore, the (cognitive) state of humans should be translated by the interface into commands for the swarm clusters. This is referred to as passive or implicit interaction, that is, unconscious control, which can be contrasted to active/explicit control (e.g. deliberate gesture control).

This feeling of being in control over the swarm clusters (alias artificial body parts) 

The SAH [swarm amplified human], therefore, relates to the notion of a cyborg that ‘[…] deliberately incorporates exogenous components extending the self-regulatory control function of the organism in order to adapt it to new environments’

-Clynes, M. E., Kline, N. S. (1960). Cyborgs and space. Astronautics, 5, 26–27.

Rather than claiming that neural networks and biological swarms share the actual same computational basis, we argue that both can be modelled as self-organizing systems. Thus, both humans and swarms are abstracted into one common computational reference frame to integrate the swarm at the low-level of neural sensory–motor loops. 

swarm amplified human - figure 11

Humans also need training to learn sensory–motor patterns for their real body parts. No human baby is able to walk after birth... Similarly, the operator should be exposed to different situations so that he is able to develop an intuition of swarm dynamics as well as how his own states influence these dynamics. 

A more biologically plausible and more efficient algorithm may be a searching robot chain that originates from the human, similar to growing biological axons that are guided by molecular cues.

Human agent moving through a swarm gradient. 

By convergence, global information about the environment can be estimated by the swarm connectome and provided to the human, similar to sensory upstreams in the biological nervous system.

To include the swarm in the human’s nervous system, the brain must be tricked into integrating the swarm into its body representation. This is achieved if the human operator has the illusion that the swarm feels like part of himself, if it feels like an artificial body part. 

In the future, Tom may be equipped with an advanced brain–computer interface technology that provides high-resolution classifications of cognitive states and adapted sensory–motor signals. This could allow him, for example, to feel the location (i.e. the direction and the distance) of a victim, alike to having a sixth sense, while allocating more robots to the estimated location of the victim, similar to closing your hands around an object.

Rather than being the target of the interaction, the swarm should self-organize as the interface between the human operator and relevant features of the environment. This mimics the formation of neural pathways in the nervous system that are tuned to relevant environmental stimuli.

Notes:

via Fraunhofer Institute for Communication, Information Processing and Ergonomics (FKIE) and University of Bonn in Germany: The design of self-organizing human-swarm intelligence. Jonas D Hasbach, Maren Bennewitz. Adaptive Behavior (2021). DOI: 10.1177/10597123211017550

http://dx.doi.org/10.1177/10597123211017550

New Word:

Excursively - given to making excursions in speech, thought, etc.; wandering; digressive. Example: Robustness and scalability is created by treating the swarm as a distributed neural machinery that excursively relies on local interactions. 

Post Script:

"So quite ya yappin' fore I get to clappin'

And have your body parts mix and matching fella"

-What Happened to That Boy, Birdman feat. Clipse (Neptunes), 2002

Post Post Script:

Happened to see this from an older post, but it doesn't hurt to plaster this one all over town until it gets old (it never gets old)

Rats free each other from cages

Dec 2011, Nature

Neutral Networks

The image you see here is a partial map of the internet, circa 2005. It's a colorful organic explosion of lifewebs. It's the closest thing to seeing the noosphere that we have ever come. It's beautiful, and I think we need to see it once in a while, but it's totally unrelated to this post.

Study finds no media bias when it comes to story selection
Apr 2020, phys.org

Hassell's work on the study began in 2017 and embraced a number of research-gathering methods, including a survey of 6,000 journalists, election returns, Twitter data and a novel correspondence experiment design.

"There is an institutional set of norms that dictate newsworthiness," he said. "Lots of things drive those norms, but reporters' personal, ideological preferences about what they view as valuable is not one of them."

Notes:
Hans J. G. Hassell et al. There is no liberal media bias in which news stories political journalists choose to cover, Science Advances (2020). DOI: 10.1126/sciadv.aay9344

Sync or Swarm

On Entrainment

Svjetlana Tepavcevic

Means of Reproduction no. 627

Svjetlana Tepavcevic

Means of Reproduction no. 701

Steven Strogatz on Sync, TED2004

Mathematician Steven Strogatz shows how flocks of creatures (like birds, fireflies and fish) manage to synchronize and act as a unit -- when no one's giving orders. The powerful tendency extends into the realm of objects, too.

http://www.ted.com/talks/steven_strogatz_on_sync.html

“What do you need to produce spontaneous synchronization? Do you need to be alive? No. [There is a] Deep tendency towards order in nature that opposes what we've been taught about entropy. [The tendency towards spontaneous order is a counter force.]”

How swarms work, 3 (+1) rules:
1. all the individuals are only aware of their nearest neighbors
2. all the individuals have a tendency to line up
3. they're all attracted to each other, but they try and keep a small distance apart
(4.) when a predator is coming, get away

video still:

at ~14 minutes, he entrains de-synchronized metronomes via a common substrate

Entrainment (physics)

Entrainment has been used to refer to the process of mode locking of coupled driven oscillators, which is the process whereby two interacting oscillating systems, which have different periods when they function independently, assume a common period. The two oscillators may fall into synchrony, but other phase relationships are also possible. The system with the greater frequency slows down, and the other speeds up.

Entrainment (biomusicology)

Entrainment in the biomusicological sense refers to the synchronization of organisms to an external rhythm, usually produced by other organisms with whom they interact socially. Examples include firefly flashing, mosquito wing clapping as well as human music and dance such as foot tapping.

Brainwave entrainment

Brainwave entrainment or "brainwave synchronization," is any practice that aims to cause brainwave frequencies to fall into step with a periodic stimulus having a frequency corresponding to the intended brain-state (for example, to induce sleep), usually attempted with the use of specialized software.

see also:

Sync or Swarm: Improvising Music in a Complex Age, David Borgo, 2006

syncbots - MIT firerly robot swarm

Vijay Kumar: Robots that fly ... and cooperate, TED2012

In his lab at Penn, Vijay Kumar and his team build flying quadrotors, small, agile robots that swarm, sense each other, and form ad hoc teams -- for construction, surveying disasters and far more.

How Music Works

David Byrne, in describing a process of whittling-down potential dancers in his group, recounts the following experience

Noemie began with an exercise I’ve never forgotten. It consisted of four simple rules:

1. 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.)
2. When you find a phrase you like, loop (repeat) it.
3. When you see someone else with a stronger phrase, copy it.
4. 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. Unbelieavable! It only took four minutes for this evolutionary process to kick in, and for the “strongest” (unfortunate word, maybe) to dominate. It was one of the most amazing dance performances I’ve ever seen. Too bad it was over so quickly, and that one did have to know the rules that had been laid out to appreciate how such a simple algorithm could generate unity out of chaos.

After this rigorous athletic experiment, the dancers rested while we compared notes. I noticed a weird and quite loud wind like sound, rushing and pulsing. I didn’t know what it was; it seemed to be coming from everywhere and nowhere. It was like no sound I’d ever heard before. I realized it was the sound of fifty people catching their breath, breathing in and out, in an enclosed room. It then gradually faded away. For me that was part of the piece, too.

How Music Works, David Byrne, 2012, pp. 67-68

https://store.mcsweeneys.net/products/how-music-works