(Engineered) diehards

[squareroot12621]

Rules:

• The diehard's bounding box cannot have an area of more than 10,000. (This is to rule out arbitrarily large patterns, e.g. a G crashing into a blinker.)
• The diehard has to live at least 200 generations. (This is to rule out the same kind of patterns, only shorter.)
• If you have (at least partly) engineered the diehard, put it in the post. (Informative.)
• The diehard has to be interesting—in my definition. (Technically, an XWSS far away enough crashing into a blinker would satisfy all of these conditions, so this rules the others out.)

Here's my first engineered diehard, DH227. (Interesting objects have been marked.)

Code: Select all

x = 46, y = 54, rule = B3/S23
11bo$12bo$10b3o8$2b2o$2b2o$7b2o$7bo2bo3bo$8b3o2b2o$14b2o$8b3o$7bo3bo$
7b2ob2o5$8b2o$7b2o$8bo19b2o$3o25bo$2bo23bobo$obo23b2o$2o$13b2o$13b2o$
44bo$43bobo$43b2o2$9b3o$8bo2bo19b2o$9b2o20bobo$20b2o10bo$20bobo$21bo3$
12b2o$12b2o6$19b2o$19bobo$19bo!
[[ AUTOSTART GPS 45 THEME Mono ZOOM 8 T 0 PAUSE 1.5 ]]
[[ LABELT 0 0 0 LABEL 0 16 10 "Meta-bookend\nand house" ]]
[[ LABEL -4 26.5 10 "Gen. 1\nof B" ]]
[[ T 227 PAUSE 1 LOOP 228 ]]

(Edit: Added [[ THEME Mono ]].)

[77551enpassant]

Would this fit better in the sandbox thread?

[dvgrn]

Would this fit better in the sandbox thread?

Nah, it just so happens that there's been interest in this exact topic very recently, that hasn't made it to the forums yet. This seems like a very reasonable title for a dedicated thread.

I've been writing a series of "NewLifeCA" emails in the last couple of months, mostly to people who were active in Life research and experimentation before the conwaylife forums came along in 2009, and who have never really moved over to keeping a close eye on the forums to find out about new developments. Dean Hickerson has written back a few times lately, to describe some recent experiments with engineered diehards.

I won't give away the punchline yet, in case Dean wants to post something here, but I'll quote the first couple of exchanges. The full archive of recent NewLifeCA stuff will end up in its own locked thread eventually when I can find some time; preparation for G4G14 is keeping me too busy at the moment.

[dvgrn]

NewLifeCA 1 March 2022: What's That Floating In My Soup?

... An entertaining diehard showed up on February 21. Catagolue collects
these things now, so we have a lot of them to choose from.
Impressively, this new one beats the previous record for symmetric
"messless methuselahs" by over 400 ticks:

#N 2474-tick C4_4 diehard
#O Charity Engine, 21 February 2022
#C viewtopic.php?p=141951#p141951
x = 32, y = 32, rule = B3/S23...

As it happens, I've been working on diehards recently, both by random searching and by constructions. I think that random searches are the way to go up to about 18x18, but that constructions, using objects found by specialized searches, are better after that. In particular, the best 16x16 found by Catagolue beats my best construction by 101 generations, but my best 32x32 beats the one above by 6570 gens. Eventually I'll post my findings on the conwaylife.com forum, but for now I'll just show my 32x32. (I doubt that this is anywhere close to maximal for this size.)

Code: Select all

#N 9044-tick diehard
#O Dean Hickerson
x = 32, y = 32, rule = B3/S23
18b2o$14b2obo2bob2ob2o$14bob2o2b2obob2o2$6b2o$obobo2bo$bo13bo$bob2obo
7bobo10b3o$2ob3o8bobo10bo$o3bo11bo11bo$2o5bo$2o4b2o8b2o$3bo10bobo$3bo
11bobo$5bo3b2o4b3o$9bo$3bo7bo2bobo$3b2o5b2o3b2o$15bo9bo$13bobo6b5o$13b
obo5bo4b2o$14bo6bo4bo$24b2o$2b2o4b2o15bo$2bobo2bobo2b2o13b3o$4bo2bo4bo
5b2o5b2obob2o$4b2ob2o5bobo2bo5b2o3b2o$7bo2bo2b2ob2o8bobob2o$7bob2o14b
2ob2o$3b2ob2obo15b3o$3b2obo2bo5b2o$7b2o6b2o!

Re: NewLifeCA 1 March 2022: What's That Floating In My Soup?

I'll have to see if I can hit five digits at least, with a 32x32
diehard -- this example gives me some ideas, for sure.

[dvgrn]

NewLifeCA 6 March 2022: Re: Better 32x32 diehard

I did spend a little time looking for a 32x32 diehard with five-digit survival time, investigating collisions between 2c/5 spaceships and *WSSes that could then be cleaned up with a c/10 copperhead. The best I've come up with so far is this, which isn't quite good enough -- the 2c/5 is too big, and having to generate *two* LWSSes at the last moment would leave too little room in 32x32 for any decent delay circuitry.

Code: Select all

x = 104, y = 31, rule = B3/S23
4b3ob2o$bo4b2o2b2o$2o5bo4bo$2o5bo4bo$bo4b2o2b2o26bo52bo$4b3ob2o29bo50b
obo$35bo3bo47b3o3bo$36b4o48b3obo$90b2o2$92bob2o$91bo2bobo$92bo3b2o$92b
obobo$91b2ob2o$92bo2$93bo$97bo$94bo3b2o$71bo23bo2b2o$72bo21bob4o$68bo
3bo$69b4o$99bob2o$98bob2obo$99bo3bo$100b2obo$99bob2o$97bobo$97bobo!

Unfortunately none of the collisions of *WSSes with really small 2c/5s seem to leave an object or constellation behind that can be cleaned up with a single copperhead. I haven't done a really complete survey, but I think I've covered all of the obvious options. Didn't try a fireship, but that's probably too big to fit in the starting pattern.

