What about a metastable reflector?

[pcallahan]

I am not sure I am using "metastable" precisely, but I like the term. By now the "stable reflector" is old news. We have still life patterns than reflect one or (a lot) more gliders when hit and restore themselves. Before that, we had higher period reflectors like buckaroo.

What about a pattern that seems completely ephemeral and soon vanishes or stabilizes to ash by itself, but when hit by a glider, emits another glider and resets back to its state n generations ago? Of course, unlike a reflector, it can't survive unless it is hit, but it could be the basis of a period n oscillator with a strangely ephemeral engine that only worked by getting hit repeatedly (or gun if you could tease an extra glider out of it).

This is not quite new. The AK47 reaction can be stabilized by sending gliders back into it to remove the unwanted traffic lights. The first stable reflectors that required a glider to come back for reset could be run using a full pipeline of recirculating gliders with lower than single-glider reset time.

The above aren't quite what I mean because they have non-ephemeral components. Something that would qualify, I think, would be a b-heptomino that when hit reappears translated and rotated and can be brought back to the initial position (has anyone found an oscillator that works like this?).

A dubious example would be an unstabilized p30 gun using gliders to shoot out the hives. Perhaps it can be ruled out because the glider only removes something instead of fundamentally changing the reaction.

Even better would be some anonymous explosion that coincidentally works like this and does not need to be rotated back into place. I am not sure such a thing exists, mainly because if it's asymmetric, it's really unlikely to come back into the same place.

Most of the searches I have implemented assume there is some stable product to look for. It's not entirely clear how to go about searching for something like this.

[Moosey]

for instance, one of the prime examples (based on a gun I made earlier today)

Code: Select all

x = 37, y = 30, rule = B3/S23
34bobo$34b2o$4bo30bo$4b3o$7bo$6b2o7bo7b2o$15b3o5b2o$18bo$17b2o$33b2o$
19b3o11bo$18bo3bo8bobo$17bo5bo7b2o$17bo5bo$b2o14bo5bo$o2bo2b2o10bo3bo$
b2o2bobo11b3o$3b2o$3bo25b2o$2obo25bo$o2bob2o23b3o$2b2ob2o25bo4$7b2o$8b
o10b2o$5b3o11bo$5bo7b2o5b3o$13b2o7bo!
[[ STOP 94 ]]

I believe these are called "dependent reflectors".

[pcallahan]

for instance, one of the prime examples (based on a gun I made earlier today)
...
I believe these are called "dependent reflectors".

It's not exactly what I want, as I stated above. What I want is more like a hassler in which the glider turns the reaction into something completely different instead of just removing a component.

To get back to the p30 example, this is also not what I want, but it also illustrates the dependency (I just pieced it together now).

Code: Select all

x = 30, y = 48, rule = B3/S23
25b2o$25b2o5$26bo$26bo$25bobo$10bo13b2ob2o$8bobo12bo5bo$6b2o18bo$2o4b
2o15b2o3b2o$2o4b2o9bo$8bobo5bo$10bo5b3o2$24b2o$23b2o$25bo2$9bo$9bobo$
9b2o$19b2o$18bobo$20bo2$4bo$5b2o$4b2o2$11b3o5bo$13bo5bobo$12bo9b2o4b2o
$2o3b2o15b2o4b2o$3bo18b2o$o5bo12bobo$b2ob2o13bo$2bobo$3bo$3bo5$3b2o$3b
2o!

Maybe a better question (because it's very specific) is if a b-heptomino can be used to reflect a glider and produce another b-heptomino rotated and translated. This is not enough to have an oscillator because you need clear glider paths. I suspect people have looked at this (I might have even at some point) but I don't recall seeing one that works.

ADDED: Above or similar would be cool, but it would not be my fantasy pattern. What I am imagining is a small explosion (confined, say, to a 30x30 box) that left alone vanishes completely. Also, it can be restarted in empty space with a collision of a few gliders. If hit by a glider at exactly the right place and phase, it would emit a glider and reset back to an earlier period. Then it could be sustained indefinitely with a periodic stream of gliders, but would vanish once the stream ended.

