Hi there, I'm the author (of the blog post, not of the achievement itself)! So glad this is spreading. Feel free to ask here or on the post for more clarification if stuff is too unclear
Almost everything was unclear to me, but then I'm not familiar with the Game of Life lingo. Perhaps it would make sense to write a version that the educated public can understand, even without any Life background?
Funny. I first saw life over 40 years ago. I saw some crazy objects creates in my college days. I've seen occasional articles about breakthroughs over the years. Understanding gliders and spaceships has been my foundation to grok everything since. Being able to think in the abstract was a key to understanding this article for me, but without a few concrete foundational concepts... I stopped a few times reading it to laugh at how absurdly abstract and full of jargon it is. Completely meaningless techno-babble to the uninitiated. How much of my own specialization sounds so opaque to outsiders? Maybe all of it ;-)
I would say "the educated public" is already the target audience for my blog. Game of life topics are notoriously hard to disentangle from their jargon, and I went to some effort here but needed to balance that against the goal to remain accurate.
My hope is that by reading only the amount of background on the blog already in the Waterbear post (referenced immediately in the introduction), you have all you need to grok the post. But that's certainly an optimistic hope, and maybe unfounded.
This is a very fine piece of writing, communicating the excitement well! I could almost forget I didn't understand all the details. Which is the goal of popular science/maths writing, I guess - to communicate what something looks and feels like at the coal-face to people who don't know all the details, sufficiently that they can share and appreciate the excitement. And bewilderment - How the hell does that super-complicated epic construction come out of 15 gliders?!
I have read quite a bit about GoL before over the years, programmed and experimented with it and many variants etc But never tried to build a.. well, it's high level programming in GoL isn't it, or like building UNIX tools in GoL and doing cool things with complex combinations of them. I had my mouth open in amazement reading it. Bunch of maniacs. This is an extreme sport. Thank you!
Definitely worth trying to learn!
As with most topics, it starts out seeming hard to grasp, and then you start naming things and recognizing them. What looks like jargon to an outsider is just a compressed way of communicating. The people in the community are smart and tend to compress their ideas really far which makes the jargon even more extreme.
Advanced gol is just getting past that first hurdle of understanding the densely compressed info behind the jargon. And it doesn't ever need to be done for all of the concepts. You can be versed in just one. I started out in a super specialized corner in self constructing spaceships. That said I'm a bit of a whiz in other areas so I can't be used as evidence that it works for everyone..
I think the biggest prerequisite for getting good at "advanced GoL" is just an unreasonable amount of patience.
Probably I'm a good case in point. I'm definitely not a particularly clever mathematician, but it seems like it's possible to understand any new Life technology just by tinkering with the pieces for long enough.
If anyone wants to follow along with that kind of learning process, just start working through the Life textbook that kryptiskt mentioned. (Full disclosure, I'm one of the authors.)
To be fair, that's the definition of jargon. Using domain specific language is something that's universal - it's a compression technique you see any domain where there's a need to communicate dense information. Abstraction affords precision, not ambiguity.
I just want to say that I love everything the GoL community has built and discovered over the years. Big crazy things like this always fill my heart with awe and wonder.
Even though in my life, I can't make the time for doing something on the grandiose scale required, I can live vicariously through reading about your sheer dedication and intellectual effort expended.
I can recommend the recent book "Conway's Game of Life: Mathematics and Construction" (downloadable free at https://conwaylife.com/book/), it starts gently and builds up to these kind of constructions (minus what has been discovered in the last year or so).
It's a bit hard to see how this RCT trick could be useful for reducing anything besides the number of gliders.
RCT is basically one very unreasonable end of a wide spectrum: you can use a very small number of gliders to build something, as long as you're content to have the construction take a ridiculously long time. Conversely, you can build that same thing in a lot less time, but it will take a lot more gliders.
That's definitely completely true. We can specify the relative positions of the initial gliders at each of the three corners of the RCT pattern in just a few dozen bytes.
But the number that says how far apart those corners are from each other has very roughly half a million digits. The exact number depends on exactly what pattern is being encoded by the RCT pattern -- I think the example construction of Alan Hensel's decimal counter pattern needs somewhere around a 450,000-digit number.
There are some optimizations underway to decrease that number by a few percentage points, but it's always going to be a very big number!
