dvgrn

Adam P. Goucher's pi-calculator pattern is quite elegant, I'd say. It prints the decimal digits in-universe, with Conway's Life blocks for pixels.

https://conwaylife.com/wiki/Pi_calculator

Would you be satisfied with a Lisp implementation?

https://conwaylife.com/wiki/Lisp_in_Life

That shares the impressive inefficiencies of the Quest for Tetris project, though. For something that's much more practical to run, and can be programmed to do things like print out the digits of pi in-universe, see

https://conwaylife.com/wiki/APGsembly

This is one of those tricky things, highly dependent on context.

If you're talking about Conway's Game of Life patterns, then "gliders" are the 5-cell spaceships that travel diagonally, and all other moving things are "spaceships" but not "gliders". If you call a Conway's Life non-glider spaceship a "glider" you'll mostly just confuse people.

But if you're talking about other CA rules -- especially rules where there isn't any 5-cell diagonal spaceship -- then "glider" is very commonly used to refer to other moving patterns.

For example, David Eppstein's "Gliders in Life-Like Cellular Automata" database was active for decades -- recording spaceships across a large rulespace, not just Conway's Life. It's an accepted generalization of the term, somewhat like saying "Xerox machine" for any old copying machine whether or not it was built by Xerox.

There has been no true replicator found yet in Life as far as I know...

Actually more than one true replicator has been constructed. The 0E0P metacell

https://conwaylife.com/wiki/0E0P_metacell

can be programmed to self-replicate in any number of ways, but it's so big that it's very hard to simulate it through a full cycle. By contrast, Pavel Grankovskiy's "DOGun SaGaQR"

https://conwaylife.com/forums/viewtopic.php?&p=138191#p13819...

only has one pattern of replication, but it's much simpler than the 0E0P metacell and can easily be run through many cycles in Golly.

There are also patterns -- both stable patterns and oscillators -- that have an unbounded chain of predecessors, but still can't be glider constructed. That is, there are proven solutions to Conway's "Unique Father Problem" from over half a century ago:

  https://conwaylife.com/wiki/Unique_father_problem

Thanks, that's a big help! I think actually the Conway's Life community does quite regularly have "interesting things" that could fit the Show HN model.

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 ...

  https://conwaylife.com/forums/viewtopic.php?p=153609#p153609

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.

People have definitely tried this kind of thing, but so far -- from what I've seen -- Game of Life problems seem to be highly resistant to neural-net types of solutions.

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.

I took a day off of work yesterday to try this AMA idea out, and I'm thinking it turned out pretty well all in all. It was definitely a one-time experiment, though, not something I'll do again.

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.

Heh, I'm not actually sure whether Nathaniel meant to invoke Eric Raymond's hacker emblem on the book cover or not. The grid is there, and the glider orientation is right, but the cells are squares and not circles. That orientation of the glider is kinda canonical, independent of the hacker emblem -- e.g., it's the phase that shows up in the "glider" LifeWiki article.

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.

I'm thinking the most successful "automated exploration" so far has been Catagolue's method: simply generate a whole lot of random-soup initial configurations, run them until they settle, and then poke through the ashes looking for interesting stuff:

  https://catagolue.hatsya.com/census

There's definitely plenty of material for a Volume II book (and several volumes after that, for that matter). At the moment, though, Nathaniel and I think that it might be somebody else's turn to write those!

  https://conwaylife.com/forums/viewtopic.php?p=136037#p136037

  https://conwaylife.com/wiki/Tutorials/Coding_Life_simulators

Definitely I have lots more to say about 15-glider universal construction! It was a really exceptionally interesting collaboration, where several people working together were able to complete something that would have taken any one person a ridiculously long time to sort out.

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.

My sense is that people don't usually play the Immigration Game for very long -- it just doesn't seem all that interesting to most folks ... and so there hasn't been much interest in developing a computer opponent for the game.

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:

  https://conwaylife.com/wiki/Category:Lifeline_issues

I don't want to say that there's no possible role for AI in Life research, but it's hard to see how something like ChatGPT can be helpful.