However, in the meantime Dean has found a way to get several thousand ticks past the five-digit mark, using a c/3 target instead of a 2c/5 one -- see below. 14,011+ is the new target!

NewLifeCA 6 March 2022: Re: Better 32x32 diehard

I'll have to see if I can hit five digits at least, with a 32x32 diehard -- this example gives me some ideas, for sure.

I've been trying to do that too, and today I succeeded.

The pattern that I sent before used 2 spaceships to delay its death. If the leading one has speed S, the trailing one has speed T, and the LWSS (or other c/2) is formed in generation N, then the pattern dies at about generation SN/((1-2S)T). We want the factor S/((1-2S)T) to be as large as possible. For that we'd like S to be large (but < 1/2) and T to be small.

The 9044-tick pattern used 2c/5 and c/3, giving a factor of 6. Using 2c/5 and c/10 would give a factor of 20, but I never found a combination that works; the c/10 spaceship tends to create a big mess when it hits something. I was able to fix it by adding two c/3 spaceships between the leader and the trailer, but that won't fit in a 32x32 box.

Yesterday I decided to try c/3 and c/10, for a factor of 10. I didn't really expect it to work, but it does. My first attempt lived for about 13000 gens, but adding a couple of one-time glider reflectors, and backing up a few gens with lifesrc increased that to 14010. That could probably be improved with enough searching.

Code: Select all

#N 14010-tick diehard
#O Dean Hickerson, 3/6/2022
x = 32, y = 32, rule = B3/S23
3b2o2b2obobo4bobo3bo$3bo5b2obobo2bo3bobo$2obo2b4o2b2o4bo2bo$bob2ob2o3b
2o4bo4bo$bo2bobobo2bo2bo$2ob2o4bo4bo4b4obo$3b2o2b2obo2bo3b2o5bo3bo$3bo
bo2bo9bobo6bobo$4b2o4bobo6b4o6b2o$3bob2o4bo2bo3b2o2bo6bo$10b2o2bo13bob
o$30bo$31bo$7b2o3b2o15bobo$b2o5bo2bobo6bo7bo2bo$b2o2b3o3b2o6bobo$5bo
13bo2bo6b3o$b2o17bobo7b2o$ob6o13bo7bo$o4bo2bo15b2o4b2o$b3o3b2o14bobo2b
obo$3b2o18b2o4bo2$6b2o$5bobo5b2o4b2o$5b2o6bo2bo3bo$17bo5b3o$14bob3o5b
2o$ob2o2b2o8b2o3b2o$2obo2b2o6bo$15b3ob2o$14bo2b4o!

NewLifeCA 6 March 2022: Re: Better 32x32 diehard

The best I've come up with so far is this, which isn't quite good enough -- the 2c/5 is too big, and having to generate *two* LWSSes at the last moment would leave too little room in 32x32 for any decent delay circuitry.

For what it's worth, my solution using 2 intermediate c/3 spaceships is shown in this 36x36 diehard:

Code: Select all

# 18477-tick diehard
x = 36, y = 36, rule = B3/S23
13bo4bo$14b2o3b2o$7bo6b2o3b2o$2bob2o2bo4bo4bo$4b3o3bo4bo4bo$o8bo3bobo
3b3o$o4b2o2b2o2bobo5bo$obobo3bobo3bo6b2o$o8bo5b2o3bo5bob2o$2bob3o8bo3b
obo3b3o2bo$4b2o2bobo2b3o3bobo2bob2o2bo$7bo6bo6bo7b2o$12bo6bo7b3o$13b2o
5b2o5b3obo$13b2o5b2o6bob4o$12bo6bo8bo2bo2bo$35bo$31bo2bo$31b3o$28bob2o
$29bo2$2ob2o19b2o3bo2bobo$2obobo6b2o9bobo2bo4b2o$4bo7bo2bo7b2o3bo2b2ob
o$14b2o13b2o4bo$34b2o$3b2o13b2o4b2o$3b2o13bobo2bobo$20bo2bo5bo3bo$12b
2o5b2ob2o4bobobobo$12b2o3bo2bo8bo3bo$17b2obo$18bob2ob2o8bo$18bo2bob2o
7bobo$19b2o11b2o!

I didn't find a way to do it with only 1 intermediate c/3, but I could have missed something.

NewLifeCA 7 March 2022: Re: Better 32x32 diehard

Intermediate c/3 spaceships! There's no reason those have to be c/3, and in particular they take up more space than a single c/7 loafer would. Not sure the geometry will allow for shrinking to 32x32, but there's a lot of search space to explore.

[squareroot12621]

Would this fit better in the sandbox thread?

Nah, it just so happens that there's been interest in this exact topic very recently, that hasn't made it to the forums yet. This seems like a very reasonable title for a dedicated thread.…

I (pretty much always) think of original ideas, so I think that was by pure coincidence.
Ooh, I've got a bonus: Can anyone find/engineer a qualifying diehard such that each cell in its bounding box turns on during its lifetime, but is dead for an infinite amount of generations?

[hotdogPi]

• The diehard's bounding box cannot have an area of more than 10,000. (This is to rule out arbitrarily large patterns, e.g. a G crashing into a blinker.)

You might want to specify 100×100.

Code: Select all

x = 253, y = 6, rule = B3/S23
249bo$248bo$248bo3bo$248b4o$2o$2o!

As for a legitimate one, 245 generations

Code: Select all

x = 18, y = 16, rule = B3/S23
b2o$o2bobo$4b2o5$2b2o$2b2o12b2o$16b2o5$13b2o$13b2o!

[wwei47]

Ooh, I've got a bonus: Can anyone find/engineer a qualifying diehard such that each cell in its bounding box turns on during its lifetime, but is dead for an infinite amount of generations?

Sure.

Code: Select all

x = 1, y = 1, rule = B3/S23
o!