Whenever I read one of these deep dives into GoL achievements, and let me preface this by saying I mean this as a compliment, I feel like I'm reading the extended universe lore on a wiki page for a giant fantasy franchise. It's maths but feels so much more narratively rich than most other mathematics somehow, and the community around it has such a unique subculture vibe to it too.
in my opinion Jeffery Ventrella's clusters are a more promising avenue than Conways GoL. The rules are in comparison very interesting as well: No creation out of nothing, only particles that attract or repel each other.
Oh that is very nice! Will play with that idea a bit soon :)
(I have to say the presentation style of the video gets on my nerves a bit though, especially the "typing on a keyboard" sound effect. But hey, if it helps them reach a wider audience)
EDIT: why didn't you also link the original website of Jeffery Ventrella though?
This is an incredible achievement. The most impressive piece of GoL engineering I've ever seen!
Clearly, number of gliders is no longer a good measure of complexity of constructions. Perhaps one should fix a straightforward way to encode a set of gliders by position (e.g. using [1]) and orientation and take the minimum number of bits of such a description.
Just one question:
> 1274729 – build a DBCA and pass control to it
> 192584 – build a new constructor that reads stored data instead of live data
> The final 200093 bits get stored in the Binary Storage and Retrieval device, these same 200093 bits are counted below:
How come this adds up to 1667406, which is 1615 more than the claimed total of 1665791 bits?
Ooh, I appreciate the diligence! The numbers here came from manually fiddling with more granular output from Pavgran's special purpose "profiler" script. One of those steps, where the DBCA assumes control of the bit stream, takes 1615 gliders. I would bet I made a mistake and added it twice, probably to both the DBCA building and the task of the DBCA itself. It belongs in only one of them!
The basic idea is to use the distance of the gliders to encode information, so when they hit each other allows for an embedding of a Turing machine.
I'm no expert here but some basic ideas are that some small number of gliders (two?) can hit each other and produce a "glider gun", allowing for just a few gliders to "upgrade" to producing a steady stream of gliders. There's a "Reverse Caber Tosser" (RCT) structure which has a stationary element that "tosses" a glider back and forth with a structure moving away (or towards?) it, emitting another glider in another direction after each toss, allowing for logarithmic glider/population growth. Another key idea looks to be the "glider producing switch engine" (GPSE) which incorporates the ideas of the RCT with a delay and some other logic?
The distances involved are astronomical because they're encoding everything in the distance but they still manage to make it Turing machine equivalent with only 15 gliders.
Anyway, I'm floored at the ingenuity of the GoL community. It's as close to programming with butterflies as I've ever seen [0].
4 gliders hit each other to make a stream of gliders. This isn't a gun, because a gun costs more. instead it's a GPSE, which looks like a gun from the barrel end, but has a limit. As it approaches that limit, the RCT mechanism lets another three GPSEs generate an arbitrary list of bits, controlled by the precise location of the first (as a binary number). The final count 15 comes from the naive 4×4 minus one from being able to piggyback one of the constructions off a neighbor to save a single glider.
From bits to an embedded turing machine is gol magic that the blog post treats better than my comment could.
The reference that comes to mind for me is something out of one of Martin Gardner's _Aha! Insight_ books from decades ago -- the idea of encoding something like the Encyclopedia Britannica into one big long bitstring, then converting it into a fraction... and putting one single very careful mark on a stick to represent that fraction.
The difference is that where the real world doesn't allow for storing anywhere near that level of precision in a mark on a stick, the Conway's Life universe is considered to be unbounded, so there's as much room as we need to implement this RCT trick.
Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encoding the time at which a certain pattern (a glider) appears where it's needed. In a rigid system like the GoL, we can't trade space with time easily, since everything happens at a constant speed, but it makes one wonder...
Far from being relativistic, it is a miniature simulated universe with a rigid flat geometry and a universal clock. it is interesting precisely because it is very simple and yet permits remarkably complex events.
There have been a lot of GoL variants over the years, but I don't remember running into any attempts to vary the speed of evolution in different locations on the same grid.
The idea that all neighbors move to the next tick simultaneously is a fundamental assumption in cellular automata in general. If you try changing that, the optimizations that allow us to simulate CAs at any kind of reasonable speed ... all stop working, pretty much. It's kind of painful even to think about.
Which means there are probably very interesting rules out there somewhere, where CAs run faster/slower depending on pattern density -- it's just going to be very tricky to explore that particular search space.
