Another thing I stumbled into was helping Nathaniel Johnson complete an improbably thorough 480-page Conway's Life textbook, with end-of-chapter exercises and everything. The book could be used to teach a college-level class on the subject. https://conwaylife.com/book/ has a free PDF download for the book.
So... I'm not the cleverest Lifenthusiast by a long shot, but for a random question about the Game of Life, I'm more likely to know something about it than at least 99.9999% of the world's population. Ask me anything!
Two questions:
1) How are people building things this complex? Are there open source libraries and toolkits for this - building blocks for chunks of functionality that can be assembled?
2) For you, what are the most interesting, impressive and varied things that you've seen with Life? Is it just these increasing levels of complexity, or maybe something else?
But at the moment, pretty much all we have is tools to copy and paste rectangular sections of patterns at the cell level -- plus we've got good scripting tools (in Golly) that can be used to string together whatever pieces we might want, but it's up to individual pattern-builders to write those scripts for each specific purpose.
So our "library" is pretty much just the LifeWiki and a few other pattern repositories, and we borrow liberally from existing large constructions -- but when we're building something new, we usually just build flat bitmaps, not anything with built-in annotations or metadata.
Question 2: The thing that's been the most interesting to me in the last decade or so is the increase in collaboration. Projects used to be done by just one person more often than not -- but now a very large fraction of the biggest discoveries are completed via a large group effort over the course of a few weeks or month. One big recent example has been the RCT fixed-cost universal glider synthesis project, which needed contributions from quite a few people to solve all of the tricky little sub-problems:
I'm currently finishing up my OU MSc and the project I picked was specifically around cellular automata - only in this case relating to them calculating any arbitary automatic sequence - which are sequences you can create from finite state machines - that really opened my eyes to the fact these sorts of very, very simple machines can, with the right (and rather complex) setup, be made to do pretty much whatever you want from a computational PoV. In that paper by Rowland and Yassawi they give a constructive proof to calculate the required update rules for a CA that outputs any particular automatic sequence. That itself gives some hints at some ways of deriving the input and rules for these systems to do some particular job. [2]
I know Wolfram often gets dunked on for ego/hubris but in Chapter 11 of a New Kind Of Science he goes into how the Rule 110 CA can be setup to "calculate" (output) other CAs. From there it starts to become a little less mysterious that these systems can generate behaviour you could imagine running on a CPU of some sort.[3]
[1] https://mirror.explodie.org/universality_in_elementary_cellu...
[2] https://arxiv.org/abs/1209.6008
[3] https://www.wolframscience.com/nks/chap-11--the-notion-of-co...
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
And generalizing Games from there:
https://en.wikipedia.org/wiki/Life-like_cellular_automaton
Question #1: How far has Lifeology(?) advanced since 2001, for people similar to your younger self (without awesome skills, or huge time investment) to have a chance at making their own lucky discoveries, and becoming modest Somebodies in the community?
Question #2: How highly (or otherwise) would you rate Wikipedia's articles on Conway's Game of Life, and closely-related topics?
There are definitely areas that haven't really been explored fully yet, like the use of SAT solvers in new and inventive ways to tackle difficult Life problems that are currently just beyond our reach.
Just for example, there's the problem of finding a fast elbow for a 2c/3 "signal wire" --
It's not clear if SAT solvers can be applied usefully to glider synthesis questions, like "is it possible to collide gliders to build a Sir Robin spaceship?" At the moment that particular question seems way beyond reach, but maybe in a few years we'll be running an AI that is experimentally setting up new SAT solver problems, and something will pop up that we just haven't managed to think of yet.Question 2: Wikipedia's articles tend to be very good quality -- partly because if they weren't, there are a lot of Lifenthusiasts with some experience maintaining the LifeWiki who would immediately go and fix any technical errors that might show up on Wikipedia. But the really detailed documentation on Life is definitely kept in the LifeWiki, not on Wikipedia:
https://ppqty.com/anyone-beaten-stockfish/
The qualifier "serious" is needed because GM Andrew Tang won games at hyperbullet time controls (15 seconds) against a weaker version of Stockfish.
