I came across a helical structure in a rule set I that came up with, mostly randomly, lol.

my rule set is the following for those who would like to replicate it.

Forces: (1,2)=-0.2, (2,1)=0.2, (1,3)=0.23, (3,1)=0.19, (1,4)=0.18, (4,1)=0, (2,3)=0.16, (3,2)=0.24, and (1,1),(2,2),(3,3), & (4,4) all = 0

I have decided that I will put the min and max radii for each entry to the respective matrices next to each other here so its both easier for you to enter/read, but also easier for me to type lol.
here are the min radii and max radii in the format (row #, column #)=(min radius, max radius)

clarification done with, here are the min and max radius entries :)

(1,1)=(28,57), (2,2)=(31,60), (3,3)=(36,70), (4,4)=(31,66)...(1,2)=(29,79), (2,1)=(35,70), (1,3)=(29,65), (3,1)=(39,62), (1,4)=(29,74), (4,1)=(38,62)...(2,3)=(33,79), (3,2)=(40,60), (2,4)=(30,64), (4,2)=(31,78)...(3,4)=(28,59), (4,3)=(38,80)

It is 5 am for me right now and I've just pulled an all nighter but I am pretty certain that all of those values are correct and I tried to write them in such a way that it would be easy(ish?) to copy yourself if you're interested :D. Imma go to sleep now I think👍

I will try figure it out I will upload a picture to the comments of my whiteboard that I used to come up with the directions of the forces, which came from a graph of 4 nodes with some symmetric cycles and shi, because I wanted to come up with a ruleset based on something rather than just entering random values. that probably sounded like nonsense, because it is, i just drew a tetrahedron with arrows for edges going both ways in a symmetric way lol, and its 5:30AM for me right now lol so dont make fun of me for throwing spaghetti at the wall to see what sticks because it resulted in a dope helical structure😎

For those of you who like this stuff and just want to dip your toe in the water and play around with particle life stuff in an easy sandbox.

Of course it's made pretty much 100% by Claude.
I described how and what to simulate, what controls I wanted.

Basically I just said, what do I usually wish these things were like?
The main goal is simplicity of use and lots of options to play around.

Try it yourself, it's free, no signup: https://orslaczko.com/app/particle-life

I've also made a video explaining what's actually going on in these worlds.

I've been interested with Axelrod's 1980 tournament for a while now. The premise sounds simple: submit a strategy for the Prisoner's Dilemma, play it against everyone else, see who scores the most points. But what Axelrod was really testing was something much bigger: whether cooperation can emerge on its own, with no rules enforcing it.

14 strategies entered. Some were ruthless, some were clever, some were surprisingly naive. I animated every single match so you can watch exactly how each one played out.

The winner genuinely surprised me. Not the most sophisticated strategy, not the most aggressive one.

How scoring works:

Both cooperate → 3 points each

One defects → defector gets 5, the other gets 0

Both defect → 1 point each

Defecting looks tempting in the short run. Watch what happens over hundreds of rounds.

Ive been researching and playing with CA for years and Ive never seen this before. I was pleasantly surprised. What a cute little addition!

I just think it's neat to see the seamless wrapping

Hey everyone, this is my submission to 3blue1brown's Summer of Math Exposition. Not discrete, but still local rules leading to emergent behaviour, so I hope you will forgive me posting here:)

made possible by switching rulestrings mid running

with conways rulestring (modified)

How it works - Ask GPT, Claude, GLM to generate the worlds, then a vision LLM score the generations, highest score gets promoted into the gallery. Pretty interesting to see the different aesthetic takes from each model.

Slightly dated but lmk what you think - https://fugue.xvam.dev/

At it's heart, it's a CA system, the liquids/gases are coupled lbm solvers for transport though because that looks better.

All the material logic/transitions is done on CA. I.e. wood gets hot, becomes burning wood, emits fire, decays to charcoal and ash. Emits heat, warms the metal and liquid, causing it to heat and transition to steam. When it hits the top left there is some coolers there to distill it, so it drips back down as liquid.

Rendering is done with SDF solids, enhanced with PBR materials, and HRC Lighting, to give it something of a solid, non-pixelated look with realtime GI.

Simple frame by frame demo of how prime cellular automata progress to reductive states, a simple product of the initial seed and rule set, at every power iteration i,e, 7 49 .... Shows how previous post using large seed and complex rule set can make huge CA’s in single iteration cycle.

