(Engineered) diehards

[toroidalet]

Adding 3 eaters to the northwest tub chain multiplies the lifespan by 121^48 (about 9.4*10^99), and the guns have been backed up a few generations (multiplying the lifespan by about 1.004), giving a total of about 3.383*10^1176:

Code: Select all

x = 99, y = 101, rule = B3/S23
17b3o12b2o2bo32bo7b3o2b4o$17bo2bo10bob4o31bobo5bo3bo$17bo2bo10bo36bo2b
o4bo$21bo7b2ob7o30b2o6b3obo$19bobo5bo2bobo6bo$20b2o5b2o3bob2o2b2o32b2o
$18b3o10b2ob2o7b2o4bo21bo2bo$18b2o24bo3bobo8b2o11bobo$18bobo21bo6bo8bo
2bo11bo9bo$18bobo21b5o12b2o23bo$18b2o13b2o11bo16b2o4bo12b3o4b2o$33b2o
5b4o18bobo3bobo19bo4bo$30bo9bo2bo19bo5b2o16b3o4b2o$24bo4bobo50b2o3bo8b
2o$23bobo4bobo14b2o33bo12bo2bo$13b2o8bobo5bobo8b2obo2bo18b2o14b3o12bo$
14bo9bo7bobo7b2ob2o20bobo15bo12bo$14bobo16bobo32bo25bo2bo$15b2o3bo13bo
bo22b2o33b2o$19bobo13bobo6b2o12bo2bo15b2o12bo$20bo15bobo5b2o13bobo14bo
2bo10bobo$7b2o8bo5bo7b2o4bobo20bo15bobo12bo$8bo7bobo3bobo7bo5bobo36bo$
8bobo6bo5bo5b3o7bobo22bo20b2o$9b2o3bo14bo4b2o4bobo19b3o19bobo$13bobo
17bo2bo4bobo5b2o10bo14b2o7bo$14bo18bo2bo5bobo3bobo10b2o12bo2bo$b2o8bo
5b2o4b2o9b2o7bobo2bo26bobo$2bo7bobo4b2o4b2o13bo5bo2b2o27bo$2bobo6bo25b
obo$3b2o3bo5bo22b2o46b2o$7bobo3bobo10b2o23bob3o9b2o5b2o11b2o$8bo5bo11b
2o14b2o5b2obo3bo8b2o5b2o$5bo5bo30b2o6bo4b2o$4bobo3bobo10b2o26b4obo11b
2o$5bo5bo11b2o43b2o$8bo6b2o$o6bobo6bo$2o6bo7bobo20b3o$2o3bo11b2o26b2o$
o3bobo38b2o$5bo8bo$14bo7b2o17b2o5b2o21b2o7b2o$9bo4bo6b2o18b2o5b2o21b2o
7bobo$3b2o4b3o11bo57bo$3b2o7bo$11b2o70b2o$66bo16bobo$53b2o6bo3bobo4b2o
10b2o$53b2o5bobo3bo4bo2bo$18bo2bo11b3o14bo10bo10b2o$2o5b2o9bo3bo4b2o4b
3o13bobo$2o5b2o8bo4bo4bo4bo3bo13bo31b2o$17bo4bo3bobo2b5o20bo25bo$4b2o
11bo3bo9b4o19b3o6b2o9bo9bo$4b2o12bobo32bo10bo8bobo7b2o$53b2o9bobo5bobo
6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o3bo13b2o7bobo3b2o6bob2o$27b2o
5b2o10bo13bo2bo5bobo4b2o3b2obobo$27b2o10bo6b3o11bo2bo4bobo10b2obobo$
38bobo20b2o4bobo14bob2o$24b2o5b2o6bo26bobo15bo$24b2o5b2o32bobo14bobo$
35b2o13b3o13bo15b2o$34bobo12bo3bo9bo11b2o$34b2o12bo5bo7bobo11bo$48bo5b
o8bo7b2o3bob2o$ob3o46bo19b2o2b2obo2bo$ob4o24b2o13b2o2bo3bo4b2o7b2o9bob
2o$o5bo17bo4bobo13b2o3b3o5b2o7b2o2b2o5bo$bobobo2b3o14bo3b2o20bo10b2o7b
o5b2o$2bobob4o13b3o30bo5bo10bo$3bo2bob2o38b2o5bobo5bo8b2o6bo$3bo3b3obo
37bo6bo5b2o15bobo$4b3o2b2obo27bo5b3o4bo5bo20bo$10bo11b2o15bobo4bo5bobo
3bobo5b2o$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo$13b2o3bo21bo
8bobo3bobo$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$15bobo22b2o3b
obo4bobo7bo$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$14bo2bo2b2o54bo
$15b2obob2o$17bo2b2o$18bo10bo21bo5b2o$19b3o6bobo19b3o4b2o$28b2o18b2o2b
o$48b2o21b3o$49bob2o11bo$24b2o22b5o10bobo$23bobo20b5o11bo2bo$24bo21bo
4b4o8b2o$30b2o17bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b3o2b2o$20bo5b2o
5b2o9bo2bo6b2o$26b2o5b2o10b3o6bo!