[squareroot12621]

[…]

Code: Select all

x = 253, y = 6, rule = B3/S23
249bo$248bo$248bo3bo$248b4o$2o$2o!

As for a legitimate one, 245 generations

Code: Select all

x = 18, y = 16, rule = B3/S23
b2o$o2bobo$4b2o5$2b2o$2b2o12b2o$16b2o5$13b2o$13b2o!

[…]

Code: Select all

x = 1, y = 1, rule = B3/S23
o!

First one: Too boring.
Second one: That's not quite all of it. Look:

Code: Select all

x = 20, y = 18, rule = LifeHistory
20D$D.2E15.D$DE2.E.E12.D$D4.2E12.D$D18.D$D18.D$D18.D$D18.D$D2.2E14.D$
D2.2E12.2ED$D16.2ED$D18.D$D18.D$D18.D$D18.D$D13.2E3.D$D13.2E3.D$20D!
[[ ZOOM 20 STOP 245 ]]
[[ LABEL 13 2 20 "These spots don't\nget touched." ]]
[[ LABEL 4.5 14.5 20 "These spots don't\nget touched." ]]

Third one: Not long enough.

[GUYTU6J]

Second one: That's not quite all of it. Look:

Oh, so you need to rephrase your question like

Can anyone find/engineer a qualifying diehard such that each cell in [the rectangular] bounding box [of its whole evolution] turns on [at least once] during its lifetime, but is dead for an infinite amount of generations?

Giving straight edges at the envelope is not how Life typically behaves naturally. Do you really prefer touching every cell at the cost of lifespan? If so, I present a highly artificial pattern modified from an example this thread

Code: Select all

x = 10, y = 10, rule = B3/S23
obo2bob2o$bobob5o$ob8o$b8o$2b8o$8o$b8o$8obo$5obobo$b2obo2bobo!

It does not expand, and in my opinion it is boring.

Here are two die hard patterns, from Lifeline vol4p4 and vol2p13 respectively, that were what I wanted to note:

Code: Select all

x = 26, y = 3, rule = LifeHistory
A.A17.3A$A2.A16.A2.A$3.A.A14.A2.A.A!

[squareroot12621]

Bounding boxes are usually rectangular.

[hotdogPi]

I wasn't trying to answer the bounding box question, just give an example of a 200+ engineered methuselah.

[wwei47]

3x3 and 4x4:

Code: Select all

x = 12, y = 4, rule = B3/S23
2o7b2o$3o5b4o$b2o5b4o$9b2o!

[gameoflifemaniac]

3x3 and 4x4:

Code: Select all

x = 12, y = 4, rule = B3/S23
2o7b2o$3o5b4o$b2o5b4o$9b2o!

Code: Select all

x = 4, y = 3, rule = B3/S23
o$4o$3bo!

3x4 45-gen diehard

[squareroot12621]

Ok, I made another one which I'm labeling "DH2279." I spent quite some time compacting it from 103×102 (10,506 > 10,000) to 103×97 (9,991 < 10,000). Here it is:

Code: Select all

x = 103, y = 97, rule = B3/S23
11bo$10bobo$9bobo$9b2o7bo$17bobo$17b2o$47bo$46bobo$47b2o$22b2o$22b2o3$
27bo$26bobo$26b2o21bo$48bobo$48b2o4$33b2o$32bobo$33bo3$38b2o$38b2o7$24b
2o5bo5bo$24b2o4bobo3b2o$31bo5bo$20b2o19b2o$20bo2bo17bobo$22b2o19bo37b
2o$43b2o36bobo$14b2o66bo$14b2o$27bo$28b2o$9bo17b2o$8bobo$9b2o$2o32b2o
$obo32bo$bobo29b3o$2bo4$78b2o$76bo2bo$76b2o2$84b2o$84b2o2$36b2o$36bob
o51bo$11b2o24bo51bobo$10bobo76b2o$11bo48b2o13bo$60b2o12bobo$74b2o3$55b
2o$55bobo38b2o$56bo39b2o2$101b2o$100bobo$80bo18bobo$79bobo18bo$79b2o4$
99bo$98bobo$98b2o6$83b2o$83bobo$84bo$33b2o37b2o$33bobo36bobo$34bo38bo
! [[ AUTOSTART ZOOM 5 THEME Mono STEP 3 T 0 PAUSE 1.5 T 2279 PAUSE 1 LOOP 2280 ]]

[dvgrn]

Ooh, I've got a bonus: Can anyone find/engineer a qualifying diehard such that each cell in its bounding box turns on during its lifetime, but is dead for an infinite amount of generations?

Edit: I solved the bonus one. It's just two centuries, like this:

Code: Select all

x = 9, y = 9, rule = LifeHistory
.8D$.D4.E.D$.D3.3ED$.D2.2E2.D$.D6.D$.D2.2E2.D$.D3E3.D$.D.E4.D$.8D!
[[ AUTOSTART STEP 1 ZOOM 14 T 0 PAUSE 1.5 T 270 PAUSE 1 LOOP 271 ]]

As an extra bonus, none of the cells in the original bounding box are alive. ;)

It doesn't seem like that's an extra bonus, and it's not clear that it's a solution at all, since the problem statement asks for a qualifying diehard, not just a qualifying methuselah.

However, several people in this thread have been playing fast and loose with the definition of diehard -- seems like a lot of the bounding-box-filling solutions above are "die-ridiculously-easy", nowhere near qualifying.

[squareroot12621]

Ooh, I've got a bonus: Can anyone find/engineer a qualifying diehard such that each cell in its bounding box turns on during its lifetime, but is dead for an infinite amount of generations?

Edit: I solved the bonus one. It's just two centuries, like this:

Code: Select all

x = 9, y = 9, rule = LifeHistory
.8D$.D4.E.D$.D3.3ED$.D2.2E2.D$.D6.D$.D2.2E2.D$.D3E3.D$.D.E4.D$.8D!
[[ AUTOSTART STEP 1 ZOOM 14 T 0 PAUSE 1.5 T 270 PAUSE 1 LOOP 271 ]]

As an extra bonus, none of the cells in the original bounding box are alive.