I don't think there is a way to rule out the existence of such a thing (and there's probably some humongous universal constructor implementation) but I also doubt there is really a small one that could be found with a search. I'd love to be wrong.

Something like this could even be useful in establishing a movable elbow in a glider stream, though it would be less versatile than a stable component.

Maybe "ephemeral reflector" is a better term. If you remove the requirement that it emits a glider, you get an ephemeral eater, which would still be sort of interesting. If you remove the requirement that it vanishes, it is sort of a messy ephemeral eater.

My guess is that such pattern may exist if it can be moved through a 180-degree or 90-degree rotation (and maybe one is known). I think you'd have to be very lucky to get one that works like the fantasy version, though it might happen in other CA rules.

[Sokwe]

The closest thing I can think of to what you describe are these two dependent reflectors:

Code: Select all

x = 116, y = 39, rule = B3/S23
114bo$114b2o$113bobo2$40b2o$bo37bobo$2bo38bo$3o$65bobo38b2o$66b2o37bob
o$66bo40bo$33b3o$8bo26bo$6bobo25bo$7b2o$74bo$75bo22b2o$27b2o44b3o23b2o
$14bo11bobo69bo$15bo12bo$13b3o2$31b2o68b2o$31bo49bo19bo$23b3o3bobo50b
2o9b3o3bobo$22bo3bo2b2o50b2o9bo3bo2b2o$21bo5bo63bo5bo$21bo5bo63bo5bo$
21bo5bo63bo5bo$22bo3bo65bo3bo$23b3o67b3o$101b2o$101b2o$26bo$22b2obobo$
20bo2bob2o$20b2o2bo$25bobo$26b2o!

They still rely on stable components, but the exact nature of the reaction is highly dependent on the collision of the glider. These were found by starting with the honey-farm + eater combination that would eventually be used in the Snark:

Code: Select all

x = 12, y = 9, rule = B3/S23
10b2o$10bo$2b3o3bobo$bo3bo2b2o$o5bo$o5bo$o5bo$bo3bo$2b3o!

Your problem seems to involve two steps: (1) releasing or reflecting a glider and (2) restoring the original reaction. This HF+eater combination accomplishes the first step very quickly, and since the honey farm is so common there's a decent chance of achieving the second step.

I tried many other catalyst combinations with this starting reaction and only found these two reflectors (but my search was far from exhaustive, so someone should definitely try this idea again). To find something similar I think you would need a similarly compelling starting reaction.

[pcallahan]

The closest thing I can think of to what you describe are these two dependent reflectors:

Thanks! I haven't seen those before. The stable components make them not quite ideal, but it's the same idea.

I was just experimenting with bheptominos and found this collision that turns a bheptomino 90 degrees in 60 steps (which makes it compatible with p30 technology, and thus fairly useless). Maybe it's known, but it's new to me. Here is an oscillator using p240 guns to keep it rotating (I was stunned to find the smallest p240 gun is not based on the queen bee shuttle; I've been away a long time.)