Well, there is SmoothLife (e.g. https://www.arxiv-vanity.com/papers/1111.1567/#S4) where the time step is also made continuous. I suppose you could extend this so that this isn't some uniform value across the entire space, but instead a value that is constantly recomputed based on neighbourhood density.
The "superstep" that we practically impose upon simulations of entropy and emergence is out of accord with our modern understanding of non-regularly-quantizable spacetime. The debuggable Von Neumann instruction pipeline precludes "in-RAM computing" which conceivably does converge if consensus-level error correction is necessary.
The term 'superstep' reminds me of the HashLife algorithm https://en.wikipedia.org/wiki/Hashlife for computing the Game of Life. It computes multiple generations at the same time, and runs at different speeds in different parts of the universe, but only with the purpose of computing CGoL faster, not to introduce any relativity.
I think that was just saying "more space between initial gliders implies a longer time needed to complete construction". There's no Einsteinian relativity to be found here.
(A Doppler effect does show up in Conway's Life sometimes, but that's about as far as we get with analogies to the physical universe...!)
How nonlocal are the entanglements in Conway's game of cellular automata, if they're entanglements with symmetry; conservation but emergence? TIL about the effect of two Hadamard gates upon a zero.
> In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.
> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
> The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).
There are "garden of eden" patterns which can only exist as an initial configuration: there is no pattern which evolves into a garden of eden, hence there can be no constructor capable of building them https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_autom...
I wonder if you could bypass this with a level of indirection.
If the GoL wizards can construct an expanding and initially configurable 'GoL in GoL' grid [1], they could configure the 'garden of eden' as the initial configuration for their 'GoL in GoL' simulation.
It's not the same thing, of course, but it would allow you to run Garden of Eden patterns still starting with just your initial 15 gliders.
To construct a garden of eden pattern, you must first construct the universe :)
Sure, we can build them with "meta cells"; but that's just emulation (the same way a SNES emulator doesn't make my laptop a SNES).
We already have GoL turing machines (with "tape factories" that travel faster than the read/write head); we could likewise use those to emulate GoL with arbitrary input, just by setting up an appropriate "tape". The result is far less pretty though ;)
This is a really good and not at all easy to answer question. The most I can say is that folks earlier this year used some SAT solver equivalent to find notable patterns that cannot be constructed - including a still life and an oscillator https://conwaylife.com/wiki/Unsynthesizable_oscillator_1. This doesn't have much bearing on the probability of constructability for an arbitrary large pattern.
Yeah, I was wondering, with todays computing power, if it were possible to run outrageously large random Life universes and use some sort of software to look for "interesting patterns" (whatever that means).
A lot of discoveries have come from 'soup search' where you start with a random 16 by 16 square and let it evolve. We've run over 156 trillion soups https://catagolue.hatsya.com/statistics. This tends not no produce complicated machines, but rather small components that can then be engineered into larger patterns.
There exists an 'orphan' pattern that cannot arise in any configuration after the first generation. When we look at large patterns, the proportion of them that contain an orphan tends to 1.
On the other hand the smallest known orphan is 12 by 8, and we also know that all still lifes (unchanging patterns) with up to 21 cells can be built.
If you want to see what these 21-bit still lifes look like, their glider construction recipes are all stored online, on Catagolue (no, that's not a misspelling):
Also we can only do the strict still lives (i.e. those which are connected https://conwaylife.com/wiki/Still_life#Strict_still_lifes). We can't necessarily put down a 10-cell still life and an 11-cell still life near to each other.
Heh, not necessarily, that's true, in the sense that all the possible arrangements haven't been tested and shown to be constructible.
On the other hand, pseudo-still-life and quasi-still-life arrangements are much easier to construct on average than strict still lifes with the same number of cells.
I think the consensus is that someone could figure out how to construct any given stable 21-bit configuration. The non-strict cases are just a bit too numerous and not interesting enough, so nobody has gone through and formally checked them off the list.
Seeing behind the curtain on this amazing work does nothing but make me think that the universe we're in has to be some kind of higher level cellular automata, somehow.
This result is really beautiful! At the same time, it's like GoL has been conquered, and in that it leaves me a little sad. But just a little bit. Congratulations!
