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I will give it some thought -- not immediately sure how to program that. Yes, flat 2-d layers can be stacked parallel to each other (with gaps between them) to fill a 3-d volume. One idea is to horizontally offset the layers from each other so that the cells define a face-centered (close-packed) 3-d array of voxels (shown as spheres). That would be a really bizarre form.

@hex-automata maybe arbie roo will chime in, he does the 3d sandpile sims a lot

@@6AxisSage After further thought, I do know how to get my platform to produce perspective images of 3-d patterns of spheres within a FCC array (in which the cells are the same positions as the vertices in Bucky Fuller’s Vector Equilibrium). I actually made dozens of such videos based on randomly generated rule-sets. The neighborhood consisted of 12 adjacent cells around each central cell. They were a challenge to visualize, had to show them rotating in order to get a good look (since they tend to be opaque). I wish and I still had some of those videos. I lost them off my computer when it crashed. and I deleted my original RUclips channel back in the day when I was pissed at them for their censorious tendencies. Arbie Roo requested that I show my 3-d videos again. I will resurrect and adapt that old code to my new platform. Then I will be able to try your idea of stacking 2-D patterns to form a 3-D pattern.

I wonder what would happen if we mutate this rule-set 🤔

@hexagon-multiverse its a fun one, will make for some content ill 100% be tuning in for 😁

@@6AxisSage Yes, I saw that video last night, and I thought this is an important phenomenon that I want to think more about. So that my reply can make sense. Will reply in the video’s comment section. Meanwhile, one question: does the simulation have 2 CA running simultaneously, so that one triggers the other? Or is criticality achieved by changing a variable within a single CA?

@hexagon-multiverse in this simulation its just simply random based on the branch ratio value, so i guess this is the CA rule: // Simulation logic function updateGrid() { const newStates = new Array(grid.length).fill(0); for (let i = 0; i < grid.length; i++) { if (grid[i].state > ACTIVATION_THRESHOLD) { // Activate neighbors based on the branching ratio for (const neighborIndex of grid[i].neighbors) { if (Math.random() < BRANCHING_RATIO / grid[i].neighbors.length) { newStates[neighborIndex] = 1; } } // Deactivate the current cell newStates[i] = Math.max(0, grid[i].state - DEACTIVATION_RATE); } else { // Spontaneous activation (input drive) if (Math.random() < 0.001) { newStates[i] = 1; } } } Also I found a way better explanation in my codes comments! I'll put those in the videos description while im at it.

I was very preoccupied and didn’t remember to check my email last 2 days, but I’ll definitely reply later today. Thanks for the reminder.

That could be possible. Wherever the 2 patterns overlap, interference might not occur if the rules for the 2 patterns give the same new state for the neighborhood configuration around each overlapping cells. Even if my explanation is wrong, I certainly can't rule out what you suggest -- the rule-set/neighborhood tools for this system are so rich that we have a rule-space (number of possible different rule-sets) that is comparable to the estimated number of atoms in the known universe (10^80).

@@hex-automata I do it on purpose often in my grids utilizing critical point cascades/neuronal avalanches. It allows for multiple concurrent uninterrupted loops to form at once. I will try find an old demo.

I have only recently given some vague thought to how to have 2 distinct but interacting CA simultaneously on one grid. Your very interesting and appealing results are inspiring me to delve deeper into this. I have so far relied almost exclusively on random generation of rule-sets, whose study has brought some insights. Manually designing rule-sets to achieve specific tasks should be the next step. Concurrent stable CA on the same grid sounds like a feasible project.

@@hex-automata Thats great, your work also inspires me. What I've learned is often our most innocuous experiments can have significant meaning even we don't recognise it right away.

I don't know if YT has any specific rules or guidelines regarding strobe light warnings (intended for people suffering for epilepsy). I add warnings as a courtesy, after seeing others (like @NilsBerglund) do so. Every once in a while someone complains that I should have added a warning when I didn't. But the amount of strobing is a matter of degree, a judgement call.

@hexagon-multiverse im still not sure myself when to cut it off too but I did make a guide. If you ever see anything too eye bleedy on mine, please let me know 😅

You never know what will pop out of this CA multiverse. The number of different rule-sets is exceedingly huge, and even though most are wastelands, there should still be billions of interesting things to see.