Code: Select all

x = 114, y = 114, rule = B3/S23
88b2ob2obo$87bobobob2o$88bo5$91b2o5b2o$91b2o5b2o2$94b2o$94b2o3$7b2o$7b
2o62b2o$26bo44b2o12b2o$24b2obo56b2ob2o$10b2o12bo3bo38b2o5b2o8b2ob2o$2o
8b2o10bo5bo38b2o5b2o10b3o$bo20bo5bo2bo$o6b2o13bo7bobo$2o5b2o15b4o2b2o$
88bo3bo$24b4o2b2o54b2obobob2o$22bo7bobo37b2o13bo3bobo3bo$22bo5bo2bo38b
o13bo3b2ob2o3bo$22bo5bo39bobo13bobo7bobo$24bo3bo38bobo15bo9bo$24b2obo
35b2o3bo$26bo36b2o23b2ob2o$8b2o77bobobobo$8b3o77bo3bo$7bo2bo$7b3o$7b3o
$26bo$27b2o$18b2o6b2o$18b2o2$15b2o43bobo$15b2o8bo34b2o$25b3o33bo$28bo$
18b2o7bobo3b2o$18b2o8bo3b2o$34bo2$29b2o$29b2o3$60b3o$59bo2bo$59b2obo8$
83b2o$83b2o3$85bo8b2o$84bobo7b2o$85bo$86b3o$88bo8b2o$97b2o2$94b2o$94b
2o3$104b3o$104b3o$103bo2bo$21bo3bo77b3o$19b2obobob2o76b2o$18bo3bobo3bo
20b2o33bo$17bo3b2ob2o3bo15bo3b2o31b2obo$17bobo7bobo14bobo35bo3bo$18bo
9bo14bobo34bo5bo$43bo36bo5bo2bo22bo$21b2ob2o16b2o36bo7bobo20bobo$20bob
obobo55b4o2b2o22b2o$21bo3bo$82b4o2b2o15b2o5b2o$80bo7bobo14b2o6bo$80bo
5bo2bo22bo$25b3o10b2o5b2o33bo5bo15b2o8b2o$25b2ob2o8b2o5b2o35bo3bo15b2o
$25b2ob2o52b2obo$27b2o12b2o41bo$41b2o62b2o$105b2o3$18b2o$18b2o2$14b2o
5b2o$14b2o5b2o6$19b2obo$19bob2o!

The collision produces a glider, but unfortunately, it's on the input path, so I used eaters to remove them.

[Sokwe]

Here's a p436 reaction from jslife (osc-supported/s0436.lif) that is similar to your B-heptomino rotator, but the output gliders do not collide with the input:

Code: Select all

x = 386, y = 404, rule = B3/S23
bo$2bo$3o71$346bobo$346b2o$347bo34$110bo$111bo$109b3o71$237bobo$237b2o
$238bo30$212bo5bo$211b3o4bo$210bo2bo$210bobo$211bo$217bo$215b2o$216bob
o$217bo33$274b2o$274bobo$274bo35$146b2o$147b2o$146bo70$383b2o$383bobo$
383bo35$37b2o$38b2o$37bo!

Here's a p40 double dependent reflector based on a reaction by Ivan Fomichev:

Code: Select all

x = 62, y = 61, rule = B3/S23
60bo$59bo$59b3o8$50bo$49bo$49b3o5$30bo$30b3o$33bo$32b2o6bo$39bo$27b2o
10b3o$21b2o4bobo$21bobo3bo16b2o$23bo19bobo$23b3o17bo$26bo3b3o8b3o$23b
3o3bo3bo6bo$23bo4bo5bo6b3o$21bobo4bo5bo8bo$21b2o5bo5bo8bobo$29bo3bo10b
2o$30b3o2$33b2o$33bo$34b3o$20b3o13bo$22bo$21bo8$10b3o$12bo$11bo8$3o$2b
o$bo!

And finally a p34 double dependent reflector by Nicolay Beluchenko on June 12, 2010 (also in jslife):

Code: Select all

x = 65, y = 40, rule = B3/S23
bo$2bo$3o7$10bo$8bobo$9b2o6$18bo$19bo13b2o$17b3o10b2ob2o$30b2ob2o10b3o
$30b2o13bo$46bo6$54b2o$54bobo$54bo7$62b3o$62bo$63bo!

[pcallahan]

Here's a p436 reaction from jslife (osc-supported/s0436.lif) that is similar to your B-heptomino rotator, but the output gliders do not collide with the input:

Thanks. I like those, particularly the third one.

BTW, one or all (?) of the gliders in the bheptomino rotator can be rescued with buckaroos. This is as far as I got with it tonight.

