Big natural ship in B358/S23

Here’s another big spaceship evolving from a soup. The rule here is B358/S23, and the soup has D2_+1 symmetry.Screen Shot 2016-07-17 at 7.06.44 AM

x = 143, y = 41, rule = B358/S23

It goes left to right (right to left in the original soup) at speed 36c/72.

Again, the way this comes about is through development of a small seed. In this case at generation 83 you get a couple of these objectsScreen Shot 2016-07-17 at 12.09.26 PMwhich in four generations recur, inverted, but with some debris.Screen Shot 2016-07-17 at 12.09.44 PMBy itself, this seed becomes a 36c/72 puffer.Screen Shot 2016-07-17 at 12.09.02 PMBut two of them, mirror images at just the right separation, have their smoke trails interact in such a way as to extinguish them, and the result is a spaceship. If you start with this pairScreen Shot 2016-07-17 at 12.24.37 PM

x = 9, y = 29, rule = B358/S23

you end up with a ship, plus a couple of blinkers.

These puffer seeds crop up fairly regularly — they develop into puffers 214 times out of 5,274,253,500 C1 soups — though this looks like the first time two of them have produced a spaceship. This symmetric object isn’t the only way to kill the puffer smoke, though. Here are six other ships produced by placing two puffers at various relative positions and phases. Undoubtedly there are lots more.Screen Shot 2016-07-17 at 7.38.24 AM

x = 363, y = 80, rule = B358/S23


Big and natural and (5,2)c/190

Generally speaking the larger a Life object is, the less likely it is to arise from a random soup. Going by the current Catagolue census, for instance, gliders arise in Life 684 times as often as lightweight spaceships, which are seen 3.8 times as often as middleweight spaceships, which turn up 5.8 times as often as heavyweight spaceships. Or look at the statistics page: All of the still lifes of size up to 13 have arisen, and 616 of the 619 size 14 still lifes, but only 1256 out of 1353 size 15, 2484 out of 3286 size 16, 4199 out of 7773 size 17 and so on… to only 7769 out of 4,051,711 still lifes of size 24.

Now, the smallest known Life spaceship that isn’t a glider, a *WSS, or a flotilla of *WSSs is the loafer, which has population 20 in a 9 by 9 bounding box. For comparison the HWSS is 13 cells in a 7 by 4 bounding box. There are 2^81 possible states for a 9 by 9 box versus 2^28 for a 7 by 4, or 2^53 times as many — about 9 quadrillion. From that point of view it’s not too surprising no loafer has evolved naturally from a soup so far. Only 111 trillion objects have been seen so far, after all.

So what are the odds of natural occurrence of a population 49 spaceship in a 47 by 17 bounding box? Incomprehensibly tiny, you would think — never in many times the lifetime of the universe would it happen.

Well, so you might think, anyway. Evidently that thinking’s not entirely correct:Screen Shot 2016-07-09 at 6.55.05 PMBecause that pattern evolved, not in Life but in the Life-like B38/S23, from a random D2_+2 soup, on my computer in the past few hours. It may not look like much… but it’s a spaceship. A spaceship which in 190 generations travels obliquely, 5 cells up and 2 cells to the left.

I was pretty excited by this discovery, until I checked the census for B38/S23 C1 soups, and saw that a bunch of p190 ships have been found already, the first by David S. Miller last April. Then I found out, well, re-found out these ships had been discussed extensively in a forum thread shortly after that. A thread which I read. And forgot about.

All these ships are based on the same fundamental engine. Take a look at the part on the right of the above ship. Run just that for 190 generations and you get this:Screen Shot 2016-07-09 at 7.28.16 PMThree of the pieces of the original pattern come back, shifted by (5, 2). The fourth piece gets changed. So this is a near spaceship by itself.

Now if you look at the part on the left and run that 52 generations you get:Screen Shot 2016-07-09 at 7.31.34 PMThe same thing as the right half at generation zero, minus the boat. So the ship consists basically of two out of phase copies of a single engine, plus a boat, evolving in such a way that the interaction between them makes up for the lack of a boat for the left engine, and changes the evolution of the 7-bit piece in both engines to make it recur in 190 generations.

Another way to look at it: Start with an R pentomino and a boat:Screen Shot 2016-07-09 at 8.34.21 PMAfter 192 generations you get this:Screen Shot 2016-07-09 at 8.35.04 PMAnd if you add a second R pentomino in just the right place at just the right phase, it’ll react with the first R and boat in just such a way as to make a spaceship. Seems kind of miraculous, but in fact there several ways to accomplish it. According to David S. Miller, at least 692 ways. Of which, as of today, apparently 11 have turned up in soup searches. There are also another 120 combinations of two Rs and a boat that produce puffers, rakes, and so on.