Sometimes it seems like it's trying to spin, like a propeller.

@@hex-automata But it just judders back and fore, like the piston engine won't start.🛩

I think the smooth steady motion of the cell patterns matches the feel of the music.

The more I observe & learn, the more it seems that Nature uses CA-like processes in many different ways, both in the inorganic & biological realms. My creations here are motivated by both art and science (I'm a chemist by training, but interested in all sciences).

@@hex-automata 100%. Everyone thinks im preaching witchcraft when i bring up that the universe doesnt exhibit euclidean geometry 😅🤣 thank f theres no witch burnings these days.

@@6AxisSage I guess most people aren't familiar with General Relativity and space-time curvature...

Even standard cosmology admits to the possibility that the geometry of the universe is hyperbolic. We know empirically that the universe is approximately flat, but with some uncertainty. So the overall curvature of the universe could be slightly positive or negative, instead of exactly zero. If we observe on very large scales, we might make more precise measurements to finally settle the question.

@@hex-automata Empirical observations can never eliminate all doubt about this unless it turns out that the universe isn't asymptotically flat. If it is flat, the observational error will always admit of some doubt. If it isn't flat, then a small enough error would rule out the possibility of flatness. Some cosmological models depend crucially on the universe not being flat, so it is an important question.

I'm interested in learning more about how your hex grids are set up. I'm willing to share code here for anyone interested in implementing something themselves. I use 2 methods for hex grids: one using columns & rows, and an alternative approach using 3 axis mutually at 60 degrees to each other. I should making a narrated video about this.

@@hex-automata I started going through my old code over this last couple months. I must have made a dozen different systems but I think they boil down to maybe 2 or 3 also. Just need to work my way through and turn into words 😅 (im unfortunately a visual thinker, so I understand it really well, I just struggle to encode it into verbal language, thanks for sticking through my communication issues )

I think you're thinking about thought. Interesting to ponder if the neural correlates (nerve pulse cascades) associated with thought can be modeled by CA. But even if specific brain states correlate with experience, I conjecture that the brain is not the source of consciousness -- it is a filter that reduces the infinite background consciousness to the finite subjectivity of the ego person. From the viewpoint of idealism, when we see a brain, we see only a partial image of the process of infinite consciousness tying itself into a knot in order to become an individual limited being capable of interacting with this energy realm. Any processing of information requires a machine (or symbolic system). I think CA-like processes may be involved in generating thought, with the process occurring below the level of conscious thought.

@@hex-automata Sounds like you've put some thought into it also 😊 Yeah, I made the mistake of taking that to its conclusion and writing about my Unified Theory of the universe, now theres a dozen plagiarists with watered down versions all trying to grandfather themselves in, all with a million times more reach than I have. Because of that I have reservations releasing any more written content or seeking out academics or most other outside the box thinkers anymore or walking anyone through anymore steps. Maybe I'll follow in others footsteps and leave something for everyone else to imagine.

I understand -- you've worked hard on original ideas, and you'd like to have recognition if you share it, not just have others steal the credit. Likewise, I have not (yet) shared the details of my CA neighborhood configurations. Yeah, share some aspects so as to give some idea of what you can do, but keep the core technical details confidential until the right time.

When we use large grids (at least 160 x 160), large-scale structures can appear.

Yes, I wrote the program "Hexagon-Multiverse. It's used to make all of the videos on this channel. Each of trillions of possible seed number inputs gives a different universe. The plan is to release it as an app (currently being translated into the Kotlin language). Sorry, it is not available for download yet -- aiming for early next year.

@@hex-automata cool, I'll definitely check it out when it's finished!

Thanks! Next I want to work on using automata to generate their own listenable audio tracks. I think that will be a real challenge.

@@hex-automata nice, that would be awesome!

The final cell pattern will look different depending on what grid size is used. I try different grid sizes & look for interesting patterns. It's a mixture of luck & tweaking the parameters when I find something interesting.

@@hex-automata its just, my original 4 fold spiral that evolved a way around its cartesian plane nightmare it would move itself around the grid and probe the walls. I thought it was randomly asymmetric causing a drift to the walls..

