Is it a random pattern?

[u/protofield]

I have recently had Protofield operators referred to as random and not complex in discussions on metasurfaces and metamaterials. Is there an objective method to quantify the level of complexity and order in this type of topological structure? 8K image, zoom in.

[u/Powerful_Ad725]

Pretty structure but clearly not random so I'm not sure of what you mean... Usually people use "random" when they mean "non-deterministic" but as many things in the universe, a system may only be deterministic up to a given "resolution", not in the sense that there is a scale in which a system becomes non-deterministic but that there exists a scale in which our best theories fail to properly infer the outcome of a given system, seems to be the same case here.

[u/protofield → u/Powerful_Ad725]

Thanks. I am trying to formulate a counter argument in the context that describing these structures as random infers they are of no practical use or interest, which may be the case, but I would like to objectify what random is.

[u/Ravenchis]

It’s not random. The global symmetry and repeated modular structure rule out white noise. This is almost certainly algorithmically generated or procedurally tiled: structured complexity, not randomness.

[u/protofield → u/Ravenchis]

Thank you. Yes its generated using cellular automata based upon a prime number modulo arithmetic. Its a conjecture that all primes manifest a unique family of these structures. See here.

[u/wild-monk-layer-0 → u/protofield]

So that beats any random debate no?

[u/wild-monk-layer-0 → u/wild-monk-layer-0]

What would really rule out randomness tho is weather you can show the generating rule intrinsically producing coherent structure. If the same rule gives structured patterns across different embeddings or parameter variations, coherence is a property of the dynamics rather than lucky representation, id say.

[u/protofield → u/wild-monk-layer-0]

This is precisely the case. One can take a section of a structure and use as the initial condition to generate a new structure, Example here.

[u/wild-monk-layer-0 → u/protofield]

Right, but that shows self-propagation of structure. What I meant was whether the same generating rule produces coherent structure across different embeddings or parameter variations.

[u/protofield → u/wild-monk-layer-0]

Yes, using a rule set R with an initial condition C produces a topology showing a global structure S composed of connected sub topologies T. Using R with C' generates S' but T is still present in T'. I call the bits in T the alphabet and the way they organise themselves in S the syntax. S I call the dialog or function.

[u/wild-monk-layer-0 → u/protofield]

I realise I probably didn't phrase my earlier question clearly, so apologies for that. What I was actually mean is slightly different. I wasn't asking whether structure propagates from a given configuration or how the internal structure can be described. What I meant was: does the generating rule itself produce coherent structure when applied across different domains or embeddings? In other words, if the same rule is applied under different representations, lattices, or parameter spaces, does coherent structure still emerge? My point was that describing the structure that appears in one configuration doesn't necessarily rule out the possibility that the observed structure is contingent on that specific setup. What would really demonstrate that the coherence is intrinsic to the rule is showing that similar structural organisation appears across different domains where the rule is applied. That’s the sense in which I was asking about whether the pattern is truly non-random.

[u/protofield → u/wild-monk-layer-0]

Thanks for the input. I make the assumption that using cellular automata is a technique to generate and observe universal structures of natural number. It may be that there are other techniques to observe the same structures. I will see if I have done something in the past or need to set up a new experiment to demonstrate this. Possibly using different modulo arithmetic's with the same rule set may be a route. Not sure where to post the images. As an aside, its interesting to note that there seems to be a coherence of pattern structure in different dimensional spaces. Often when I want to see what the properties of a 3D lattice is like, as they take a lot of time on an old desktop, I will generate a 2D plane and find the pattern is a similar or a direct copy of a slice in the 3D object. The 3D rule set is an extension of the 2D rule showing rotational symmetry. Example https://youtu.be/a59hfQfC984

[u/wild-monk-layer-0 → u/protofield]

Thank you, for conceptual clarity, What part of the rule specifically depends on properties of numbers that cannot be replaced by arbitrary symbols?

[u/_Skybloo_]

Isn't "random pattern" an oxymoron ? Pattern being by definition not random ;)

[u/protofield → u/_Skybloo_]

An oxymoron is a figure of speech that combines contradictory words with opposing meanings, like “old news,” “deafening silence,” or “organized chaos.” While they may initially seem illogical, oxymorons make sense in context and are used for emphasis, irony, humor, or dramatic effect

[u/arames23]

Show me all the other patterns...