It doesn't seem like that's an extra bonus, and it's not clear that it's a solution at all, since the problem statement asks for a qualifying diehard, not just a qualifying methuselah.[…]

I forgot that. Let me fix that real quick. (If I can find a solution, that is.)

[Pavgran]

90x86 bounding box, 50716-tick diehard.
Consists of nothing but common SLs and gliders
The bounding box could be optimized a bit, but I didn't bother. Also the time could be extended by adding something to self-destruct sequence, but I didn't bother. And don't ask me where did these gliders come from.

Code: Select all

x = 90, y = 86, rule = B3/S23
65bo9b2o$64bobo7bobo$45b2o18b2o7bo$45b2o26b2o2$54bo25b2o$52b3o24bo2bo$
51bo28bobo$43b2o6b2o28bo2b3o$43bobo38bo$44bo40bo2$49b2o$49b2o5b2o$56b
2o$52bo$51bobo$39b2o11bo$39b2o8bo10bo$48bobo8bobo$49bo4b2o3bobo$46bo7b
obo3bo$45bobo8bo$46bo9b2o$43bo$35b2o5bobo$35b2o6bo7b2o$40bo10b2o$39bob
o13bo30b2o$40bo13bobo29b2o$37bo17bo$36bobo11bo7bo$26b2o9bo11bobo5bobo$
26b2o6bo14bo2bo5bo7b2o14b2o$17b2o14bobo14b2o9bo3bo2bo13b2o$16bo2bo14bo
19b2o4bobo3b2o$17b2o12bo22bo6bo$30bobo19bobo18b2o$11b2o8bo9bo20b2o10b
2o7b2o$11b2o6b3o6bo6bo28bobo$18bo8bobo4bo30b2o$3b2o13b2o8bo5b3o3bo41b
2o$4bo9bo9b2o13bobo27bo11bobo$4bobo6bobo8b2o14bo14b2o5b2o4bobo11bo5b2o
$5b2o7bo40b2o5b2o5bo18b2o$10b2o5bo25b2o6b2o$10b2o4bobo23bobo6b2o5b2o
12bo$17bo21b2o2bo14b2o11bobo4b2o$20bo17b2o32bo5b2o$2o17bobo18bo23b2o9b
o7b2o$2o5bo12bo34b2o7b2o8bobo6bobo$6bobo14bo11b2o18b2o18bo9bo$6b2o14bo
bo10b2o25bo7b2o13b2o$23bo37bobo7bo$31b2o5b2o11b2o9bo5b3o6b2o$15b2o9bo
4b2o5b2o11b2o6bo8bo8b2o$15b2o8bobo30bobo$26bo32bo11b2o$20b2o24b2o8bo
13bo2bo$20b2o7b2o15b2o7bobo13b2o$29bobo24bo5b2o$30b2o9b2o10bo8b2o14bo$
40bobo5b2o2bobo23b3o$40b2o6b2o3bo27bo$26b2o9bo42b2o$27bo8bobo$23bo3bob
o7bo16b2o$22bobo3b2o4bo19b2o19bo$22bobo8bobo38bobo$23bo10bo8b2o5bo22bo
2bo$31bo11b2o4bobo22b2o$30bobo16bo2bo$31bo18b2o20b2o$26b2o43bobo$26b2o
5b2o38bo$33b2o$50b2o$39bo9bo2bo$38bobo9bobo$31b2o6b2o10bo$32bo$29b3o
13bo$29bo14bobo$44b2o$37b2o$37b2o!

Edit: reduced bounding box a bit

Edit:
And there is enough space left to include that crazy spaceship-chasing idea. Although the purity of "only gliders and common SLs" is lost. At that point there is probably something much more efficient with quadri-Snarks, for example.
90x86 bounding box, 518476 ticks.

Code: Select all

x = 90, y = 86, rule = B3/S23
8b2o6b2o47bo9b2o$8bobo5bobo45bobo7bobo$9bobo5bo27b2o18b2o7bo$10bo34b2o
26b2o$14b3o8b2o$16bo8bo5b2o21bo25b2o$15bo10b3o2b2o19b3o24bo2bo$28bo22b
o28bobo$31b2o10b2o6b2o28bo2b3o$26b6obo9bobo38bo$16b2o7bo2bo4bo10bo40bo
$15bo2bo6b2o3b3o$6b2o8bo2bo9b2o18b2o$6b2o9b2o30b2o5b2o$21b2o4bo28b2o$
20bobo3bobo23bo$20b2o5bo23bobo$10b2o27b2o11bo$10b2o27b2o8bo10bo$48bobo
8bobo$49bo4b2o3bobo$46bo7bobo3bo$b2o42bobo8bo$b2o43bo9b2o$43bo$35b2o5b
obo$35b2o6bo7b2o$40bo10b2o$39bobo13bo30b2o$40bo13bobo29b2o$37bo17bo$
36bobo11bo7bo$26b2o9bo11bobo5bobo$26b2o6bo14bo2bo5bo7b2o14b2o$17b2o14b
obo14b2o9bo3bo2bo13b2o$16bo2bo14bo19b2o4bobo3b2o$17b2o12bo22bo6bo$30bo
bo19bobo18b2o$11b2o8bo9bo20b2o10b2o7b2o$11b2o6b3o6bo6bo28bobo$18bo8bob
o4bo30b2o$3b2o13b2o8bo5b3o3bo41b2o$4bo9bo9b2o13bobo27bo11bobo$4bobo6bo
bo8b2o14bo14b2o5b2o4bobo11bo5b2o$5b2o7bo40b2o5b2o5bo18b2o$10b2o5bo25b
2o6b2o$10b2o4bobo23bobo6b2o5b2o12bo$17bo21b2o2bo14b2o11bobo4b2o$20bo
17b2o32bo5b2o$2o17bobo18bo23b2o9bo7b2o$2o5bo12bo34b2o7b2o8bobo6bobo$6b
obo14bo11b2o18b2o18bo9bo$6b2o14bobo10b2o25bo7b2o13b2o$23bo37bobo7bo$
31b2o5b2o11b2o9bo5b3o6b2o$4bo2bo7b2o9bo4b2o5b2o11b2o6bo8bo8b2o$5b2o8b
2o8bobo30bobo$26bo32bo11b2o$20b2o24b2o8bo13bo2bo$2b2o4b2o10b2o7b2o15b
2o7bobo13b2o$2b3o2b3o19bobo24bo5b2o$5b2o23b2o9b2o10bo8b2o14bo$3bo4bo
31bobo5b2o2bobo23b3o$2bo6bo30b2o6b2o3bo27bo$5b2o19b2o9bo42b2o$3b2o2b2o
18bo8bobo$5b2o16bo3bobo7bo16b2o$22bobo3b2o4bo19b2o19bo$22bobo8bobo38bo
bo$23bo10bo8b2o5bo22bo2bo$31bo11b2o4bobo22b2o$30bobo16bo2bo$31bo18b2o
20b2o$26b2o43bobo$26b2o5b2o32bo5bo7bo$33b2o31bobo11bobo$50b2o14b2o12b
2o$39bo9bo2bo$38bobo9bobo20b2o$31b2o6b2o10bo20bobo$32bo40bo$8bo20b3o
13bo$7bo3bo3bo5bo7bo14bobo$8b3o3bo2bobo2bo21b2o21b2o$9bob2o4b2ob2o15b
2o28bobo$13b3ob2obo16b2o29b2o!

