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If you run them in B37c/S23, the pre-loaf stabilizes quickly, but the pi takes a while — and some space. It needs 110 generations to settle down.
If you run them in B37e/S23, though, the pre-loaf just becomes a loaf immediately and the pi stabilizes much more quickly, in only 23 generations, and without spreading out so much.
That lame explanation seems even more lame when you consider this: The non totalistic rule B37c/S23 (meaning birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor in the corner of the neighborhood) is explosive, but B37e/S23 (birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor on the edge of the neighborhood) isn’t.
Here’s an even more perplexing (to me, at least) instance of different CA behavior under similar-but-different rules. Consider this 32 x 32 soup: B36/S23 is a Life-like rule sometimes called HighLife. Many objects behave the same way as in Life; in particular, blocks, loaves, boats, and beehives are still lifes; blinkers are p2 oscillators; gliders are c/4 diagonal spaceships. So after 378 generations in B36/S23 when that soup looks like this, it’s stabilized: B38/S23 has no nickname I know of. Under that rule, the same soup stabilizes in 483 generations: And in B37/S23… here’s what it evolves to after 10,000 generations:Population 17,298 and growing, presumably forever.
Fairly typical. I’ve seen some soups take several thousand generations to stabilize in B38/S23, and I’ve seen a few — very few — stabilize in B37/S23. But most soups stabilize in 1000 generations or so in B36/S23 and B38/S23… and almost all soups explode in B37/S23.
Does that make any sense to you? Explain it to me, then.
It surprises me how hard it can be to guess what kind of behavior a given CA rule will produce. There are some things that are fairly obvious. For instance, under a rule that doesn’t include births with fewer than 4 live neighbors, no pattern will never expand past its bounding box. (Any empty cell outside the bounding box will have no more than 3 live neighbors, so no births will occur there.)
But beyond a few observations like that, it’s hard to predict. At least for me.
Consider the rule B34/S456, for a semi random example. Start with a 32 by 32 soup at 50% density: Then let it run for 1000 generations. It expands to a blob 208 by 208 in size, population 21,132:But change the B34/S456 rule to B3/S456 or B4/S456 — removing one number or the other from the birth rule — and either way, the same initial configuration dies.
Here’s another big spaceship evolving from a soup. The rule here is B358/S23, and the soup has D2_+1 symmetry.
x = 143, y = 41, rule = B358/S23 47b2o$49bo$51b2o$45bo7bo32bo$b2o21bo20bob3o36bo35b3o$o2bo19bobo24bo3bo 30bobo34bo14b2o$bobo18bo3bo14bobo5b2o32bo5bo32bo4bo12b2o$5bob3o12bo3bo 17b3obo2b4o2bo24bo7bo17bobo12bo12b2obo2bo$7bo2bo12bobo15bo3b2ob2o3bo3b o25bobobobo18bobo14bo2bo4bo3bob2obo$3b5ob2o13bo15bo2b3o11b2o25bo3bo35b 2o2bo4bo3bo2b3o$2bo2bo36bo3b2o3b2o4bobo19b2o34b2o6bo4bo4bo$2bo2b2o5b2o 30bob2o8bo2bo19b2o4bobo20bobo4b2o6bo4b2o4bo2bo$6bo6b2o2bo22b3ob2o2bo7b o27b2ob2o19bobo13bo4bo6bo$4bob2o4b2o2bo3bo23b2o2bo7bobo26b3o37bo$2bobo 12bobobo24bobobo6bo28bo39bo$2bobo4bo7bob4o25b2o$4bo3bo3b2o4b2obo26b2o$ 8b3ob2o3b2obo$18bo4$18bo$8b3ob2o3b2obo$4bo3bo3b2o4b2obo26b2o$2bobo4bo 7bob4o25b2o$2bobo12bobobo24bobobo6bo28bo39bo$4bob2o4b2o2bo3bo23b2o2bo 7bobo26b3o37bo$6bo6b2o2bo22b3ob2o2bo7bo27b2ob2o19bobo13bo4bo6bo$2bo2b 2o5b2o30bob2o8bo2bo19b2o4bobo20bobo4b2o6bo4b2o4bo2bo$2bo2bo36bo3b2o3b 2o4bobo19b2o34b2o6bo4bo4bo$3b5ob2o13bo15bo2b3o11b2o25bo3bo35b2o2bo4bo 3bo2b3o$7bo2bo12bobo15bo3b2ob2o3bo3bo25bobobobo18bobo14bo2bo4bo3bob2ob o$5bob3o12bo3bo17b3obo2b4o2bo24bo7bo17bobo12bo12b2obo2bo$bobo18bo3bo 14bobo5b2o32bo5bo32bo4bo12b2o$o2bo19bobo24bo3bo30bobo34bo14b2o$b2o21bo 20bob3o36bo35b3o$45bo7bo32bo$51b2o$49bo$47b2o!
It goes left to right (right to left in the original soup) at speed 36c/72.
Again, the way this comes about is through development of a small seed. In this case at generation 83 you get a couple of these objectswhich in four generations recur, inverted, but with some debris.By itself, this seed becomes a 36c/72 puffer.But two of them, mirror images at just the right separation, have their smoke trails interact in such a way as to extinguish them, and the result is a spaceship. If you start with this pair
Hot on the heels of Rich’s p16, here’s a period 18 oscillator, once again found using apgsearch. It even bears a family resemblance to the p16: D2_+1 symmetry and shuttle behavior. But… it doesn’t work in Life (B3/S23). It works in B357/S23.
x = 13, y = 5, rule = B357/S23 b2ob2ob2ob2ob$o4bobo4bo$5bobo5b$4bo3bo4b$3b3ob3o3b!
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.
Tim Coe has found a symmetrical spaceship with a new speed, 3c/7 (left, below) after a series of searches that took a total of "one or two months". At 29 cells wide, it is the minimum width odd symmetric spaceship -- an exhaustive width 27 search was run some time ago by Paul Tooke. The author seems to have officially chosen a name of "Spaghetti Monster" for the new 3c/7 spaceship.
Matthias Merzenich has pointed out that two of these spaceships can support a known 3c/7 wave (right, below).
#C 3c/7 FSM spaceship: Tim Coe, 11 June 2016
#C Period-28 3c/7 wave found by Stephen Silver on Feb. 2, 2000
x = 187, y = 139, rule = B3/S23
#C [[ AUTOFIT AUTOSTART GPS 4 ]]
This is the twenty-second spaceship velocity constructed in Conway's Life -- counting each of the four infinite families of spaceships (Gemini, HBK, Demonoid, Caterloopillar) as one velocity each.
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: 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: 39 generations later, and several cells to the south, this becomes an r pentomino: And another 48 generations later, quite a bit further south, it becomes a herschel.That herschel gets sucked up into a downward conduit (purple line below). It gets converted into two parallel southwest-going gliders. One 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:Again 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.
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:What 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:
Two 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.