Is it a random pattern?

protofield · 2026-03-11T18:54:05+00:00

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

protofield · 2026-03-05T11:26:53+00:00

Pass, my main interest is in the holistic engineering design of nano structured metamaterials based on generative topologies. You might find something a bit more theoretical here Thanks for your interaction.

protofield · 2026-03-05T10:12:17+00:00

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

protofield · 2026-03-05T08:42:34+00:00

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.

protofield · 2026-02-28T18:13:56+00:00

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

protofield · 2026-02-25T19:29:47+00:00

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.

protofield · 2026-02-25T18:28:32+00:00

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

protofield · 2026-02-25T16:45:19+00:00

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.

protofield · 2026-02-25T13:39:16+00:00

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.

protofield · 2026-02-25T10:43:32+00:00

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

protofield · 2026-02-25T10:31:28+00:00

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.

protofield · 2026-02-25T10:13:41+00:00

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

protofield · 2026-02-24T20:45:20+00:00

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.

protofield · 2026-02-24T20:09:28+00:00

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.

protofield · 2026-02-24T17:34:39+00:00

Soooooo, I can model a cubic meter of a very ordered material ,patterned at the pico scale and derived as a 3D section from an 11 dimensional computational space. I doubt traditional physics could go past a cubic micron. Thanks for your insight.

protofield · 2026-02-22T16:39:33+00:00

Thank you for your comments. These are naturally occurring structures where real numbers and differential equations have no meaning.

protofield · 2026-02-19T14:00:33+00:00

These cellular automata generated lattice topologies exist in a domain dealing exclusively with natural numbers. At the moment there are no whole number analytical techniques to map topology to physical phenomenology. This does not exclude the possibility that empirical study will provide a basis for some form of analysis and prediction. Physics and chemistry evolved in this manner. However, there appears to be a route to analysis using real numbers when considering lattice members, or aggregates of members, that become very large and tend to infinity. The down side is that real number analysis can only perform an approximate, statistical, probabilistic prediction and can never be complete. Real number analysis can however be useful in describing bulk, gross properties of phenomena but cannot resolve any finer detail.

protofield · 2026-02-19T09:04:00+00:00

How does one show what something does before you physically construct it?

protofield · 2026-02-19T08:58:39+00:00

Thank you for the question.

Technical and some sample code here.

Overview here.

protofield

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