Article is dated Oct 2023.
Citation?
I'm willing to believe that someone used the gambit to win against an engine, but in response I would've expected the engines to be modified to restore their absolute dominance against human players.
So, I would be very interested to see any evidence that this gambit continued to work against the version of the engine released after the gambit's effectiveness became widely known.
The project has at least one unnecessary extra layer of abstraction in it, but somehow nobody has quite gotten around to rebuilding it 100x smaller. A "HashLife-friendly" version could run thousands of times more quickly in Golly.
Since then, several people have invented their own independent computer architectures in Conway's Life, so that kind of experimentation is still going on. See, e.g.,
This is kind of true in all academic publishing, that your success is due to your publications’ ability to inspire follow-up publications. But for abstract mathematics the “street cred” follows three rules: you get more cred based on,
• the wimpier the building blocks look
• the larger and more complex the structures you can build with them
• the more memorable or intuitive the blocks are (so like marketing... SK-calculus is the same as lambda calculus but lambda can say “I am the abstract mathematics of template substitution!” while SK-calculus can't, directly.)
All a way to say that the field is full of “fun little toys” and the key about criterion (2) is that we have figured out how to build structures of arbitrary complexity in Life, because we have discovered it is Turing-complete. It therefore is also NP-hard and a lot of other good stuff. Really revitalized work into cellular automata by giving some good marketing, which led to Stephen Wolfram's success etc etc.
> which led to Stephen Wolfram's success etc etc.
Wolfram's A New Kind of Science takes the idea a bit too far, in my opinion. It's an exposition of the hypothesis that the underlying stratum of life and the universe is, like cellular automatons, discrete—and therefore can be understood in terms of discrete processes, which he views as analogous to real life. He points to emergence in cellular automatons as evidence that an analogous emergent phenomenon was the reason biological life came into existence.
Mathematically and philosophically, it's a very interesting idea, but I'd hope that at this stage in scientific history, we'd understand that step 2 to validating an interesting hypothesis is testing it.
[1] https://mathworld.wolfram.com/PrincipleofComputationalEquiva...
eg: Lawrence Gray in his 12 page review: https://www.ams.org/notices/200302/fea-gray.pdf
Cosma Shalizi's infamous Rare Blend of Monster Raving Egomania and Utter Batshit Insanity review: http://bactra.org/reviews/wolfram/
In fact, the game of life is Turing complete -- you can build whole processors[0] or programming languages in it. You can even implement the game of life in the game of life. Someone did that and implemented infinite zooming between GOL levels.[1]
[0] https://github.com/nicolasloizeau/scalable-gol-computer
[1] https://oimo.io/works/life/
It's a fun toy because it's implemented in pixels with arbitrary rules, but the concept is exportable to other domains.
The eeriness of it I think comes from that we still don't understand a lot about the world - concepts like consciousness, the origin of the universe, origin of life - or, any mystery where we don't understand how a whole became greater than the sum of its parts - when you see a model like this, it shows visually how such unknown complexities probably originated in far simpler forms.
When I see those epic Game of Life videos where there's a giant stealth bomber looking structure steaming across the screen creating sub-processes in its wake, to me it's like a blue whale moving through the ocean, or a vast alien spaceship silently yet steadily barreling through the void of space.
There's an ominous intelligence that seems to emerge out of what was once simple, binary, unconscious, incapable.
The local update rules provide an analogy to our universe with a kind of built in "speed of light" of how fast information can propagate in the system. Further, since there is a system clock of sorts, the system is massively parallel with further analogies to our universe.
The game looks like a toy but note that many profound models are also "toy-like". Ising systems, precolation models, Bethe lattices, self avoiding walks, etc. all provide seeding grounds for deep insights into our physical world. Just as an aside, I heard a quote, which I can't find anywhere, about how Maxwell playing with magnets could have been considered him playing with frivolous toys but his setup was critical to him figuring out the underlying mechanics of electromagnetism.
