Self-repairing pattern

[Tim Hutton]

Do we know of any spaceships that can sustain damage (adding or deleting one or two cells) and continue? GoL patterns are usually so brittle but there are examples of self-repair:

A block will reform:

oo
oo

if damaged like this:

o.
oo

So obviously a spaceship that makes blocks might be robust to such damage, but that's a bit trivial. Is there any example where the damage is on some part that is changing and wouldn't just die out anyway?

[dvgrn]

Do we know of any spaceships that can sustain damage (adding or deleting one or two cells) and continue? Is there any example where the damage is on some part that is changing and wouldn't just die out anyway?

The things I thought of immediately are mostly in the "die out anyway" category -- obviously, sparks on an MWSS or HWSS or Schick engine or what have you. Corderships have all kinds of modifiable parts toward the back, and some changes will emit gliders or do other interesting things.

There are spaceships that "remember" minor changes, let's say when they're hit by a glider -- the period of their exhaust might change permanently, or they might go from spaceship to puffer and back again. Some of David Bell's high-period rakes are built with these kind of "toggle ships", I believe.

I haven't dared to look, but I suspect there are lots of ways to shoot a "virus" glider or glider salvo at a Gemini spaceship. The gliders would insert themselves directly into the "DNA" of the spaceship without destroying it. They might encode a more efficient way of running the destructor arm, for example. Or there's lots of space to add extra gliders on the unused parts of the tapes (a lot of the time only one construction arm is running). So you could build something and then optionally destroy it again...!

But I suspect I'm getting rather far afield from your original question! What line of thought led you to ask it?

[Tropylium]

I've seen some "near-Heisenburp" reactions where a glider's tail or even parts of the body disintegrate for a while, but the tetromino engine still keeps going at c/4 and the glider eventually reforms. A two-tick and a three-tick disruption:

Code: Select all

x = 9, y = 14, rule = B3/S23
o$obo$2o9$7bo$6b3o$6bobo!

Code: Select all

x = 7, y = 17, rule = B3/S23
o$obo$2o12$5bo$4b3o$4bobo!

I suspect it might be possible to pull something similar on *WSSes, perhaps transforming them into a B-heptomino for a moment.

Then there there are the edge-repair spaceships of course.

[Tim Hutton]

What line of thought led you to ask it?

I was chatting to Stephan Rafler about the continuum between GoL and his SmoothLife, via Larger-than-Life (the Bugs rule) and RealLife. There are several other continuous systems that include 'gliders' (moving solitons), such as Robert Munafo's U-Skate world, and the swarming acorns of the Purwins group. And in continuous systems the gliders are stable - robust to small changes. So we got to wondering at what point is that robustness lost as you come down towards discrete systems. And now it looks like there is some robustness even in GoL, which is nice to see. Thanks for the answers!

(All of these systems can be explored in Ready.)

[Sphenocorona]

Now, I know this isn't quite self-repairing, but I wanted to post this as I haven't seen this mechanism in any other spaceship.
Using WLS I was able to find this large spaceship that moves at c/3. I call it the whale:

Code: Select all

x = 49, y = 23, rule = B3/S23
3$19bobo7bob2o$8b2ob2o2bo3bo4b3o2bo3bo$7bo3b4o2b2o9bo$6bo5bo4b2o4bo2bo
5b3o$7bo5bo2b3o3bob3o16bo$9b2o3bo2bo2b5obo6bobo5b2o$7b3o3bobo5bo6b3obo
3bo4b2o$6bo2bo6b2ob5o5b4o3bo6bo$6bo3bo2bob3obo10bobo8bo$7bo2b2o2bo2bo
2bobobo6b2obobo4bo$8bobo4b3o5bo9b2obo2bo2bo$10b2o3bo2bo3bo7b3o4b2o3b2o
$16bo5b2o6b3o5bobobo$16bobo3bobo14bo2b2o$17bo5bo!

Now, it looks rather fragile, and also there's part of the c/3 edge repair spaceship on the bottom edge, you cant actually get to it because tucked away between more fragile areas. However, there's a spot right on the back (in front of the tail in the gap) that seems to be immune to damage. If you fire a glider, LWSS, or MWSS at that spot from the back (unless you're firing them from the side, which is not easy at all but allows you use a HWSS aswell) they will simply fall apart before they can add a single cell to the spaceship. It's kind of like a force field.

Code: Select all

x = 128, y = 110, rule = B3/S23
2$5bo$4bo$4bo$4bo$4bo$4bo2bo$4b3o46$99bo$98bo$98b3o6$102bo$101bo$101b
3o15$55bo$56bo$56bo$53bo2bo$54b3o2$69bo7bo$68bo7bo$68bo4bo2bo3bo37bo$
41bobo7bob2o13b5o3b4o37bo$30b2ob2o2bo3bo4b3o2bo3bo61bo3bo$29bo3b4o2b2o
9bo42bobo7bob2o10b4o$28bo5bo4b2o4bo2bo5b3o25b2ob2o2bo3bo4b3o2bo3bo$29b
o5bo2b3o3bob3o16bo15bo3b4o2b2o9bo$31b2o3bo2bo2b5obo6bobo5b2o15bo5bo4b
2o4bo2bo5b3o$29b3o3bobo5bo6b3obo3bo4b2o16bo5bo2b3o3bob3o16bo$28bo2bo6b
2ob5o5b4o3bo6bo17b2o3bo2bo2b5obo6bobo5b2o$28bo3bo2bob3obo10bobo8bo17b
3o3bobo5bo6b3obo3bo4b2o$29bo2b2o2bo2bo2bobobo6b2obobo4bo16bo2bo6b2ob5o
5b4o3bo6bo$30bobo4b3o5bo9b2obo2bo2bo15bo3bo2bob3obo10bobo8bo$32b2o3bo
2bo3bo7b3o4b2o3b2o15bo2b2o2bo2bo2bobobo6b2obobo4bo$38bo5b2o6b3o5bobobo
17bobo4b3o5bo9b2obo2bo2bo$38bobo3bobo14bo2b2o18b2o3bo2bo3bo7b3o4b2o3b
2o$39bo5bo44bo5b2o6b3o5bobobo$90bobo3bobo14bo2b2o$91bo5bo!