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:

  https://conwaylife.com/forums/viewtopic.php?p=183306#p183306

  https://news.ycombinator.com/item?id=40128285

-- It's interesting to look at the different symmetries on Catagolue, where the idea is to generate a lot of random soups with different symmetry types, and then just run those patterns and see what comes out. The D8_1 and D8_4 symmetries are 8-way symmetric, which is as high as you're going to be able to get on a square grid.

  https://catagolue.hatsya.com/census/b3s23/D8_1
  https://catagolue.hatsya.com/census/b3s23/D8_4

-- 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

  https://conwaylife.com/wiki/Hexagonal_neighbourhood

  https://catagolue.hatsya.com/object/gun_14/b3s23

I'm not -- I'm just more of a Conway's Game of Life expert than 99.9999% of the world's population. But that's just due to experience and invested time, not cleverness.

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 --

  https://conwaylife.com/wiki/Reverse_caber-tosser

It's made a lot of Lifenthusiasts happy, and that's not nothing I suppose.

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.

Yup, it doesn't take a very big starting pattern to produce likely infinite novelty -- though it's not always easy to prove that any given pattern won't eventually unexpectedly "go boring" due to some kind of unexpected feedback effect.

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

Ha, well, I've mostly successfully dodged the various Wolfram-science questions so far. I just finished reading a book on cosmology -- VSL theory -- but honestly a lot this kind of thing seems to be way too far above my personal abstraction ceiling. I can't tell whether some of these ideas really even mean anything at all, or if it's just somebody who is better at waving words around than I am.

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.

I don't know about "concise", but one place to start for references is the LifeWiki. We've been trying to extend the non-Conway's-Life part of the wiki for a few years now, to cover more of the OCA space ("Other Cellular Automata"):

  https://conwaylife.com/wiki/Cellular_automaton
  https://conwaylife.com/wiki/OCA

We've tried a lot of different methods over time. Currently the LifeWiki --

  https://conwaylife.com/wiki/Main_Page

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:

  https://conwaylife.com/forums/viewtopic.php?f=7&t=5650

That background seems pretty cool as it is -- I like the changing colors. Maybe try playing with depth as well, along the lines of the T=450 point of the LifeViewer demo pattern here

  https://conwaylife.com/wiki/LifeViewer

  https://oimo.io/works/life/

The "spawn as much dots as possible" sounds like a spacefiller:

  https://conwaylife.com/wiki/Spacefiller

  https://conwaylife.com/wiki/Period-156_glider_gun

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

Heh, yes, the comparison to chess is a very good one. You probably need a similar level of focus and dedication to be a good Life pattern engineer or a good chess player -- and that level of focus is something that improves with enough practice, in both cases.

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.

This is a very good question, but I'm not sure I can give a very good answer.

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.

It was _kind of_ a historical accident, in the sense that if we ran history over again, it wouldn't be too surprising to see an alternate-history "Conway's Life" with a rule like "B36/S23" (HighLife) instead of "B3/S23". (Conway did really like the replicator and bomber and a few other fun things that HighLife has that Life doesn't.)

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

  https://conwaylife.com/wiki/Isotropic_non-totalistic_rule

---------------

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.

And what are these hypothetical candidates interviewing for, exactly?

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 --

  https://conwaylife.com/wiki/Tutorials/Coding_Life_simulators

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.

Heh -- "if you need more than one line of APL you do not fully understand your problem".

  https://news.ycombinator.com/item?id=1041500

  https://codegolf.stackexchange.com/questions/3434/shortest-game-of-life

Hadn't heard of it. Looks like it was removed sometime in the 90's, maybe, so it's not too likely that there would be a good video of it in action.

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.

Question 1: There are really surprisingly few "standard libraries" or tools for this kind of thing. You would think we'd have a CA editor capable of doing object-based editing by this time -- like, copy in a complete device made out of reflectors and converters, each of which is made out of still lifes and oscillators, each of which is made out of cells, and you could do "group" and "ungroup" operations and snap to the right locations to fit the circuits together correctly.

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:

  https://conwaylife.com/wiki/Reverse_caber-tosser