I'd be surprised if there was a computable density limit for the random plane, just because the system is Turing complete so the answer could easily end up being like Chaitin's contant where it depends on halting problems. For example, note that an infinite random plane will contain, with probability 1, purely-by-chance prebuilt artificial intelligences with goals like "maximize number of blinkers in the plane". Though I guess it's also an open question if such a system could even survive and spread, as opposed to just getting eventually crushed by the surrounding noise.
Right, but I'm hoping it might be possible to prove that the limit exists (even if it's an uncomputable number), as opposed to some oscillating behaviour where the density infinitely often goes up to 70% and then back down to 30% for example.
This "conquering" is all just proof as to the fundamental nature of the Game of Life. It's not hard to imagine a working system of walking proteins and unzipping DNA structures in light of these findings. It really is beautiful.
I think the portion that is fundamental is deeper than game of life itself. Game of life is a rule set with sufficient complexity to get this far, but it isn't the only one. Anything with this class of behavior will support systems including those resembling DNA, the question is at what scale it emerges. If the scale is too big (arguably the scale for the result in this post is too big), it's a less elegant kind of emergence.
Agreed. One aspect of CA which interests me is robustness, the ability of a system to recover from error states.
What's been done with GoL is fascinating, but I think the next emergent layer of fascination for me is universal constructors which can handle a certain level of constant distributed noise or interference. A lot of times people just shrug and say, "well this pattern will always be critical/vulnerable in these locations, and cannot be made robust. But to me that opens up the door for entire classes of patterns which measure, embed and repair state of surrounding entities.
Very interesting. A biological cell is a 3-D self-replicating pattern (or is it 2-D rather?). Does GoL give us some insight into the nature of biological cells?
Definitely! It's hard to summarize that insight in any kind of concise way, though ... The Game of Life universe seems a bit too "fragile" to allow for the kind of emergent complexity that real-world physics supports. We can build self-constructing things like the https://conwaylife.com/wiki/0E0P_metacell , but if anything gets slightly out of place, the usual result is a truly horrific catastrophic explosion.
Conway's Life design work is kind of like building robots out of masses of subcritical uranium. Everything's fine until two robots unexpectedly bump into each other... which means you have to start out with everything very carefully balanced, such that that never happens.
So I guess one fairly obvious insight is that real-world physics supports more reliable and less explosive low-level structures than Conway's Life does, and those low-level structures can then safely be used as the basis for new levels of organization -- atoms -> molecules -> DNA -> bacteria -> eukaryotic cells -> multicellular organisms -> colonies of organisms -> ecosystems.
It's not clear how those higher levels of organization would work in Conway's Life. If they're possible, then they seem to be far beyond our current ability to simulate them -- though there's some recent research vaguely along these lines, about self-replicators that might be able to exert some control over the space around them:
Imagine in 1970 someone reading Martin Gardner's Scientific American article describing 'John Conway's new solitaire game "life"'. Perhaps the reader played around with graph paper plus pencil and eraser to explore what could be done.
"Interesting", they might say. Or, "Fascinating!" even.
And then you show them this article. Just imagine how mind blowing it would be to them.
That was me, reading the original article as a youngster, working out generations on graph paper, etc. The difference is that I have been following the progress of researchers of Life through the years. It’s still astonishing!
Heh, yes, same here more or less -- I wrote an assembly-code Life program for my family's first personal computer (TRS-80 Model I) in the early 1980s, then mostly forgot all about Life for almost two decades ... until it became possible to search the Internet for "Conway's Life". At that point I was completely floored by how much progress had been made since the last time I was paying attention.
Ever since 2001 I've been keeping a close eye on new developments so I don't get surprised like that again.
15 is probably not the minimum. There are some ideas floating around for getting down to 14, and some wilder ideas that might get to 13 or 12.
Below that we'd need some significantly different mechanism that nobody has thought of yet. It doesn't seem likely that anyone will be able to prove that universal construction is impossible with a single-digit number of gliders -- but if a solution exists it might take an omniscient being to find it.
... Or maybe some clever hacker will figure it out tomorrow! That's what happened to get us to the current minimum. We were stuck at a minimum of 32 for quite a while, until Daniel Vargas (MathAndCode) suddenly showed up with a new idea.
I find every interesting the following problem: what is the minimum universal constructor with a linear string, that is, a sequence of gliders that encode information efficiently (not using exponential space, but using a combinatorial combination of N gliders, for O(N) bits)?