[squareroot12621]

Tip: If you see a deployed glider, don't bother with the rest of the evolution of the pattern. That glider, ≈99.99% of the time, won't be caught. Essentially, deployed gliders are the enemies of diehards.

[Moosey]

The interesting thing about engineered diehards (or rather, tangentially related thing) is that you can make patterns whose death is impossible to prove in a finite amount of time for halting problem reasons (pattern which self-destructs if a relevant TM halts), or, say, a pattern whose fate is tied to the consistency of zfc, like a pattern which self-destructs if it finds a contradiction in zfc (I mean, this is only unprovable if zfc is consistent in the first place but whatever)

These sorts of patterns wouldn't look very interesting, I suppose-- just some universal computer performing calculations to the end of time™ (or the end of the relevant system, whichever comes first).

Of course, this is the case for a lot more than just diehards, but whatever.

Hey, speaking of this-- has a thread been created for patterns with unknown fate?

[Jormungant]

The chasing spaceship from Pavgran is very neat, I though I had a good idea using oscilators-gun combination, but this has far more potential. Now I am wondering if one could use it several times, that is, making a loop with increasing length using a cordership, which ultimately we manage to destroy after bouncing X 2glider salvos, each cycle doubling the time required.

Code: Select all

x = 74, y = 64, rule = LifeHistory
8$47.2A$47.2A3$41.3B4.B$41.BA2B2.6B$41.2A12B$34.6B3A13B$33.9BA12B2A$
33.7B2A13B2A$32.ABABA19B$31.B3ABA18B$29.2BA2BAB2A5B2.2B2.6B$27.7B4A2B
9.5B$3.C.C21.3B.A6BA11.4B$4.2C20.4B2A3BABA12.4B$4.C21.3BA2BA3BA13.4B$
27.5B.B.B15.3B$23.5BA3B2.6B$22.8BA2B.8B$6.C.C5.5B2.5B6A11B.3B.4B.3B2.
A$7.2C5.5B.6BA4B2A24B4A$7.C3.ABA2B2A8B3AB3A23BA4BA$11.ABA13BAB2A8B.
18B2AB3A$11.A19B2A7B4.14B2ABAB2A$13.15BA4BA4.2B4.14B2A2BAB2A$13.14B2.
A3BA11.13B2A3B2A$14.13B2.B3A2B11.13BAB3A$17.9B3.6B13.10B2.3A$17.8B4.
5B15.6B.B4.A$18.2B2.2B4.6B16.5B$29.6B11.2A3.3B$28.2BA4B9.B2ABA3.2B$
22.2A4.2AB2AB.4B.5B2AB2A$22.2A4.2A15B2AB2AB$28.5BA18B$27.A4BA20B$27.A
2B2A14BA7B$27.2BA15B3A7B$28.16B3ABA6B$29.B2A4B3.4B4ABA4B$29.B2A10.3AB
2A3B$30.2A11.4BA3B$46.4B$46.3A$47.B!

I think what should be doable in a 100x100 space, the required mechanism should fit with periodic guns; however, I am not very knowledgeable in the art of seed of destruction, so I am just putting this here in case someone think clearing this cordership remotely is possible without requiring too much space.

Unrelated, found a wierd p32 gun interaction here ^^:

Code: Select all

x = 129, y = 108, rule = LifeHistory
16$66.B$66.B3$66.B$66.5B$66.7B$66.8B$66.9B$66.9B$66.8B$66.7B$66.7B.B$
66.13B$16.A23.2A24.15B$66.16B$19.2A.A.A.2A11.A3.A22.17B$19.A.2A.2A.A
10.A4.A22.17B$23.A13.A.A.A24.16B$20.2A3.2A9.A.A.A9.A2.A3.2A7.15B$20.A
.3A.A7.A4.A8.8A2.A7.15B.B$17.2A.A5.A.2A4.A3.A8.A8.2A8.21B$17.2A.A.2A.
A2.3A15.A2.A.2A.A11.23B$19.A3.2A6.A4.2A9.3A.2A3.2A8.24B$17.2A.A.2A.5A
14.4A4.A.A.A9.25B$17.2A.A2.A3.A3.2A11.2A5.A.2A.A9.25B$20.A.A3.A3.2A
14.A3.A.A.A.2A8.24B$17.2A.A.A.A.3A.A14.2A.A2.A2.A2.A8.23B$17.A.A3.A.A
2.A.A5.3A4.A2.5A3.2A10.23B.B$25.A.A2.2A4.3A6.A20.29B$24.2A.2A8.A5.A2.
5A3B2A41B$45.2A.A2BA2BA2BA40B$18.3A25.A2.BABABAB2A33BA2B2A3B$17.A9.2A
15.2A3.2BAB2A.A8.26BA2B2A3B$17.A3.A5.2A15.4A.3BA.A.A8.26BAB2ABAB$17.A
2.A.A24.3AB2A3.2A7.25B2A5B$19.A.A2.A17.A3.A2.AB2A.A10.32B.B$20.A3.A
15.A.A4.A.4B3.2A7.25BA2B2A8B$24.A8.3A5.2A5.8A2.A6.26B4A10B$21.3A9.3A
13.BA2BA3.2A6.28BA12B$32.A3.A12.4B12.40B2A$33.3A3.A9.4B12.40B2A$33.3A
3.3A7.57B$42.A6.56B$41.2A4.3BA54B$36.2A2.A2.2A3.ABA55B$30.A.A3.A4.A.A
.A3.2A15B2A39B$32.A6.3A2.A.A3.17B2A39B$28.2A4.A7.A.A.A4.15BA42B$27.A
4.A4.3A2.A2.A6.56B2A$26.A.8A.A.A2.A10.55BA2BA$26.A8.A.A2.2A12.54BA3BA
$24.2A.11A17.3BA50B3AB$23.A2.A4.A2.A21.ABA55B$23.2A2.A4.A24.2A56B$28.
A.A.A25.48BABA7B$30.A28.33B2.11BA3BA7B$60.32B2.16B2A6B$61.32B2.10BA5B
A6B$62.B.25BA4B2.9BA6BA3B$67.23BA3BAB2.8B2A4BAB$67.18B2A3BA4B2ABA6B.
6BAB$68.17BA3BA2BA2B2ABA6B3.A3BA$70.15BABA3B4A3BAB.3B4.A3BA$70.16B2A
3B2A7B2.2B5.ABA$71.B2AB2.23B9.3A$72.2A2.25B$77.25B$77.26B$77.27B$77.
28B$78.27B$78.25B$79.B2AB2.16B$80.2A4.6B.9B$87.5B2A2BA4B$88.3B.A2BA5B
$89.5BABA3B2A$91.B3A5BA2B$92.A7BA2B$93.7BA2B$93.9B$94.6B$95.5B$96.3B$
97.2B!

[biggiemac]

The question here is interesting. "Given a pattern with a initial bounding rectangle of area at most N, and the requirement that the pattern's fate is population 0, how long can it possibly live"? With N as the parameter, you could phrase it as a pseudo-busy-beaver of game of life, and I think it is well defined, at least as well as the busy beaver function is defined. You can even fill it in conclusively for small values of N.

This thread considers N=10,000 which is still probably small enough to be a good question. I am otherwise interested in estimating how big N has to be, before the inevitable busy-beaver-outpacing-the-entire-fast-growing-hierarchy explosion. Dean Hickerson and dvgrn are doing the first obvious thing, with linear multipliers based on speed differences. Pavgran did the next obvious thing, with an exponentially-slower use of the space (and then a linear multiplier to finish it off for the current record). That specific exponential machine is limited because still lives initially have to be inside the box, and we only get a doubling when we reach a corner.

The hardest part of working outside the box is limiting to objects and interactions that don't leave a trace..

[yujh]

snip

again, the bounding box isn't pushed to its limit. I'm sure there's something that does a better job but here's a 88*86 solution

Code: Select all

x = 88, y = 86, rule = B3/S23
7b2o6b2o47bo9b2o$7bobo5bobo45bobo7bobo$8bobo5bo27b2o18b2o7bo$9bo34bo
27b2o$13b3o8b2o$15bo8bo5bo22bo25b2o$14bo10b3o2b2o19b3o24bo2bo$27bo22bo
28bobo$30b2o10b2o6b2o28bo2b3o$25b6obo9bobo38bo$15b2o7bo2bo4bo10bo40bo$
14bo2bo6b2o3b3o$5b2o8bo2bo9b2o19bo$5bo10b2o30b2o5b2o$20b2o4bo29bo$19bo
bo3bobo23bo$19b2o5bo23bobo$9b2o27b2o11bo$9bo29bo8bo10bo$47bobo9bo$48bo
4b2o4bo$45bo7bobo3bo$2o42bobo8bo$o44bo9b2o$42bo$34bo6bobo$34b2o6bo7bo$
39bo10b2o$38bobo13bo30bo$39bo13bobo29b2o$36bo17bo$35bobo19bo$25b2o9bo
11b2o6bobo$26bo6bo15b2o6bo23bo$32bobo15bo9bo3b4o13b2o$15b4o14bo19b2o4b
obo$30bo22bo6bo$29bobo19bobo18bo$10b2o8bo9bo20b2o10b2o7b2o$10bo7b3o6bo
6bo28bobo$17bo8bobo4bo30b2o$2b2o13b2o8bo5b3o3bo41b2o$3bo9bo9b2o13bobo
27bo11bobo4bo$3bobo6bobo9bo14bo14bo6bo5bobo11bo4b2o$4b2o7bo40b2o5b2o5b
o17b2o$9bo6bo25b2o6bo36bo$9b2o4bobo23bobo6b2o5bo13bo$16bo21b2o2bo14b2o
11bobo4bo$o18bo17b2o32bo5b2o$2o16bobo18bo23bo10bo7b2o$2o4bo12bo34bo8b
2o8bobo6bobo$o4bobo14bo11bo19b2o18bo9bo$5b2o14bobo10b2o25bo7b2o13b2o$
22bo37bobo7bo$30bo6bo12b2o9bo5b3o6bo$4bo9b2o9bo4b2o5b2o12bo6bo8bo8b2o$
4b2o8bo9bobo30bobo$25bo32bo$20bo24bo9bo13b4o$b2o4b2o10b2o7b2o15b2o7bob
o$b3o2b3o19bobo24bo5b2o$4b2o23b2o9b2o10bo9bo14bo$2bo4bo31bobo6bo2bobo
23b3o$bo6bo30b2o6b2o3bo27bo$4b2o19b2o9bo42b2o$2b2o2b2o18bo8bobo$4b2o
16bo3bobo7bo16b2o$22bo4b2o4bo20bo19bo$22bo9bobo38bobo$22bo10bo8b2o28bo
2bo$30bo12bo4b2o23b2o$29bobo17b2o$30bo19bo20b2o$25b2o43bobo$26bo5bo33b
o5bo7bo$32b2o31bobo11bobo$49bo15b2o12b2o$38bo10b2o$37bobo10b2o20b2o$
30b2o6b2o31bobo$31bo40bo$7bo20b3o13bo$6bo3bo3bo5bo7bo14bobo$7b3o3bo2bo
bo2bo21b2o21b2o$8bob2o4b2ob2o15b2o28bobo$12b3ob2obo17bo29b2o!