On one hand, I sort of agree that there's a lot of uninteresting exploration but on the other hand, taking a step back, GoL research is exploring the more general space of cellular automata and how it could potentially map to real world simulation. For example, how small can a system be before it can do arbitrary computation? Can all patterns emerge eventually (no, garden of eden style patterns)? What do rotationally invariant patterns looks like? Can you "copy" arbitrary patterns from some setup? If so, how fast? Is it dependent on how big it is, or how complex it is? etc. GoL provides a sandbox in order to answer these questions and potentially give insight into other systems as well.
In my opinion, one of the reasons for the popularity of GoL is because it was created right when computers became commodities, allowing hackers, amateur mathematicians and others to program something simple, that could be heavily optimized for limited hardware, and create intricate and complex behavior. There was a quote somewhere, that I'm also having trouble finding, about how, at one point, GoL simulations accounted for a significant portion of wasted compute.
[0] https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Undeci...
God doesn’t play the GoL.
That absolutely sounds like a codename from one of cstross's Laundry Files novels. (I think "boojum" was actually part of one, but I don't recall which.)
edit: found it, it was from A Colder War, which is a great novellette: https://www.infinityplus.co.uk/stories/colderwar.htm
Negative testing is trying to invalidate the sample
The hunting of the snark is written in a way that reads like "normal English" from a distance. The sentences flow fine, the words look about right if you squint. So it passes a lot of "positive tests", in that it matches our expectations for what language looks like.
You have to "negative test" the story to realize you don't know the definitions for any of the words, and that the plot is uninterpretable.
Same idea as Kahneman's system 1 that comes up with instant answers, or ChatGPT hallucinating facts by association that "look right".
It challenges the reader to try to model and define a Wodwo, but provides basically no information on what a wodwo is, aside from the fact that it is something that itself is struggles to define it's relation and connection to the world.
In my opinion, it highlights how we are all physical perception machines looking for meaning and identity, but meaning and identity can not be physically perceived.
https://allpoetry.com/poem/8495307-Wodwo-by-Ted-Hughes
The Snark is described in detail, with but a single additional caution that some Snarks are Boojums, with no description whatsoever of the difference. And, in the end, only a Boojum is found.
The band of snark-hunters are _also_ described in detail, almost always emphasizing the things that they cannot do or the additional risks of having them along, but they're brought along anyway.
"For the Snark _was_ a Boojum, you see."
and ended up writing the other umpteen dozen verses just so that that would make sense as a punch line.
There's some debate whether it was the Game of Life or some other automata, but I remember the sounds of the relays clacking and the light bulbs humming so distinctly. It certainly had a "Game of Life vibe".
Are you aware of this art installation? Ever seen it?
https://www.reddit.com/r/Seattle/comments/1xzypl/something_i...
https://imgur.com/gallery/3zwVKc3
It does seem like the kind of thing I might have been drawn into staring at for hours and/or playing around with, kind of like the marble perpetual-motion machine I remember from a Toronto museum at around the same time period.
Why do you think that is?
Edit: This is the video I meant: https://www.youtube.com/watch?v=E8kUJL04ELA
I've played around with several CAs and Conway's rules stands out to me as one of the most interesting still, for many reasons (like simplicity, interesting patterns, long lived structures).
I think that’s partly the nature of pure researchers. They usually have something more interesting to them than what they got famous for, and they probably don’t want to lead an organization. This is different from BDFLs like Guido van Rossum and Rich Hickey. Neither type is good or bad, and I appreciate them all.
1. There was a two-player game called The Immigration Game [1] using GoL rules. Has anyone actually played this? Even better, has anyone developed an AI to play it? Is there really much of a game there?
2. The PSA: The Immigration Game was described in Lifeline, a 1970's era (typewritten!) newsletter about GoL. I managed to obtain a set of them. I've been planning to scan them and make them available online. I don't think there is any ground breaking info in them, after all, folk were programming on mainframes (surreptitiously).
[1]. https://boardgamegeek.com/boardgame/129088/the-immigration-g...