Code: Select all

x = 161, y = 135, rule = B3/S23
12$20bob2o$20b2obo4$54b2o$54b2o$15b2o5b2o$15b2o5b2o96b2o$69bo50b2o$19b
2o48b2o30bo2bo$19b2o47bobo29bo4bo$99bo5bo11b2o$98b2ob2o14b2o8b2o$97bo
7bo21bo$42b2o52bo2b3obobo14b2o6bo$29bo12b2o53b3obob2o15b2o5b2o$27bobo
22b2o3b2o$27b3o9b2o5b2o6b3o40b3obob2o$27bo11b2o5b2o5bo3bo38bo2b3obobo$
54bobo40bo7bo3b3o$55bo42b2ob2o7bo$99bo5bo4b3o$18b2ob2o3b2ob2o69bo4bo$
17bo5bobo5bo20b2o47bo2bo$22b2ob2o26bo$20bo7bo21b3o$17bo2bob2ob2obo2bo
18bo$18bo3bo3bo3bo$19b2ob2ob2ob2o66b2o$20bo2bobo2bo67bo$21bobobobo66bo
bo$22bo3bo66bobo13b2o$89b2o3bo14b2o$89b2o$112b2o$112b2o3$109b2o$109b2o
6$51bo$51b3o$54bo$53bo$53bo2bo$57bo$55bobo$56bo52b2o$109b2o2$53b2o3b2o
$53bobobobo$54b5o$55b3o$56bo$109bo$77bob2o27b3o$77bo2bo26b5o$77b3o26bo
bobobo$106b2o3b2o2$55b2o$55b2o52bo$108bobo$104bob3o$104bo2bobo2bo$104b
obo5bo$111bo$78bo33b3o9bo3bo$78b2o34bo8bobobobo$77bobo44b2ob2o2$90bo$
91bo20b2o6b2o9b2o$89b3o19b2o7bob4ob4obo$55b2o56bo7bo3bobo3bo$55b2o64bo
3bobo3bo$122b3o3b3o2$52b2o$52b2o$75b2o21b2o3b2o5b2o$55b2o14bo3b2o21bob
o2b2o5b2o$55b2o13bobo27bo$69bobo28b2o5b2o$69bo37b2o$68b2o3$130b2o$117b
o12b2o$65bo2bo46bobo$64bo4bo45b3o9b2o5b2o$53b3o7bo5bo45bo11b2o5b2o$55b
o6b2ob2o$38bo15b3o4bo7bo$37bobo20bo2b3obobo$37b2o22b3obob2o2$37b2o5b2o
15b3obob2o58bob2o$37bo6b2o14bo2b3obobo57b2obo$38bo22bo7bo$37b2o8b2o13b
2ob2o$47b2o14bo5bo$64bo4bo$65bo2bo$44b2o$44b2o!

[dvgrn]

I don't think there is a way to rule out the existence of such a thing (and there's probably some humongous universal constructor implementation) but I also doubt there is really a small one that could be found with a search. I'd love to be wrong.

I will probably be able to successfully resist trying to code this up, but I think my angle of attack would be to start with a list of all the distinct long-lasting three-glider sparks (from 2718281828's database), in descending order by lifespan.

Shoot all possible gliders-to-be-reflected (let's call them R-gliders) at the three-glider collision, and retain only the collisions that produce a clean glider output (call them O-gliders). For each O-glider reaction, make a hashtable containing the apgcodes for every stage of the spark from the original 3-glider collision to interaction with the R-glider. Then track each O-glider backwards in time to its first appearance, remove it, and then check apgcodes for the remaining spark (if any) against the hashtable.

That certainly wouldn't be a fast search to run to completion, but it seems like it would run through cases quickly enough to have some hope of finding a match, somewhere out there. Could maybe start with the longer-lasting two-glider vanish reactions before moving to 3G. The search might fail to find something good, e.g., in cases where the collision makes two separate dying sparks that last equally long. But it seems like that might be a relatively rare case.

[Scorbie]

@dvgrn @pcallahan
Another approach would be simulating a glider stream whose period is the one you would like to search for, and hit it with a random soup to see if it stabilizes into some reflector.

[pcallahan]

BTW, since this thread is getting renewed attention, I am still wondering if there is any historical record of this 60-step bheptomino turner using a glider collision that I mentioned above. (Stabilized here into a p240 oscillator with recirculating gliders).

This is by definition "not interesting" since p30 multiples are so easy to achieve, but it is interesting to me by virtue of being so unlucky. There aren't a lot of these kinds of turning collisions. I'm surprised I did not get a multiple that could be turned into a more "interesting" oscillator period (all moot with Herschels anyway).