So a 47 by 17 spaceship evolving naturally? Not quite as astronomically unlikely as it looks. A remarkable system, though, and there’s nothing like it known in Life. Yet.

Rich’s p18

Hot on the heels of Rich’s p16, here’s a period 18 oscillator, once again found using apgsearch. It even bears a family resemblance to the p16: D2_+1 symmetry and shuttle behavior. But… it doesn’t work in Life (B3/S23). It works in B357/S23.Screenshot - 070816 - 11:54:22


x = 13, y = 5, rule = B357/S23

Rich’s p16

Here’s a new period 16 oscillator:p16

The stubby wiki page says I discovered it, which is silly of course: all I did was install apgsearch and run it looking at D2_+1 soups in standard Life (B3/S23). I was asleep when it found this and woke up to find it’d been tweeted, retweeted, reported on the forum, used to make a smaller p48 gun, deemed awesome, and written up on the wiki.


Gun show (part 4)

The p61 gun is quite different, though it too makes use of herschel tracks. To get a better picture of what’s going on, here it is with history turned on: the blue cells are ones that were live at some point:Screen Shot 2016-04-15 at 11.45.37 PM To start with let’s zoom in to the upper right corner. You see a couple of lightweight spaceships moving west to east, and the spark on the one near the center is about to perturb a southwest-going glider:Screen Shot 2016-04-15 at 11.48.49 PM 39 generations later, and several cells to the south, this becomes an r pentomino:Screen Shot 2016-04-15 at 11.49.24 PM And another 48 generations later, quite a bit further south, it becomes a herschel.Screen Shot 2016-04-15 at 11.50.09 PMThat herschel gets sucked up into a downward conduit (purple line below). It gets converted into two parallel southwest-going gliders. marked1One of these (red line) gets bounced off a series of 90° reflectors, snarks again like the ones we saw in the p58 gun, ending up at the top where it becomes (a later version of) the glider we saw at the start, getting converted to an r pentomino. The other one (yellow line) gets kicked right by an interaction with a herschel loop (orange line). I presume this very complicated reflector is used because it can reflect one glider without messing up the parallel stream (and I’m guessing a similar loop can’t be made to work at p58, hence the different solution used in that gun?). Not quite sure. Anyway, it then gets bounced a couple more times before ending up at the top of another section of the gun, where it’ll share the other glider’s fate: getting converted by a lightweight spaceship into an r pentomino, then a herschel, to feed another herschel track.

Here’s the middle stage:marked2Again a downward track (purple) produces two parallel gliders (red and yellow). Again the yellow one gets bounced by a herschel loop to the top of a third stage for yet another r pentomino conversion. As for the red one, it bounces a bunch of times up to the top left where it runs into… something.

The third stage yet again has a downward track producing two gliders, one bounced off a loop and the other just kicked around with snark reflectors.

marked3Both of these gliders arrive at the proper phase, spacing, and direction to interact with each other and with the red glider from the second stage to produce, of course, a lightweight spaceship. And the spaceship travels east, perturbing three gliders as it goes but remaining unscathed itself. If this were all, you’d have a p61 lightweight spaceship gun, but instead there are a few more still lifes at the right edge which convert the lightweight spaceships into gliders. And there you are. A p61 glider gun.

Gun show (part 3)

Next (in reverse chronological order, but it makes sense to me) the p58 gun. I think “AbhpzTa”‘s version is pretty much the same thing as “Thunk”‘s (based on Matthias’s component), but in such a compact form it’s harder to see what’s going on. Here’s “Thunk”‘s:p58What we have here is not one but two herschel loops, both period 58. The top one is connected to the bottom one by another herschel track, and there’s a reaction that duplicates the herschels in the top track, sending one on its way around the loop again and another down toward the bottom track. But this doesn’t happen without input: it needs a period 58 glider stream. Where does it get one? Patience…

Where the cross track feeds into the bottom loop, the two herschels collide and out of the collision come not one but two gliders every 58 generations, heading southeast. They’re pretty close together. Too close, in fact, because we want to reflect one stream 90°, and that can’t be done without messing up, and getting messed up by, the other stream. So we use this cute reaction:

Screen Shot 2016-04-15 at 8.05.24 PMTwo perpendicular glider streams go in, two go out. Same directions, but displaced. Meanwhile the parallel glider stream just squeaks by. That puts the two streams further apart, but not by enough, so we do the same thing again. Now they’re separated by enough.