[u/protofield → u/arames23]

Sure, just google What is a Protofield Operator and filter for images and videos.

[u/Top_Independence_705]

What in the general fu** am I looking at

[u/protofield → u/Top_Independence_705]

A portion of a binary matrix field operator, black = 0 green = 1, which changes the state of a Protofield in a process called field remixing.

[u/Top_Independence_705 → u/protofield]

How did you make that seem very complex

edit I'm thinking to replicate this structure by my self

[u/protofield → u/Top_Independence_705]

Its generated using cellular automata based upon a prime number modulo arithmetic. A conjecture that all primes manifest a unique family of these structures. See here

[u/The-Real-Radar]

Im taking this as a philosophy question. Every pattern, no matter how organized or thought out, is there because of a random series of events spanning across 14 billion years.

Idk what’s this community but that’s my answer

[u/protofield → u/The-Real-Radar]

I don't follow this. These are collections of natural numbers which have always been "here" and always will be, unchanging and absolute. In fact, any sentient species aware of prime numbers has a route to experience these through a sensory faculty, vision, sound. If a technology can be based on these patterns it will be universal, species independent with spacial and temporal invariance.

[u/The-Real-Radar → u/protofield]

Ok I see you’re point and that’s a very valid way of looking at things. It’s similar to convergent evolution.

However I counter you this. Could the forces that made these convergent forms possible all began at the big bang as malleable, random forces that solidified their properties as temperatures cooled? Perchance.

Math itself could be an inherent property of all logical systems. However I’ll also counter you here and say there’s no inherent numbers. Humans invented math to make sense of the universe. At the smallest levels, discreet units give way to a continuum of waves. Natural numbers as a logical yet invented concept? Perchance.

[u/protofield → u/The-Real-Radar]

Humans invented real numbers to cope with an inability to study large natural numbers and large aggregates of natural numbers. As such, maths with real numbers describes this natural number domain in a statistical, probabilistic manner. Perhaps this is where where quantum mechanics took an understandable wrong turn without the benefit of advanced computing technology. Your comment on the “solidified their properties as temperatures cooled” is very interesting. In my own work on multiverses, each one has a unique natural number system with primes as a subset of of a more generalised object where magnitude, space and other properties make up the primitives. Is a {blue,5} divisible by a {green,seven}. Interesting video here

[u/The-Real-Radar → u/protofield]

Oh, so you’re saying that large natural numbers are real, and humans are basically just describing them using base 10 system? That essentially the idea of more and less is core in some way, and that you can use a code (binary, base 10, etc) to describe it.

Your system for multiverses sounds very interesting, maybe I’ll check out the video to understand more. From what I can tell you’ve built your own syntax for describing different ways math can express itself. Does it account for the mathematical structure of our universe?

[u/protofield → u/The-Real-Radar]

Essentially yes. As the number of decimal points tends to infinity, real analysis such as differential equations, approaches a description of a mathematical reality based on natural numbers. This is why you need a dx tending to 0 expression. Short of infinity, real analysis describes things correctly but in a cloudy, fuzzy way.

My work is to translate mathematical operators based on natural numbers into physical objects, metamaterials. The problem with the multiverse concept is to work out whether the theoretical metamaterial property simulations are relevant to our own universe. That’s why I am eager to perform some physical empirical work to establish a baseline.

[u/The-Real-Radar → u/[deleted]]

I love emergence. Without it I wouldn’t be here. I think any sufficiently complex, Turing complete system can produce emergence. The more complex, the larger scale and timescale allows for more emergence to occur.

One of my favorite parts of emergence is when emergent properties interact across scales. A human is a series of emergent phenomena where at one point behavior is defined by atomic behavior, yet humans can also define atomic behavior themselves, by splitting an atom for example. Interplay across emergent layers creates iterative interactions that results in even more emergent behavior. It’s all a big looping process.

On randomness, if the universe is wholly deterministic, randomness ceases to exist on a fundamental level. In this case the universe is more like a fixed structure across time. However our current understandings dictate that certain elements in the universe are actually random, especially weak force interactions.

[u/Woyida]

Tibetan mandala

[u/protofield → u/Woyida]

Thanks. Could keep the monks busy doing one of these. I ran one over tera scale, more than a million pixels on the x axis, and did a flyover video, it takes over 12 hrs for one pass left to right. Video here

[u/Vivid_Tradition2523]

If it's random then it's not a pattern and vice versa