also another thing to try is using a tub puffer at like c/12d but that will be bad for the bounding box.

Edit: i found this manually, but it doesn't seem to work anywhere...time for a boat grand parent

Code: Select all

x = 2, y = 10, rule = B3/S23
o$bo$2o$2o$o$o$2o$2o$bo$o!

Edit2: works, now chopped down to 87*86

Code: Select all

x = 87, y = 86, rule = B3/S23
7b2o6b2o47bo9b2o$7bobo5bobo45bobo7bobo$8bobo5bo27b2o18b2o7bo$9bo34bo
27b2o$13b3o8b2o$15bo8bo5bo22bo25b2o$14bo10b3o2b2o19b3o24bo2bo$27bo22bo
28bobo$30b2o10b2o6b2o28bo2b3o$25b6obo9bobo38bo$15b2o7bo2bo4bo10bo40bo$
14bo2bo6b2o3b3o$5b2o8bo2bo9b2o19bo$5bo10b2o30b2o5b2o$20b2o4bo29bo$19bo
bo3bobo23bo$19b2o5bo23bobo$9b2o27b2o11bo$9bo29bo8bo10bo$47bobo9bo$48bo
4b2o4bo$45bo7bobo3bo$2o42bobo8bo$o44bo9b2o$42bo$34bo6bobo$34b2o6bo7bo$
39bo10b2o$38bobo13bo30bo$39bo13bobo29b2o$36bo17bo$35bobo19bo$25b2o9bo
11b2o6bobo$26bo6bo15b2o6bo23bo$32bobo15bo9bo3b4o13b2o$15b4o14bo19b2o4b
obo$30bo22bo6bo$29bobo19bobo18bo$10b2o8bo9bo20b2o10b2o7b2o$10bo7b3o6bo
6bo28bobo14bobo3bo$17bo8bobo4bo30b2o14b2o3bo$2b2o13b2o8bo5b3o3bo40bo4b
2o$3bo9bo9b2o13bobo27bo11b2o3b2o$3bobo6bobo9bo14bo14bo6bo5bobo9bobo4bo
$4b2o7bo40b2o5b2o5bo12bo4bo$9bo6bo25b2o6bo34b2o$9b2o4bobo23bobo6b2o5bo
13bo13b2o$16bo21b2o2bo14b2o11bobo4bo7bo$o18bo17b2o32bo5b2o7bo$2o16bobo
18bo23bo10bo7b2o$2o4bo12bo34bo8b2o8bobo6bobo$o4bobo14bo11bo19b2o18bo9b
o$5b2o14bobo10b2o25bo7b2o13b2o$22bo37bobo7bo$30bo6bo12b2o9bo5b3o6bo$4b
o9b2o9bo4b2o5b2o12bo6bo8bo8b2o$4b2o8bo9bobo30bobo$25bo32bo$20bo24bo9bo
13b4o$b2o4b2o10b2o7b2o15b2o7bobo$b3o2b3o19bobo24bo5b2o$4b2o23b2o9b2o
10bo9bo14bo$2bo4bo31bobo6bo2bobo23b3o$bo6bo30b2o6b2o3bo27bo$4b2o19b2o
9bo42b2o$2b2o2b2o18bo8bobo$4b2o16bo3bobo7bo16b2o$22bo4b2o4bo20bo19bo$
22bo9bobo38bobo$22bo10bo8b2o28bo2bo$30bo12bo4b2o23b2o$29bobo17b2o$30bo
19bo20b2o$25b2o43bobo$26bo5bo33bo5bo7bo$32b2o31bobo11bobo$49bo15b2o12b
2o$38bo10b2o$37bobo10b2o20b2o$30b2o6b2o31bobo$31bo40bo$7bo20b3o13bo$6b
o3bo3bo5bo7bo14bobo$7b3o3bo2bobo2bo21b2o21b2o$8bob2o4b2ob2o15b2o28bobo
$12b3ob2obo17bo29b2o!

[squareroot12621]

Wow. I never knew that engineered diehards could live that long.