It seems to be rather difficult to convert cellular automata into any kind of playable game. If it's an arcade game then it's usually too arbitrary, and if it's a puzzle game then it's usually way too easy or way too difficult. There have been some good efforts, but they're mostly only playable by dedicated Lifenthusiasts, and that's ... well... not a very large market!
Re: the LIFELINE public service announcement -- no need to do the scanning and online-ing. That's been done already, though there's still some review and typing-up work left for someone to do:
In case somebody is curious to see how it might look like.
https://aplwiki.com/wiki/Conway%27s_Game_of_Life
There are a couple of big difficulties that seem to prevent 3D rules from getting a lot of attention. It's just plain a lot more computationally intensive to emulate 3D rules. Also it's a lot harder to see what's going on in the middle of an active 3D pattern -- a lot of the detail tends to get hidden.
[1] https://content.wolfram.com/sites/13/2018/02/01-3-1.pdf
[2] https://en.wikipedia.org/wiki/3D_Lifex
What are the coolest open problems you'd like to see solved?
I suppose if I get a free wish for anything I want, I'd love to see a glider synthesis for Sir Robin, which a big oblique spaceship discovered in 2018. It's currently way beyond our ability to figure out how to build it out of gliders -- but twenty years ago the same was true of just about every Life spaceship, and now we have recipes for dozens of them.
Here’s the Hacker News discussion from when this was discovered: https://news.ycombinator.com/item?id=33797799
Dave, I’m still regularly blown away by this discovery. I don’t know what else there is to be said, but do you have any other comments regarding this?
Development of the RCT has slowed down a bit, though there's a hyper-optimized version in the works that will build a spacefiller instead of a Hensel decimal counter as its example pattern:
https://conwaylife.com/forums/viewtopic.php?p=180134#p180134
There's also another long-awaited project in the works, that will use quite a bit of the same technology along with some new ideas -- a unidimensional (one cell thick) spaceship:
https://conwaylife.com/forums/viewtopic.php?f=2&t=2040
It's improbably complex and awkward, of course, just like an RCT pattern, and it's huge though nowhere near as huge as an RCT pattern -- but there will be one phase of the spaceship that fits in a 1xN bounding box.
The problem at the moment is that nobody can see how to direct those searches toward a predecessor that's made entirely out of gliders -- it's clear that the Sun will burn out long before a trial-and-error search would be at all likely to return a result.
We can easily make a huge number of non-Sir-Robin predecessor patterns that will evolve into Sir Robin -- and we can find ancestor patterns for most of those predecessors, too -- but each step backward always produces something that's a little bigger, a little blobbier, and a little more random and chaotic looking than Sir Robin was... so ultimately all we're doing is making the problem more difficult with each step.
Are they run on gpus now?
Has anyone looked into ASICs?
Is caching heavily used for optimization?
Caching is very very heavily used for running the biggest universes, which are truly mind-bendingly large. Golly's "HashLife" algorithm can in practice handle patterns that are over a trillion cells in each dimension:
Patterns with interesting behavior very often have a lot of repeating patterns, with the interesting stuff happening as complex interactions between those predictable patterns. HashLife capitalizes on remembering interactions that it has seen before, so basically the more memory your computer has available, the better HashLife will do in the long run at simulating that type of pattern.Mostly, of course, the census just reports piles and piles of blinkers and blocks and beehives and boats and everything else that you almost always see when you run a random scribble -- but every now and then something turns up that has never ever been seen in the history of Life, and that turns out to be useful and building new mechanisms that weren't possible before:
Each note is an actual flexible polyimide PCB containing a hardware storage wallet - the PCBs are translucent in parts or solid in others depending on a copper pour but overprinted with ink using a special UV process - but one of the security features is when one holds a note up to the light one can see a Game or Life program which when executed emits a corresponding number of gliders and oscillators as the notes value. This feature is to prevent one from “washing” a note and printing a different value as is done with $5 and $100 US bills for instance as the copper pour is “baked” into the medium.