(But wait, that reaction needs a second glider stream, going northeast, to work. Two of them to make it work twice. Where do we get two? Patience…)

One of the two not-so-close-together parallel streams gets kicked to the right, and the other to the left, with this apparatus. It’s called a snark, and it’s by far the smallest and fastest stable glider reflector known. Here you can see a glider coming in from the northwest and another on its way out to the northeast.

Screen Shot 2016-04-15 at 8.14.17 PMThe stream that gets kicked to the left gets kicked left again, using a different, larger, oscillatory object, I think in order to get the correct glider phase or position for the outgoing stream. It’s now heading northwest, back toward the herschel loops — in particular, toward the intersection of the upper loop with the downward connector. That’s right, it becomes the glider stream needed to make the herschel duplicator work.

The other stream gets kicked to the right three times — now it’s heading northeast, crossing perpendicularly the two parallel streams, and it runs into a block at just the right time and phase to make the stream displacer work. Then it gets bent to the right four more times, putting it perpendicular to the two parallel streams again, so it can make the other stream displacer work. We didn’t need two new streams after all for the displacers, or even one… the displaced stream and both of the auxiliary streams are in fact all the same stream! Reminds me of a Heinlein story for some reason.

Finally, in the version “Thunk” posted, there’s one more kick to the right sending this stream off to the southeast to become the gun’s output, but there’s no need to do that; it could just continue to the northeast. And that’s the gun.Screen Shot 2016-04-15 at 8.43.32 PM

Unlike, say, the Gosper glider gun, which just needs two queen bees and two blocks to get started, this one relies on glider streams to work; it regenerates those streams itself, but it has to be built in the first place with glider steams to get started with. What happens, I wondered, if you erase one of the gliders heading into the herschel duplicator? Does it just create a gap in the output glider streams, or does something more serious occur? Something more serious, it turns out.



Gun show (part 2)

For me the easiest of these guns to comprehend is the p57 one, so let’s work our way up to that.

Start by considering the heptomino that has acquired the somewhat erroneous name of herschel. It arises, along with some debris, early in the evolution of the r pentomino and spits out a glider, which is how the glider was discovered back in 1970. Without the r pentomino’s debris, the herschel stabilizes in 128 generations leaving two blocks, two glders, and a ship. But a notable thing about the herschel is that its evolution isn’t centered around its original position; most of the action happens to one side. Here’s a herschel (in red) and its stable state (in green), with the cells that otherwise were live in blue:herschelNotice how, aside from the gliders, most of the action happened off to the left of the initial state.

So you can use a hershel over here to make something happen over there. In particular, you can imagine setting up some still lifes that will interact with the herschel in such a way as to make another herschel happen over there — while preserving the still lifes. Like this. Start with this state:conduit0 and 117 generations later you have this state:conduit117plus a glider off to the southwest, which can be disposed of with another eater if you want. The eaters and snake perturb the herschel without getting injured; the block gets destroyed but is then remade in the same place.

So that’s very cool. It’s called a conduit. You could put a second conduit to the right of the first, positioned so the herschel output by the first conduit is in just the right place to be input to the second one, and at generation 234 the herschel will appear to the right of the second conduit. And of course you could put a third conduit, and a fourth, and a fifth, and so on, and transport that herschel as far as you like in a straight line, popping up every 117 generations.

What’s a little less obvious is that if you can contrive a way to feed such a track of conduits a periodic series of herschels, they’ll get transported just fine even if they turn up more often than every 117 generations. In fact, this conduit is ready to accept its next herschel as frequently as every 63 generations.

Furthermore, you’re not limited to straight lines. There are other conduits that will transport a herschel around a corner. Some conduits do a mirror flip of the herschel, some don’t. Some even manage to send a herschel backwards.

So with some ingenuity, you can set up a track of conduits that goes around four corners and connects back on itself in a loop! All of this was pioneered by David Buckingham in the 1990s, and his period 61 loop was the first period 61 Life oscillator discovered.

Since then there’s been lots of herschel conduit exploration going on, involving discovery of both new conduits and new ways to make use of them. And that’s what’s going on in the p57 gun; you have a loop, built of conduits that can accept herschels every 57 generations. Unfortunately you can’t just leave out one of the tub-with-tail still lifes that eats the gliders emitted by the herschels without breaking the conduit, but hanging off the bottom of the loop is a crazy lump of a period 3 oscillator. It hassles the nearby conduit into spitting out a glider while preserving the conduit action, and, boom, p57 gun.p57