This will go deeper ... mutant of a mutant of a mutant ... a sort of Forced Spice-Gas Evolution.

@@hex-automata can you transplant an encoded wavefront pixel..? Ive wondered if i can do that between simulations..

If you mean can I copy a cell pattern off an individual image from this video and paste the image to a new automata run , then answer is yes. Let me know if you would like to have any specific patterns (any subset) isolated and run on their own. This is how I "captured" many of my seeds in the wild..

@@hex-automata wow! yeah, i know some of my encoded wavefront information may contain entire universes in a sense.. Today i was wondering if i save my thoughts like that in the allocortex, just capture a few pixels from a few grids and unpack it later

I need to try again and understand your program. I've been sidetracked by Helene, but I am gradually getting back to CA research. It sounds like you might have a holographic effect going on, where a piece of the pattern encodes the whole pattern? (literally, or al least approximately). And the piece-encodes-the-whole phenomena is of course common with fractals too. Now I am wondering how the concepts of fractal and hologram, might be related.

@@6AxisSage , the pattern continues to gradually grow in size and complexity, at least until step 499 when I stopped looking. As the the pattern grows, if we let auto-zoom enlarge the cell grid, the individual cells shrink accordingly to keep the object in frame. This ultimately makes the 3 primary colors blend to give muddy tones. The grid is finite, and therefore the number of live cell configurations is also finite, and the pattern must ultimately repeat or die out. But with 4 states available per cell, this could take many thousands of time-steps to happen. This system must be computationally irreducible, meaning that even the only way to find out what will happen is to run the simulation.

You have excellent taste in music! Or did you suspect that I like the electronic genre? Jean Michel Jarre is one of the best. Vangelis & Tangerine Dream are also favorites of mine.

@@hex-automata I've been a fan of JMJ since childhood!

I've been a fan for many years -- hey we have something in common ;-)

@@hex-automata Besides hexagons, you mean? I'm not so familiar with Vangelis, but I loves me some Chariots of Fire soundtrack or State of Independence. Tangerine Dream escaped my notice somehow, though.

Please have a listen: //------------------------------------------- Vangelis - Elsewhere ruclips.net/video/8pzMtOOEX6E/видео.htmlsi=KWICUwKUvQiQNkcM //------------------------------------------- Tangerine Dream: Sleeping Watches Snoring In Silence ruclips.net/video/OrJcs85kr-Q/видео.htmlsi=23nqyHFwVG9j9PbU //---------------------------------------------- Ray Lynch: The Oh Of Pleasure ruclips.net/video/SinL1sRrV1Q/видео.htmlsi=xMrCcDZBhPOg9Tn3

How does she manage to endure? One day at a time, … one day at a time.

The book "Alien Information Theory" by Andrew R. Gallimore (brain & DMT researcher) mentions something relevant, speaking about the human brain: "The smallest functionally-segregated area of the cortex is known as a CORTICAL COLUMN, a cylindrical structure contains about 100 neurons, and the cortex can be described as a mosaic of columns packed side-by-side. At any point in time, the entire cortex displays a complex pattern of activation of these columns." Gallimore gives a reference to the medical literature with more detail. I haven't read that reference, and I don't know about physiology, but I would not be surprised if the cortical columns are arranged in a hexagonal array. I would like to know more about your views regarding these cortical columns.

@@hex-automata Sounds pretty interesting, ill look him up. Regarding natural packing of cortical columns, I'll be breaking down my research into a full video with parts and several visualizations including packing, but if you are curious to learn more before that, I recommend Jeff Hawkins thousands brain theory to understand the 6 layers of the neocortex, the hexagons are the bestagons video, videos on neuronal cascade avalanches, evolution of maths from the perspective of naturally occuring yet geographically seperated cultures starting with a natural affinity for base 6 counting systems.

If a hexapus has similar qualities to its intelligent cousin octopus, living among and studying the hexapi would be an exobiologist's dream job -- sign me up! We might need only to travel as far as Jupiter's moon Europa to find them (hope I live long enough to witness a probe relay scene of life below the ice there).