Writing a c program to encode arbitrary numbers into a Game of Life program was a very fun distraction during an otherwise thorny project that involved connecting people from the print world to people from the electronics world while shaving a few thousand cycles off a crypto library with ECDSA P256 operations before the smart phone powering the chips via NFC turned off. Real engineering work to bring cryptographic proof of authenticity that unfortunately gets written off as a 'crypto scam' when the poc token attached to the circuit boards was the least interesting part.
One can see some of the denominations here: https://twitter.com/NoviolNFT/status/1341468948416512000
A while ago I was toying with the idea of introducing a "macro" stimulus. Basically coupling the local rules of the game to global metrics like how many nodes are alive. This is emulating a bit agent based modeling in economics and in particular the role of regulators raising or lowering rates, alternatively a physical system exposed to higher or lower temperature. But what happens (at least with a simple implementation) is that whatever "stimulus" is introduced tends to overwhelm the known patterns, there seems to be little new "emergent" behavior in the coupled system.
https://www.openriskmanagement.com/game_of_life_with_macroec...
https://scholar.google.com/citations?view_op=view_citation&h...
I think it would be interesting to try transfering some of the automated search techniques to Minecraft's redstone mechanics, even though it probably doesn't fit the definition of a celular automata. Redstone is a feature in a videogame Minecraft that acts similar to logic circuits. Because building mechanics in Minecraft is inately restrictive (building is snapped to the 3d grid of "blocks", and there is only a limited number of blocks that all have predefined behaviour), there is naturally a community of people using redstones in ways that serve no purpose to the core gameplay loop, such as flying machines (think GoL's ships) [0], computers (since Minecraft's redstone is practically Turing-complete) [1] [2] or printers/autobuilders [3]. I would go so far as to say that redstone is the GoL for nerdy Zoomers.
[0] https://minecraft.fandom.com/wiki/Tutorials/Flying_machines
[1] https://www.minecraftforum.net/forums/minecraft-java-edition...
[2] https://minecraft.fandom.com/wiki/Tutorials/Redstone_compute...
[3] https://minecraft.fandom.com/wiki/Tutorials/Printing
2. Has any discovery made in life been used in real life or any practical application?
https://github.com/fchollet/ARC
I've mentioned in other answers that Life can make a good teaching tool for various mathematical and computer-science topics, mostly because it's entertainingly eye-catching. When you get a design right it's very satisfying -- like one of those huge domino chains that you see on YouTube, except that (for some designs) it keeps on setting itself back up again as it's in the process of falling down.
I was also thinking there must be a better way than knowing exactly how big the board is vs an infinite board. Also making the edges either always dead or alive VS letting the shapes pass through like pac-man.
Here is my horrible implementation using HTML canvas, JS/JQuery.
https://github.com/JoshuaMichaelHanson/GOL/blob/master/js/go...
Yes, I also made a new green account so as to not dox myself with my other accounts.
Do other games (or simulations) demonstrate similar ideas, or are cellular automata a rare case?
What makes Conway's Life particularly "catchy" (along with other 2D CAs) seems to be the motion. Humans love watching stuff move, especially when the motion is partly predictable and partly surprising -- i.e., like a screen-saver, not like TV static. And they like watching things blow up. A lot of Lifenthusiasts probably got their start by aiming gliders at carefully balanced Life patterns and gleefully watching the resulting explosions... it's a lot more fun than actually blowing things up, because you can always hit Undo and run it all over again, no harm done!
I would really have appreciated an "Undo" button for rewinding entropy and running those things over again, especially when they went disappointingly wrong halfway through...!
For music generation you'd want to somehow avoid ending up with the music "going boring" when the highway appears... As with a lot of math-inspired art (I guess I'm thinking about Mandelbrot-set colorizations here) the key is going to be in very specific presentation choices -- color choices for still frames or videos, or the specific method of mapping sounds to frames in a Langton's Ant evolution. So you'll just need to have (or develop) tools to try a lot of options and see what looks the most compelling.
Still frames are probably not going to be that interesting -- the fun part about CAs is the predictable-yet-surprising motion, which can be either the usual visual form or converted to sound somehow.
