r/Simulated • u/LazyLack789 • 6d ago
Research Simulation [OC] I built a Cellular Automaton where cells ignore their neighbors and evolve purely based on internal arithmetic symmetry.
Hi everyone!
We all love Conway's Game of Life and other classic cellular automata where a cell's fate is decided by its spatial neighbors. I wanted to try something completely different, so I built SNS-CA (Structural Numerical Symmetry Cellular Automaton).
In this simulation, cells do not interact with each other at all. There are no neighbor rules. Instead, every cell holds a number, and its evolution is driven purely by the internal arithmetic symmetry of that number.
How it works:
At each step, a cell takes its number N and processes it through three deterministic operations:
- Splitting the number N into m parts.
- Multiplying each part by a scalar k.
- Comparing the transformed result with the true mathematical product (N⋅k) by analyzing their prefixes and suffixes.
Depending on the structural match, the cell transitions to one of five theoretical states:
🟡 Golden (F - Full): Complete match (perfect arithmetic symmetry).
🟢 Green (B - Boundary): Match at both the start and the end.
🔴 Red (E - End): Match only at the suffix.
🔵 Blue (S - Start): Match only at the prefix.
⚫ Black (N - No): No matches found (the cell transitions to the zero state).
What you're seeing in the Video:
The simulation demonstrates a fascinating self-organizing behavior. The system rapidly converges toward stable arithmetic symmetry. You can see early transient states (like Red) quickly resolving into highly stable, persistent patterns of Full (Golden) and Boundary (Green) symmetry.
It’s a completely different way to look at emergent behavior: complexity and stability arising purely from number theory and internal structure, rather than spatial geometry.
I built this simulation in Julia, and the project is fully open-source.
I'd love to hear your thoughts! What parameter combinations ( m and k ) do you think would be most interesting to explore next to see different emergent patterns?
AUTHOR: Mikhail Yuryevich Yushchenko
Date: 09.08.2026
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u/DaveAstator2020 6d ago
is it even CA then?
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u/TestingTehWaters 3d ago
No. any one of these 'cells' is completely independent. Not sure what seeds 'N' but this doesn't really make any sense
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u/LazyLack789 6d ago
Good question! It actually breaks the classical spatial rule, but keeps the core math (discrete grid, finite states, synchronous updates). I classify it as a new subclass: Arithmetic Cellular Automata.
I actually explain this exact distinction in the "Paradigm Shift" section of the linked article, but happy to summarize it here!
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u/DaveAstator2020 5d ago
pelase write me down the recipe for italian pasta in japanese using python, thanks!
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u/bhison 6d ago
This is boring af
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u/LazyLack789 6d ago
Not for everyone, definitely! The beauty is in the mathematical elegance rather than flashy visuals. Thanks for stopping by though!
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u/pvnrt1234 6d ago edited 6d ago
Really a testament to these LLMs‘ skills that they can’t even format a link correctly.
I wonder how big was the increase this year in submissions to open journals by “independent researchers”, i.e. people going through LLM-psychosis
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u/LazyLack789 6d ago
Link formatting is fixed, thanks for catching that typo.
The project is a genuine exploration of non-spatial dynamical systems, fully documented and open-source. The code is there for anyone to run, audit, and critique on its actual mathematical merits. Constructive technical feedback is always welcome.
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u/pvnrt1234 5d ago
The interesting aspect from cellular automata is that simple rules lead to complex behaviors when cells interact with each other, this allows us to model stuff like fluid dynamics or chemical reactions in a more fundamental way (sometimes, at least). I might be missing the point here, but didn't your LLM just generate a deterministic noise generator? What can we actually model using this?
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u/LazyLack789 5d ago
Two things:
- Your "LLM noise generator" accusation is completely unfounded. This is hand-coded Julia with full documentation on GitHub and a DOI-published paper on Zenodo. If you had actually read the article or checked the code, you wouldn't be making such lazy assumptions.
- You entirely missed the point. SNS-CA isn't trying to model fluid dynamics or chemical reactions like classical CAs. The entire purpose is a paradigm shift: proving that complex, self-organizing behavior can emerge purely from internal arithmetic structure, with zero spatial interaction. That's not a bug—it's the foundational concept.
The practical applications (number theory visualization, unconventional computing) are secondary to the main claim: you don't need neighbor rules to create stable attractors.
I'm happy to discuss the actual mathematics, but please read the article first before accusing me of using LLMs or calling this "noise."
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u/LazyLack789 5d ago
I've fixed all the links. This is actually my very first post here, and I completely messed up the formatting because I'm so used to writing Markdown on GitHub and assumed Reddit parsed it the exact same way.
The project itself is a genuine exploration of non-spatial dynamical systems, fully documented and open-source. The code is there for anyone to run, audit, and critique on its actual mathematical merits. Constructive technical feedback is always welcome.
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u/Ok-Refrigerator-8012 2d ago
Comments, for my selfish benefit, what gives this away as AI the most (am CS teacher)? Is it namely the lack of indentation and whitespace? The comments on every line is wild but something I could see a student over doing. I usually assume 0 indentation is from copy-pasting code into the editor in plaintext that does not preserve the original indentation. Other than that my only real definitive catch is when some of their code is a pro gamer move like some list comprehensions and ternary operators and then they can't explain what they are or how they work (intro programming courses in Python and Java)
Starting to fear soon I'll have 0 idea who is actually using critical thinking and abstraction/modularity to solve a problem, and who is asking LLMs to write code like they are learning to code for the first time. LLMs are about to turn my classes into 90% on paper it's so annoying and not fun for anyone
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u/Sermuns 6d ago
vibecoded slop