EDIT: While I tried making a quadratic glider fuse using pentadecathlons to cap off the crystals, it proved less cost-effective than the 3-block version. However, it's possible that by increasing the spacing of the snakes (not necessarily all of them the same amount), one could make an end that stays usable for longer periods of time. Of course, this is all moot because it's easier to add a quadri-snark (is a quinti-snark version in the books?), and there usually isn't enough space for them anyway.

EDIT2: Whoops! I forgot to back up the guns. Pattern fixed.

[EvinZL]

The right side can be tucked in by 1 cell:

Code: Select all

x = 98, y = 101, rule = B3/S23
17b3o12b2o2bo32bo7b3o2b4o$17bo2bo10bob4o31bobo5bo3bo$17bo2bo10bo36bo2b
o4bo$21bo7b2ob7o30b2o6b3obo$19bobo5bo2bobo6bo$20b2o5b2o3bob2o2b2o32b2o
$18b3o10b2ob2o7b2o4bo21bo2bo$18b2o24bo3bobo8b2o11bobo$18bobo21bo6bo8bo
2bo11bo9bo$18bobo21b5o12b2o23bo4bo2bobo$18b2o13b2o11bo16b2o4bo12b3o4bo
3b2o$33b2o5b4o18bobo3bobo19bo3b2o$30bo9bo2bo19bo5b2o16b3o4bo$24bo4bobo
50b2o3bo9bo$23bobo4bobo14b2o33bo13b2o$13b2o8bobo5bobo8b2obo2bo18b2o14b
3o8bob2o$14bo9bo7bobo7b2ob2o20bobo15bo10b2o$14bobo16bobo32bo25bo2bo$
15b2o3bo13bobo22b2o33b2o$19bobo13bobo6b2o12bo2bo15b2o12bo$20bo15bobo5b
2o13bobo14bo2bo10bobo$7b2o8bo5bo7b2o4bobo20bo15bobo12bo$8bo7bobo3bobo
7bo5bobo36bo$8bobo6bo5bo5b3o7bobo22bo20b2o$9b2o3bo14bo4b2o4bobo19b3o
19bobo$13bobo17bo2bo4bobo5b2o10bo14b2o7bo$14bo18bo2bo5bobo3bobo10b2o
12bo2bo$b2o8bo5b2o4b2o9b2o7bobo2bo26bobo$2bo7bobo4b2o4b2o13bo5bo2b2o
27bo$2bobo6bo25bobo$3b2o3bo5bo22b2o46b2o$7bobo3bobo10b2o28b2o7b2o5b2o
11b2o$8bo5bo11b2o14b2o21b2o5b2o$5bo5bo30b2o11bobo$4bobo3bobo10b2o28bo
14b2o$5bo5bo11b2o24b2obob2o12b2o$8bo6b2o33bob2o$o6bobo6bo23bo10bo$2o6b
o7bobo21bo$2o3bo11b2o21bo4b2o$o3bobo38b2o$5bo$13b3o25b2o5b2o21b2o7b2o$
9bo31b2o5b2o21b2o7bobo$3b2o4b3o69bo$3b2o7bo$11b2o70b2o$33b3o30bo16bobo
$33bo2bo16b2o6bo3bobo4b2o10b2o$33bob2o16b2o5bobo3bo4bo2bo$18b2o2b2o26b