A recent version of Golly ( https://golly.sourceforge.io ) added support for listening to evolving patterns -- see pop-sounds.py / pop-sounds.lua in the Scripts directory. That reduces patterns to a single dimension in an obvious way (just looking at population), ignoring a lot of the 2D complexity. No doubt there are a lot of other possible avenues to explore there.
Are there other interesting and unexpected algorithms in implementations of GoL?
Every now and then a lucky or inspired SAT solver problem setup will throw out an answer to a really difficult-looking problem, with no apparent effort. But then that tends to tempt people into setting up more difficult problems to solve... and of course it's still very easy to set up problems that cover such a large search space that the search would take billions of years to complete on a planet-sized supercomputer.
So it's still very much an art form, rather than an exact science, to figure out what searches to try next.
In 2001 I had already been playing around with things like the Mandelbrot set and aperiodic tilings and Douglas Hofstadter's strange loops for quite a few years, so I knew the kinds of magical things that the iterative application of simple rules could produce.
Are their any algorithms or techniques for generating interesting starting states?
This is wandering off of the Wolfram physics project a fair distance, but it's hard to see how space could be quantized in a Fredkin "Nature is finite and digital" kind of way, without the underling "grain" of the universe becoming obvious in some kind of experiment, and/or without causing deep contradictions in various experimentally well-supported relativistic effects that require that there isn't any such thing as a unique fixed frame of reference.
But quite possibly that's just a failure of imagination on my part, not anything wrong with the actual theories in question -- I'm probably complaining about some apparent implausibility two levels above or below where the information is actually flowing. And there are certainly all kinds of properties of our physical universe that are quantized in one way or another, for utterly mysterious reasons.
Long story short, there is certainly still room for some big surprises in theoretical physics, and I'm not about to claim that I'm clever enough to rule out any of these wild options.
One thing that particular piques my interest is the diversity of possible automata, not just forms in any particular one, but diversity of rule sets as well.
What do you think is special about the GOL rule set compared to other life-like rules?
Do you think it was a historical accident this particular rule set became so famous, or not?
Are there alternatives you are also interested in?
On the other hand, Conway had some very specific criteria for the rule he was looking for. "B3/S23" is about as simple a set of rules as you can find for a range-1 Moore-neighborhood outer totalistic cellular automaton on a square grid.
So unless Conway's eye had happened to get caught by some slightly more complicated rule before he and his team happened on B3/S23, he'd be quite likely to settle on "B3/S23" all over again. It's one of the few candidates for the simplest rule that does obviously interesting things and seems likely to allow for computational universality. I mean, there are untold numbers of equally promising rules in larger rulespaces like the "isotropic non-totalistic" rules
... but most of those have rulestrings like "B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e": it's just not anywhere near as simple to describe the rules, as it is for Life.---------------
If we meet up with an alien civilization some day, it would be extremely amusing if we happened to show them some Life patterns and they said (in so many words) "Hey! You know about Pnurflpeef's Game of Life?!?" Not a likely scenario, by any means, but not quite impossible either.
Do you have any particular thoughts about the glider as a Hacker symbol?
I emailed back and forth a little bit with Eric Raymond when the hacker-emblem proposal first came out, but I don't remember that I had anything very interesting to say. Mostly I was hoping to get the Life Lexicon factoid about the unix oscillator into the "Anticipations" section on the official Hacker Emblem page --
Unix: ... The name derives from the fact that it was for some time the mascot of the Unix lab of the mathematics faculty at the University of Waterloo.
https://en.m.wikipedia.org/wiki/The_Game_of_Life
It seems like I rarely have dreams about Life patterns, though it does happen. Maybe some people with better-resolution imaginations might have a different experience, but Life patterns need a lot of precision and focus, and in my dreams everything is always fluid and shifting and I can never find my car keys or my homework, let alone any interesting Life configurations.
I'm not sure the "probability" part of the question is even well-defined, let alone answerable, unless you state a specific rulespace -- two-state range-1 Moore-neighborhood CAs on a square lattice, or three-state range-2 isotropic CAs on a hexagonal lattice, or what have you.