@@hex-automata Some people are saying Enceladus is the most likely candidate. JUICE should provide much new knowledge.

@@arbieroo5679oh, that’s right, adding even more excitement. Wasn’t Enceladus spraying liquid water into open space? And the probe will fly through & sample that juice?

@@hex-automata I'm not up on the JUICE mission details, unfortunately.

I was unsure, so looked it up. The JUICE probe will study 3 icy moons of Jupiter in 2031: Ganymede, Callisto, and Europa. Only remote sensing -- won't physically get under the ice. "JUICE" is ashort for "Jupiter Icy Moons Explorer". There is also a privately-funded space exobiology space probe "Breakthrough Enceladus" which is planned to collect spray from Saturn's moon Enceladus (launch year not set yet). Exciting times to live in.

Nils does an amazingly wide variety of high-resolution simulations on his channel -- he's operating at a much higher level than me. His simulations are mostly intentionally based on physics equations, whereas mine are more accidental (or serendipitous) discoveries. But thanks for the compliment of mentioning me alongside @NilsBerglund.

It appears to result from interference between the expanding cell wavefronts. This run is carefully tuned for the size of the cell grid (108 x 108). If I change the size even a little, the pattern begins turning into roiling chaos as soon as the expanding wavefronts meet at the edges of the screen. BTW, I will finally get to experiment w/ your hex app today.

@@hex-automata oh sweet, ive been trying to make something more of that demo but getting nowhere fast. Might continue with the Moiré quasicrystal wheel stuff, thats getting fun, and my first draft for a hexgrid fpga design is able to learn and repeat the sinewave i played it!

Yes, this one is fun too watch.

I've been sidetracked with personal matters, so I haven't been able to follow up on possible new directions yet. Using a tessellation with non periodic tiles will be a challenge as far as how to track and update the coordinates of the individual cells. I haven't searched, but maybe someone has already done something like that. I will probably need to put this automata research "on the back burner" for a while since I'm planning to focus on learning how to program a quantum computer. Ultimately I want to try quantum cellular automata. The beta testing of my present CA platform is essentially done. So I now can focus on this new direction (which also includes trying to get a job with it).

@@hex-automata that’s awesome man! I would love to see videos on that lol so keep me updated! This week I’m moving into training my own math and function calling LLM models and will be uploading some tutorials for those! These are exciting times and you definitely have a realized that hexagons are the bestagons and this path seems to be what the original flaw was with Conways game of life, would also love to see hexagon Minecraft and other things based in non rectangular coordinates. Best of luck @hexagon-multiverse

Strange patterns that remind of us of other things -- that is the norm in theses automata universes revealed here.

Before running the automata, I do not know what images will appear. I think the creature-like forms occur by chance. It's like staring at clouds -- if you look long enough, you'll see some forms that resemble something from memory. I do many more automata runs that are published here. I sort through the mess so you don't have to. And then I share the juicy ones here.

​@@hex-automata😊 yeah i watch them and i imagine them on this network of geometric grids, each hypercolumn a pinwheel, each cortical region a series of theses, a conscious mirror we "see" that shows us a recreation of the world and subconscious mirrors that we dont see. The conscious mirror is something that we can write onto. In the case of light from the retina (look closely at the hexagonal pattern and think for a second if light becomes an electon in the wavefront, it can be rescaled later into perfect geometry, as long as u know the basic rules of geometry.. theres a bit more but look up retina, cortex v1, gyrus, Sulcus

I think I know what you mean. The brain is very good at generating visual imagery. As we know form the visions induced by certain substances, that fractals are heavily involved at the basic levels of processing. If images can arise this way, why not thoughts? Seems to me that consciousness is also fractal in the way that universal consciousness fragments and forgets itself on finer levels to produce us apparent individuals. And then in our dreams at night we again forget who we really are, and mistake our mental imagery as real. A dream within a dream.

@@hex-automata perfect! Now add a wavefront to encode the pixels and you get a 12 period image you can animate with various moire overlays from the second grid and you can losslessly compress data by zooming in or out into pixels.. still working on that demo but lemme know if u need more help to meet in the middle.

@@hex-automata im glad someone can see it other than me! Lets help others see it together?