Bonus question: can this string be "folded" so that it occupies a radius of O(sqrt(N))?
(now we have a close analogue of DNA! It's fascinating that indicates the universality of DNA and life -- we seem to be somewhat limited universal constructors)
Other questions: are there "Constructor classes" -- non-universal constructors specialized in building a certain "chemistry", a useful subset of all structures? What is the minimum (restricted) efficient contructor capable of building (a) A copy of itself; (b) A Turing machines; (c) Turing machine and construction tapes.
Also I've been thinking about reliability. Is there a constructor that can tolerate a flip ("error") anywhere inside? That can tolerate any single glider collision? Or can tolerate "most" bit flips? An interesting difference between CGoL and our universe is that we live in a thermal and quantum bath. So in a sense (that's up to QM metaphysics) there is inherent randomness in particles, and of course all particles chaotically "wiggle" at positive temperatures (it might be argued CGoL also has wiggle, but in CGoL you can have non-chaotic, periodic large systems -- it's essentially easy to have 0 temperature systems).
I've been playing with simulation of CGoL that have a proportion of random flips each generation. I've been investigating whether interesting structures come out of the "soup" -- this is more interesting, I believe, that just starting from a soup and seeing if something survives (in a deterministic universe), because you can have "multi-step evolution": maybe some small structure comes up, and then random perturbations slowly make more interesting structures emerge -- in a faint analogue to the origin of life, or just faint analogues of chemistry/proto-evolution -- the population of patterns evolves with time. It would be really cool to have a crowdsourced set of long-time simulations of such a field.
Another important open problem related is how to define a 'Life detector' (in Life). A Life detector is an algorithms that given a pattern and a few generations, tells you how complex, interesting, and 'alive' that pattern is. Very fun and significant problem I believe. Together, this means we can run massive crowdsourced searches to understand environments that tend to evolve interesting patterns (although of course anything close to a bona fide lifeform is probably still far out of reach of our computing power, and might benefit from other kinds of analysis)..
It can! A seed constellation for the initial gliders would be possible using the extra debris from the original collision. Without using that debris, there might be a problem reaching far enough without adding extra bits that each double the amount of reaching to get to the right starting point. So I think would be a specialized recipe for a couple reasons.
The principle is the same as von Neumann's "universal constructor", so it doesn't really prove anything we didn't know in theory.
However, von Neumann's design uses a cellular-automaton with many more rules, and those were specifically chosen to help define that constructor (Langton Loops are a more extreme example of choosing rules to make construction easier). In constrast, the rules for Game of Life (GoL) were chosen to be simple and interesting, not fine-tuned for any particular patterns (for an even simpler set of rules, see the Rule 110 cellular-automaton).
We know the GoL is Turing-complete, so it can emulate any computable system; including those other cellular-automata, e.g. von Neumann's universal constructor. Such emulations will typically use a large GoL pattern to represent each emulated cell (e.g. see "life in life"): if we emulate a universal constructor, we can use it to assemble any pattern of those emulated cells. We could also emulate GoL inside some other cellular-automaton, and hence use a universal constructor to assemble any pattern of emulated GoL cells. But the question still remains: can we assemble any pattern of "native" GoL cells? That's what the constructors in the article are doing (at least, for a broad class of patterns).
The rest is a matter of "code golf", trying to make the patterns smaller and faster (and indeed feasible to run on a real PC!)
Heh, oddly enough, the RCT can probably be better thought of as a way of explosively _decompressing_ a glider construction recipe. There are lots and lots of reasonable-sized recipes for constructing different patterns. When you apply the RCT trick to any of them, the cost in gliders always shrinks to 15, but the pattern's bounding box always expands to something gargantuan.
The Life pattern that most evokes DNA and self-replication is another megapattern from several years ago, the 0E0P metacell, which even has a visible "nucleus" for its "DNA":
As a biologist with nearly no physics knowledge, this sort of work seems to have more in common with setting up quantum computers than it does with thinking about self-replication in living organisms, at least in terms of the lack of robustness to environmental noise. Maybe that is just overly metaphorical thinking on my part.
It’s mathematics and computer science, not biology. Nobody is claiming that a setup requiring 2^1500000 units of space to run is anywhere near a realistic simulation of biological processes :)
Nevertheless, it’s a fantastic example of how simple rules can give rise to complex systems.