Code: Select all

x = 182, y = 174, rule = B3/S23
71b2o3b2o$71b2o2bob3o$75bo4bo$71b4ob2o2bo$71bo2bobobob2o$74bobobobo$
75b2obobo$79bo2$65b2o$66bo7b2o$66bobo5b2o$67b2o5$84bo$85b2o$77b2o5b2o$
77bo$78b3o$80bo6$26b2o3b2o$26b2o2bob3o$30bo4bo$26b4ob2o2bo$26bo2bobobo
b2o10bo$29bobobobo9b5o14b2o$30b2obobo8bo5bo13bo$34bo9bo2b3o12bobo$43b
2obo15b2o$20b2o21bo2b4o69bo$21bo7b2o13b2o3bo3b2o62b3o$21bobo5b2o15b3o
4b2o61bo$22b2o22bo69b2o$43b2obo$43b2ob2o$124b2ob2o$125bob2o$54b2o69bo$
55bo61b2o4b3o$32b2o18b3o62b2o3bo3b2o$32bo19bo69b4o2bo$33b3o72b2o15bob
2o$35bo71bobo12b3o2bo$107bo13bo5bo$106b2o14b5o$95b3o26bo$95bobo$95b3o$
95b3o20b2o3b2o$95b3o20b2o2bob3o$4bo90b3o24bo4bo$2b5o14b2o72bobo20b4ob
2o2bo$bo5bo13bo73b3o20bo2bobobob2o$bo2b3o12bobo99bobobobo$2obo15b2o61b
2o38b2obobo$o2b4o8bo65b2o43bo$b2o3bo3b2o2b2o67bo$3b3o4b2o2bobo95b2o$3b
o109bo7b2o$2obo109bobo5b2o$2ob2o109b2o3$11b2o78b2o$12bo52bobo22bo2bo$
9b3o54b2o21bo2bo$9bo56bo21bo$88bo2bo3b2o27b2o$54bo4bo28bobo6bo26bo$52b
2ob4ob2o34b2o27b3o$54bo4bo37b2o28bo7bobo$68bo23bo43b2o$69b2o23bob2o38b
o$68b2o23b2ob2o$96b2o5$73bobo18b2o$73b2o19b2o$74bo6$54bo67bo4bo$54b3o
63b2ob4ob2o$57bo64bo4bo$56b2o$90bo81bo$88b2o80b3o$89b2o78bo$169b2o3$
66b2o109b2ob2o$59b2o5bobo109bob2o$59b2o7bo109bo$68b2o100b2o4b3o$170b2o
3bo3b2o$55bo119b4o2bo$54bobob2o101b2o15bob2o$54bobobobo99bobo12b3o2bo$
53b2obobobo2bo20b3o73bo13bo5bo$54bo2b2ob4o20bobo72b2o14b5o$54bo4bo24b
3o90bo$55b3obo2b2o20b3o$57b2o3b2o20b3o$84b3o$84bobo$57bo26b3o$55b5o14b
2o$54bo5bo13bo$54bo2b3o12bobo71bo$53b2obo9bobo3b2o72b3o$53bo2b4o5bo2bo
60bo19bo$54b2o3bo3b6o58b3o18b2o$56b3o4b2o61bo$56bo69b2o$53b2obo88bo$
53b2ob2o86b2o$126bo7b2ob2o5bobo$125b2o8bob2o$64b2o56b4ob2o6bo22b2o$65b
o56b2o2b2o2bob4o15b2o5bobo$62b3o56b2obo2b2o7b2o13b2o7bo$62bo59bo2bobo
2bo2b3o2bo21b2o$118b2o2bo4b2o6bob2o$117bobo12b3o2bo9bo$117bo8bo4bo5bo
8bobob2o$116b2o5bo2bo5b5o9bobobobo$123bobo8bo10b2obobobo2bo$146bo2b2ob
4o$146bo4bo$147b3obo2b2o$149b2o3b2o6$101bo$101b3o$104bo$103b2o7$113b2o
$106b2o5bobo$106b2o7bo$115b2o2$102bo$101bobob2o$101bobobobo$100b2obobo
bo2bo$101bo2b2ob4o$101bo4bo$102b3obo2b2o$104b2o3b2o!