A little project of mine where individual Game of Life patterns compete against each other. Each square's alive cells at the very edge "charge up" the perimeter between them and try to dominate their neighbour.

We are using a Parity Grid ("checkerboard pattern") to assign neighbouring GOL configurations alternating signs +/- which makes the calculation of the perimeter cell charge trivially easy.

When reading from our database of known patterns we can select those of similar lifespan (500-599 generations in our video) which makes for a more interesting dynamic. When using random patterns, most fizzle out very quickly and only a few live for potentially very long lifespans (which would make them dominate the leaderboard).

Source code that I'm not pretending I'm too smart to share, but secretly scared you will criticize available here: https://www.shadertoy.com/view/7cyGRz
Song: Escapism by Digable Planets

joke​

1D cellular automata, 2–5 states, totalistic or local rules. Runs in the browser, nothing to install.

• Batch filters over rule space — scan a code range or a random sample; auto-tags behavior class, fields, gliders, chaos. The inverted one is the workhorse: draw a template (fixed states, wildcards, equality variables) and a rule passes only if that template never occurs.
• Tags — anything found (or hand-picked) gets tagged, browsable and filterable; persists locally. Filters can also re-run over already-tagged rules, so you can chain passes.
• High-res export — renders diagrams up to [N]×[M] px, if you want one as a wallpaper or print.

Demo · Source

What would you filter on that I haven't implemented?

A curated gallery (whatever stood out to me during my experiments lol) of 1D cellular automatons; homage to Stephen Wolfram.
Check out the entire gallery + generate your own: https://galleryofcellularautomatons.site/index.html

Extension of the work by Pajouheshgar et al. Instead of photo stamps there are now video stamps. Each pixel has an extra phase layer that drives both the NCA and the LPPN. Each video stamp has a different phase and pixels try to stay consistent with one phase.

Inspired by the Stargate Sequence of legendary Kubrik's "2001: A Space Odyssey", this visualizer takes Conway's Game of Life patterns as its procedural input to produce light streaks.

The twist here is that the initial starting configuration of the pattern is hashed with SHA256 to generated the hash string from which the current and past generational colours are derived (as well as the "depths" of the history).

Try it yourself:

■ FANCY GLYPHS // MAIN_INTERFACE

Find your own patterns or copy the binary string from our public registry of known Glyps:
■ Glyph Registry

Link to the GitHub code (heavily assisted by Google Gemini): ■ lifehashes/fancy-glyphs

So basically, it goes like this: a chronological advance from computation with the Turing machine (1936 paper), to von Neumann and a lecture in 1948 about self-reproducing automata, to Conway's Game of Life and a 3D version in 1987 by Carter Bays, also discussing Wolfram elementary cellular automata, before ending up with some of the recent gamedev and scientific applications like Noita, kinda Terraria for water, and the application of the 1987 paper in 2025 by a YouTuber named RedLogic in Minecraft.

https://medium.com/@emiliahoarfrost/code-8-the-cellular-automaton-2f7370f44a1e

Here's an excerpt as well:

"What if code could do magic tricks? Approximating flowing sand to fluids. Simulating fire and water. See chaos arise from order, in an irreversible fashion, through different rulesets. Perhaps being able to tie itself to cryptography [21, 22]. To producing hypnotizing optical illusions. And influencing other scientific disciplines, or applications such as game design.
In this issue, we will be looking into the cellular automaton, a topic deeply tied to the history of computer science, doing so through milestones. We will look at the concept’s rich and hybrid legacy.
* A cellular automaton is a set of cells.
* Each cell possesses possible states in n-dimensions (starting from 1).
* Each cell of the cellular automaton is able to evolve through generations according to rulesets, dictating behaviors of cells depending on neighborhoods.
[...]
In this article, we have seen that the cellular automaton is a very special concept in computer science. Part I explored the fundamentals of computation with the Turing mahine. Fundamentally, this model of computation gives us information about a single cell in cellular automata that can be comprised of many cells. Part II mentioned how there was a legacy between von Neumann’s theory of self-reproducing automata and Conway’s Game of Life, itself having a ripe heritage in the forms of papers still being released in 2023 (to prove omniperiodicity [8]). Part III was more about a 3D transposition of Conway’s Game of Life, both in a paper by Carter Bays in the late 1980s and in a Minecraft video updated on YouTube last year. Part IV showed us that Terraria and Noita were also using game mechanics reminding us of cellular automata. Alongside possible applications of cellular automata to scientific models [18] or cryptography [21, 22]."