Yup, the connection to self-replication has showed up mostly in the discussion here, in relation to true self-replicating patterns like the https://conwaylife.com/wiki/0E0P_metacell -- which does have a few vaguely cell-like attributes.
The RCT design is very much a mathematical construct, as opposed to anything with a biological inspiration. And the RCT's ability to construct itself is more of a theoretical afterthought at this point -- the engineering work hasn't been done yet to produce a demo of that kind of thing.
The point is well taken, about the fragility of Conway's Life with respect to environmental noise. That topic has also come up here and there in these comments, e.g., https://news.ycombinator.com/item?id=33797799#33800301
I had a particularly hard time grokking the way the semilator works to reduce pattern size. It's a pretty difficult term to google too, being so similar to the word 'simulator'. Does anyone well versed in GoL-ogy care to share a short ELI5?
Edit: thanks you people for the explanation, makes sense. Nice hack to make it feasible.
Right, as far as I can tell the term "semilator" was coined for this task, so google won't help.
The middle of the RCT pattern where all of the action happens, reads its first bit 2^N generations B.S (before singularity, or before splat, whichever you prefer). Next bit is 2^(N-1) B.S. Next would be 2^(N-2), but this is what the semilator changes.
During the franky enormous gap between 2^(N-1) and 2^(N-2) generations B.S, extra spaceships come in at an orthogonal direction. These have two possible configurations, giving equivalent results to either of the possible bit reads. This accelerates the speed of bit reading, and means that N of millions can be emulated by a pattern with N less than 30. Much less initial distance, much less time. The addition of millions of cells of spaceships doesn't make the overall pattern smaller in an informational sense, just in the scale of time and distance between its constituent parts.
So the full-size pattern works by bouncing a signal back-and-forth between the construction site and an oncoming GPSE. Each time it does this it produces either one or two gliders depending on the positioning of the GPSE. It is these gliders that do the construction.
But the 'recipe' contains 1665791 bits, meaning the signal has to bounce back-and-forth 1665791 times. Because the distance to the GPSE halves every time, it would have to start at a distance of 2^1665791, which is impractically large.
So instead we only have it bounce back-and-forth a small number of times (26), and insert the other 1665765 bits 'manually' by adding streams of 1665765 spaceships that collide near the construction site.
I have a program called LLS that uses SAT solvers to find patterns with specified properties. https://conwaylife.com/wiki/Logic_Life_Search But it only works cell-by-cell, so it can't make big patterns like this.
Hypothesis: if the interaction of any pair of oscillators can theoretically be represented by a single oscillator, this could also be possible with 4 and 6 (larger) gliders, simply because (4 over 2) = 6, (6 over 2) = 15.
The above may only hold in a continuous-valued GoL, or it may not hold at all.
Ha -- when was that written?... Let's see, the original form of the statement showed up in 2012: "Some patterns require a very large number (scores, even hundreds) of glider collisions..."
At that time Andrew Wade had already created the self-constructing Gemini spaceship, which needed 173449 gliders to build ( https://conwaylife.com/wiki/Glider_synthesis#Spaceship_synth... ). The recipe could have been reworked to be a little cheaper, but nobody bothered at the time -- and now it can be done in fifteen gliders instead.
If you want to see the construction happening, I'd definitely recommend the old Gemini recipe over an RCT-based one, though! RCT cuts down the cost in gliders to a minimum, but at a terrible cost in the time you have to wait around to see the completed object.
It's not impossible that we could come up with a way of crashing less than 15 moving objects together to get an alternate RCT pattern.
Gliders are generally considered to be the "lowest common denominator", though, so adding complexity by allowing more types of spaceships isn't usually seen as an improvement.
... It also becomes possible to cheat: I suspect we could put together something like an "RCT8" if we allowed Corderships as well as gliders in the list of allowed moving objects that we start with. (2-engine Corderships' "engines" are switch engines, and we have to build four switch engines to get the RCT reaction started. Could probably just shoot down the extra switch engine with one glider, and go from there.)
Absolutely mind blowing result, looking at the video at the bottom is so hard to comprehend there's no human interaction in this besides setting up the 15 gliders.
At 1:57 it even looks like someone draws a line casually with a mouse.
Probably either this or the 0E0P metacell https://conwaylife.com/wiki/0E0P_metacell, a large pattern which makes copies of itself in a way that mimics another cellular automaton, or Life itself.