Basically, you just have to be able to demonstrate a working universal logic gate (a NAND gate or a NOR gate) in a candidate rule, and you've pretty much got Turing-machine equivalence.
The problem is, a lot more rules are computationally universal than you'd think when you first look at them. This is because it's often possible to get a candidate rule to act like a completely different rule, by filling the universe with something other than empty space.
So you can't just try out a few random-soup patterns, dash off a quick proof that "this rule necessarily explodes uncontrollably in all directions, so it's impossible for any circuitry to survive" or anything along those lines. What if you start with a universe of all ON cells, or a checkerboard of ON and OFF?
There are lots of rules where signals can propagate beautifully through that kind of non-empty medium, and occasionally some kind of Turing-complete mechanism might be found there, along the lines of what Matthew Cook did with Rule 110. So you really have to look at a lot of options before you can say for sure that a rule does not support universal computation -- and so far, it seems like a very tricky problem to automate the process of looking.
https://conwaylife.com/wiki/Period-24_glider_gun#Other_perio... https://conwaylife.com/wiki/Period-25_glider_gun https://conwaylife.com/wiki/Period-48_glider_gun https://conwaylife.com/wiki/Period-15_glider_gun https://conwaylife.com/wiki/Period-16_glider_gun
Are there any configs (I mean, those having any interesting behaviour) with intention having more than 4 symmetry parts? Or at least just more quadro symmetry configs? I am absolutely sure (since today) there are some for any 2^n, just all unfound.
Any attemts to create Conway's life on hexagon map with apropriate rules?
upd: for a single stream of gliders, what config gives as many gliders per 100 generations as possible? No matter what else it does, I just want a line of gliders with as little space as possible.
-- There have definitely been a number of people over the years exploring various outer-totalistic rules on a hex grid, and (to a lesser extent) isotropic non-totalistic rules: see
-- The smallest period at which gliders can follow one another is period 14. We don't have a true period-14 gun yet, though. The closest we have is a "pseudo-period" gun -- actually period 28, but it generates two gliders per period, so you end up with a period-14 stream:I came across excitable media recently and found it fascinating.
Do you have any other examples of cellular automata you found interesting or worth pursuing?
Life being Turing complete, it's also not difficult to build a pattern with an unknown fate -- like a Fermat-prime calculator that will stop growing if it ever finds a sixth Fermat prime, or the Collatz-sequence simulator described here:
https://conwaylife.com/wiki/Fate#Unknown_fate
Links you posted and hobbyist forums, formal research papers, or something else?
For a couple of years I've been trying to keep up with an informal summary of new developments, in an email-newsletter form mostly intended for "old-guard" Lifenthusiasts:
As I mostly expected, it ends up being a bit too much work for one person to do properly. But the back issues there do go into a bit more detail than there is room for in LifeWiki CurrentNews back issues.Conway regularly attended the bi-annual Gatherings for Gardner in Atlanta for quite a while, but by the time I started attending he could no longer travel that far.
Take spaceships, for example. You can train a neural net to recognize spaceships, but there aren't any reliably recognizable features that can distinguish a spaceship from a non-spaceship. To find out if a never-before-seen pattern is a spaceship with period N, you really have to run it for N ticks and see if you get the same pattern back again at an offset. Visual similarity with other spaceships just plain isn't relevant, unless the similarity is 100%; a pattern with a 99% match on a 100-cell spaceship will almost always be ... not a spaceship at all.
A good analogy for this might be training a neural net against images of prime numbers up to 997, printed in decimal in some standard font. Sure, you can train a neural net to recognize prime numbers less than 1000, with great accuracy ... but primality isn't a visual property of a printed number, it's something that you have to do some mathematical tests to find out about.
So if you try your trained neural net on prime numbers above 1000, you're going to be rather disappointed with its performance. CA spaceship recognition is the same kind of problem... possibly worse, since you could at least have some hope of a neural net correctly recognizing non-primes by their last digits.
Devs I ask this come down 50:50 on if it’s reasonable or not.
In the '80s and '90s, every time I got a new computer, one of the first things I'd do is write a very simple CGoL simulator, and then sit back and marvel at how much faster it was than the previous PC was.