The reason seems to be because there is an active site that allows an extra cell to be born, and then the back of the ship pulls away before it can cause uncontrolled cell birth/death inside the spaceship.
I've known about this for a while but since I only recently registered I'm uploading it now.

[ad_ca]

Does there exist a still life (other than block) that eventually (or instantly) repairs itself after killing (altering) any single cell?

[OHAD]

Does there exist a still life (other than block) that eventually (or instantly) repairs itself after killing (altering) any single cell?

While I can't tell you for sure, it seems unresonable for me to an other still life like this to exist.
You see, I think that Block is the only unique still life in which each sell has the exact same "property"- Number of neighbors, same location (when you spin it, reflect it and do other things), and same situation, overall.

[137ben]

You see, I think that Block is the only unique still life in which each sell has the exact same "property"- Number of neighbors, same location (when you spin it, reflect it and do other things), and same situation, overall.

I suppose you mean you think that the block is the only still life with only one orbit in its automorphism group. However, this is false:

Code: Select all

x = 3, y = 3, rule = B3/S23
bo$obo$bo!

Of course, this does not regenerate so easily. However, there is no reason that a larger still life shouldn't be able to do the same.

[MikeP]

the exact same "property"- Number of neighbors, same location (when you spin it, reflect it and do other things), and same situation, overall.

only one orbit in its automorphism group

Also the pond:

Code: Select all

x = 4, y = 4, rule = B3/S23
b2o$o2bo$o2bo$b2o!

I'm sure there are many more, too, some of them much larger.

[dvgrn]

Of course, [the tub] does not regenerate so easily. However, there is no reason that a larger still life shouldn't be able to do the same.

There's also no reason that a larger still life should be able to do the same. More to the point, I think, no such still life is known, and it's fairly clear that except for the block, no still life constructed in the last 43 years has this universal-repair property.

There are certainly other patterns that can repair themselves after a particular cell is added or subtracted somewhere, but I doubt that repairable cells make up as much as 25% of the area of any known still life. (Counterexample, anyone?)

It's also pretty clear that no stable object can repair itself with the same mechanism that the block uses, unless it is in fact a block, or a pseudo-still-life that contains a block such as an eater2. To come up with a completely new repair mechanism that works for every cell of the new still life, it's necessary to wave one's hands a lot and theorize fairly wildly.

There might possibly be some complicated self-monitoring universal-constructor-based pattern that could approach a 100% self-repair rating -- mostly by having a huge data area made out of well-separated blocks, perhaps in pairs so you could tell when one of them disappeared. The error-correction and repair circuitry would still be potentially vulnerable, unless it also was somehow made from nothing but paired blocks.

B3/S23 Life seems a good bit too volatile for a large 100% self-repairing pattern to be constructible in practice. There's no (known, or likely to become known) safe way to test for the presence of arbitrary ash objects, so testing for small amounts of damage is very likely to cause large amounts of damage.

[Tropylium]

Related question though: are there any small objects that are good at recovering from added cells in their vicinity? The standard eaters don't really handle single-cell perturbations.

[fsrm]

Does there exist a still life (other than block) that eventually (or instantly) repairs itself after killing (altering) any single cell?

Long ship, tub on long long house,two long long houses:

Code: Select all

x = 55, y = 7, rule = B3/S23
14b2o3b2o3b2o3b2o6b2o3b2o4b2o3b2o$2o5b2o5bo5bo3bo2bo2bo6bo2bo2bo4bo2bo
2bo$o6bobo5b5o5b5o8b2ob2o6b5o$bobo4bobo$2b2o5b2o6bo9bo10b5o6b5o$16bobo
7bobo8bo2bo2bo4bo2bo2bo$17bo9bo9b2o3b2o4b2o3b2o!

[muzik]

Does there exist a still life (other than block) that eventually (or instantly) repairs itself after killing (altering) any single cell?

Long ship, tub on long long house,two long long houses:

Code: Select all

x = 55, y = 7, rule = B3/S23
14b2o3b2o3b2o3b2o6b2o3b2o4b2o3b2o$2o5b2o5bo5bo3bo2bo2bo6bo2bo2bo4bo2bo
2bo$o6bobo5b5o5b5o8b2ob2o6b5o$bobo4bobo$2b2o5b2o6bo9bo10b5o6b5o$16bobo
7bobo8bo2bo2bo4bo2bo2bo$17bo9bo9b2o3b2o4b2o3b2o!

almost 3 years later

[fluffykitty]

We realize all those still lifes are vulnerable at B2 spots.

[praosylen]

So obviously a spaceship that makes blocks might be robust to such damage

Oh wait...

Code: Select all

x = 10, y = 13, rule = B3/S23
4b2o$3b4o2$2b6o$3b4o2$2b2o2b2o$2obo2bob2o$3bo2bo3$4b2o$4bo!