[…]

Code: Select all

x = 88, y = 86, rule = B3/S23
7b2o6b2o47bo9b2o$7bobo5bobo45bobo7bobo$8bobo5bo27b2o18b2o7bo$9bo34b2o
26b2o$13b3o8b2o$15bo8bo5b2o21bo25b2o$14bo10b3o2b2o19b3o24bo2bo$27bo22b
o28bobo$30b2o10b2o6b2o28bo2b3o$25b6obo9bobo38bo$15b2o7bo2bo4bo10bo40bo
$14bo2bo6b2o3b3o$5b2o8bo2bo9b2o18b2o$5b2o9b2o30b2o5b2o$20b2o4bo28b2o$
19bobo3bobo23bo$19b2o5bo23bobo$9b2o27b2o11bo$9b2o27b2o8bo10bo$47bobo8b
obo$48bo4b2o3bobo$45bo7bobo3bo$2o42bobo8bo$2o43bo9b2o$42bo$34b2o5bobo$
34b2o6bo7b2o$39bo10b2o$38bobo13bo30b2o$39bo13bobo29b2o$36bo17bo$35bobo
11bo7bo$25b2o9bo11bobo5bobo$25b2o6bo14bo2bo5bo7b2o14b2o$16b2o14bobo14b
2o9bo3bo2bo13b2o$15bo2bo14bo19b2o4bobo3b2o$16b2o12bo22bo6bo$29bobo19bo
bo18b2o$10b2o8bo9bo20b2o10b2o7b2o$10b2o6b3o6bo6bo28bobo$17bo8bobo4bo
30b2o$2b2o13b2o8bo5b3o3bo41b2o$3bo9bo9b2o13bobo27bo11bobo4bo$3bobo6bob
o8b2o14bo14b2o5b2o4bobo11bo4b2o$4b2o7bo40b2o5b2o5bo17b2o$9b2o5bo25b2o
6b2o35bo$9b2o4bobo23bobo6b2o5b2o12bo$16bo21b2o2bo14b2o11bobo4b2o$o18bo
17b2o32bo5b2o$2o16bobo18bo23b2o9bo7b2o$2o4bo12bo34b2o7b2o8bobo6bobo$o
4bobo14bo11b2o18b2o18bo9bo$5b2o14bobo10b2o25bo7b2o13b2o$22bo37bobo7bo$
30b2o5b2o11b2o9bo5b3o6b2o$3bo2bo7b2o9bo4b2o5b2o11b2o6bo8bo8b2o$4b2o8b
2o8bobo30bobo$25bo32bo11b2o$19b2o24b2o8bo13bo2bo$b2o4b2o10b2o7b2o15b2o
7bobo13b2o$b3o2b3o19bobo24bo5b2o$4b2o23b2o9b2o10bo8b2o14bo$2bo4bo31bob
o5b2o2bobo23b3o$bo6bo30b2o6b2o3bo27bo$4b2o19b2o9bo42b2o$2b2o2b2o18bo8b
obo$4b2o16bo3bobo7bo16b2o$21bobo3b2o4bo19b2o19bo$21bobo8bobo38bobo$22b
o10bo8b2o5bo22bo2bo$30bo11b2o4bobo22b2o$29bobo16bo2bo$30bo18b2o20b2o$
25b2o43bobo$25b2o5b2o32bo5bo7bo$32b2o31bobo11bobo$49b2o14b2o12b2o$38bo
9bo2bo$37bobo9bobo20b2o$30b2o6b2o10bo20bobo$31bo40bo$7bo20b3o13bo$6bo
3bo3bo5bo7bo14bobo$7b3o3bo2bobo2bo21b2o21b2o$8bob2o4b2ob2o15b2o28bobo$
12b3ob2obo16b2o29b2o!

[…]

Just as an alert for anyone who is watching this, the spaceship crashes into a wall before the would-be diehard would…well, die. It should work better in Golly.

[GUYTU6J]

What is the smallest caber tosser in terms of bounding box? With the recent period-48 glider gun I can construct one in 64x73 with expansion factor 2:

Code: Select all

#C 64x73 caber tosser
#C n-th glider appears at generation 192*2^n
#C GUYTU6J, April 1 2022
x = 64, y = 73, rule = B3/S23
17b3o$15b7o6bo$14b9o4bo$13bo7b3o2b2o$14b3o6bo3bo2bo$15b2o11b3o$18bo10b
o$19bo18b2o$20bo17b2o4$obo$3o$2o15bo$17bo$16bo$3bo13b2o$bobo12bo2bo$b
3o12bobo$4bo$5o12bo$15bo2bo$16b4o$18b2o$16bo$15b2o29bo$15bo2bo$16b3o
24b3o$17bo27bo$44bo2$5b2o$5b2o2$49bo3bo$44bo2b2obobob2o2bo$42b2obobo2b
obo2bobob2o$42b2o3bobo3bobo3b2o$44b2o2bo5bo2b2o$13b2o$13b2o$27b2o$17bo
10bo$15bobo10bobo$16b2o11b2o4$44b2o2bo5bo2b2o$42b2o3bobo3bobo3b2o$11b
2o8b3o5b2o11b2obobo2bobo2bobob2o$7bo3b2o7bo8bo14bo2b2obobob2o2bo$3b2ob
2o12bo2bo3bobo19bo3bo$2bobobo11b2o3bo3b2o$3b2ob2o9bo4bo18bo$4b2o11bo3b
obo17bo$2bob3o10bo4bo17bo$2obo4b3o7b2o4bo9b2o16b2o4bo$20bo3bo10bo12bo
3b2o3bob2o$20bo3bo10bobo9bobo7bo$21b3o12b2o8b2ob2o8bo$27b2o12bo5bo2bo
5b3o$14b2o11bobo10bob2o4bobo5bo$14b2o13bo10bob2o5bo8bo2b2o$29b2o10bobo
11b4o4bo$41b2o12bo3bo2bo$41b4o16bo$43b2o$36b2o7bo$35bobo7bo3b2o$35bo8b
o4b2o$34b2o!

Then let's see how it can be incorporated in a die hard. It is known that a 2-engine Cordership can be stopped from behind with a single glider without releasing extra spaceships, but it is unknown which collision leaves the least amount of ash.

Two other questions:

Can the O(sqrt(log(t))) pattern, with clean self-destruct mechanism that can be triggered upon reaching some threshold, break the record for a sufficiently large bounding box?

Can we make a die hard with unknown lifespan? For example, a modified Fermat prime calculator that terminates and vanishes after finding the sixth such integer (assuming it exists). Or a computer doing so when the digits of the binary representation of a transcedental number include a fraction of 1's above certain limit. Just saying.