So personally I guess I would have aced that question, in any number of languages and platforms... and yet I'm not really a particularly good programmer. It took me quite a few new-computer cycles before I started wandering down the various optimization rabbit-holes --
-- and I never got anywhere near as far as either HashLife or QuickLife. Now I just happily use other people's nicely optimized code, for the most part.So... it's a problem that a sufficiently nerdy programmer type of a certain age will be very likely to have encountered before, and you'd learn completely different things about a candidate depending on the level of that past experience.
1) The placement of a single cell in a huge pattern will very often make the difference between a working Life pattern and something that catastrophically implodes. So making a generative AI like ChatGPT do any work on Conway's Life is very much like making it play chess: sooner rather than later, something really important will end up slightly out of place, and ChatGPT will have no way of knowing.
2) Unlike a lot of other subjects where ChatGPT really shines, Conway's Life is an incredibly niche subject. There simply isn't anywhere near enough training data for ChatGPT to give reliable results, even for fairly basic questions:
3) However, there are definitely a number of areas of Life research where other types of AI might end up coming in very handy -- e.g., in monitoring and tuning parameters for very long-running and difficult searches. For this we need something much less like ChatGPT and more like Douglas Lenat's EURISKO, to try new experiments and learn what it can from the results ... EURISKO also happened to come up on Hacker News today: We just can't rely on generative AI to re-shuffle what is already known and make it into a nice new package, when what we're searching for is something that's never been seen before.It has also taught a lot of people a little something about the likelihood of emergence of complex behavior from very simple iterated rules.
And maybe you could say that several of the larger collaborative Life projects that have happened recently have been very good examples of non-political international co-operation, in a world that these days seems like it could use a few reminders that such things are still possible.
The big surprise that I've been spending the most time on lately is the utterly strange result that if you can build something by colliding gliders together -- no matter now many gliders and no matter how big the final pattern is -- then you can also build it by starting with exactly fifteen gliders in an otherwise empty Life universe:
It's a mind-bending result -- partly just a mathematical trick, since you end up encoding a whole lot of information in the space between the gliders -- but it's just really amazing that all the details have actually been figured out to make the trick work, and that it's possible to simulate the whole process on a personal computer.(I'm quite sure that I don't do anything "revolutionary" myself -- I just try to encourage Conway's Life research to continue. Discoveries have kept building on previous discoveries for fifty years now, and I'm just really curious to see what will happen next.)
Could probably add at least one more nine to the end of that number, and maybe two ... the CGOL community is very widely dispersed geographically but it's really very small. There just aren't very many Conway's Life Expert candidates out there! For me to hit 99.999999%, there would have to be fewer than eighty people out there who have more knowledge about Conway's Life than I do
At least for certain topics -- like the reverse caber tosser, for example --
-- I'm fairly confident that I can list pretty much every person in the world who has a deep knowledge of the workings of 15-glider RCT universal construction ... and there are a lot less than eighty of them.[0]: https://www.amazon.com/Alien-Information-Theory-Psychedelic-...
I could certainly try an "Ask HN" at some point, but haven't been able to think exactly what question I would ask. "How many people know what a reverse caber tosser is?" is one that I'm curious about, but I suspect I'd get mostly just crickets. Really I wanted other people to ask questions... and I'm having lots of fun with the results so far!
There isn't any harm, if anything, more experts, accidental or otherwise, should do this.
Something just occurred to me from a review of recent HN item titles: maybe what I _will_ try sometime is a "Show HN" post, for some shiny new Life discovery that seems particularly interesting.
The example I'm thinking most about is the fixed-cost 15-glider construction for absolutely anything that's glider-constructible at all --
for which we do have some eminently runnable code that showcases the entire process of 15-glider construction from beginning to end, with subtitles ...
... running inside Golly, but that's a free download, and the Lua script version doesn't need any extra Python installation or configuration or anything.So if I don't get too much "Nah don't do that" feedback here, I might try putting up a Show HN post for the new super-optimized RCT15 project, once the last pieces of that get completed.