o10bo10b2o$2o5b2o8b3o29bobo$2o5b2o15bo25bo31b2o$15bobo14b2o22bo25bo$4b
2o10b4obo2bo7bo2bo18b3o6b2o9bo9bo$4b2o11b3ob3o9b3o17bo10bo8bobo7b2o$
53b2o9bobo5bobo6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o17b2o7bobo3b2o
6bob2o$27b2o5b2o24bo2bo5bobo4b2o3b2obobo$27b2o10bo11bo8bo2bo4bobo10b2o
bobo$38bobo10bo9b2o4bobo14bob2o$24b2o5b2o6bo10bobo13bobo15bo$24b2o5b2o
16b2ob2o11bobo14bobo$35b2o11bo5bo11bo15b2o$34bobo14bo11bo11b2o$34b2o
12b2o3b2o7bobo11bo$63bo7b2o3bob2o$ob3o66b2o2b2obo2bo$ob4o24b2o13b2o11b
2o7b2o9bob2o$o5bo22bobo13b2o11b2o7b2o2b2o5bo$bobobo2b3o18b2o31b2o7bo5b
2o$2bobob4o15bo30bo5bo10bo$3bo2bob2o16b2o20b2o5bobo5bo8b2o6bo$3bo3b3ob
o13b2o22bo6bo5b2o15bobo$4b3o2b2obo27bo5b3o4bo5bo20bo$10bo11b2o15bobo4b
o5bobo3bobo5b2o$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo$13b2o3b
o21bo8bobo3bobo$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$15bobo
22b2o3bobo4bobo7bo$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$14bo2bo
2b2o54bo$15b2obob2o$17bo2b2o30bo$18bo10bo17b3o3bo3b2o$19b3o6bobo16bo6b
o2b2o$28b2o17bo5bo18bo$48b2ob2o19bo$64bo7bo$24b2o37bobo$23bobo36bo2bo$
24bo21bo5b3o8b2o$30b2o12bo4bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b3o2b
2o$20bo5b2o5b2o9bo2bo6b2o$26b2o5b2o10b3o6bo!

[Dean Hickerson]

The right side can be tucked in by 1 cell:

Or even by 4 cells:

Code: Select all

x = 95, y = 101, rule = B3/S23
17b3o12b2o2bo32bo7b3o2b4o$17bo2bo10bob4o31bobo5bo3bo$17bo2bo10bo36bo2b
o4bo$21bo7b2ob7o30b2o6b3obo$19bobo5bo2bobo6bo$20b2o5b2o3bob2o2b2o32b2o
$18b3o10b2ob2o7b2o4bo21bo2bo4bobo2bo3bobo2bo$18b2o24bo3bobo8b2o11bobo
5b2o4bobo2bo$18bobo21bo6bo8bo2bo11bo6bo4bob3obob2o$18bobo21b5o12b2o27b
o4bo$18b2o13b2o11bo16b2o4bo13bo6bo3bo$33b2o5b4o18bobo3bobo12b4o2bo4bo$
30bo9bo2bo19bo5b2o11b3o7b3o$24bo4bobo50b2obob2ob2ob2o$23bobo4bobo14b2o
42bo2bo$13b2o8bobo5bobo8b2obo2bo18b2o14bo5bobo2bo$14bo9bo7bobo7b2ob2o
20bobo12bo3b3o3b3o$14bobo16bobo32bo14bob2ob2o4bo$15b2o3bo13bobo22b2o
21b2obobob3ob2o$19bobo13bobo6b2o12bo2bo15b2o5bo4bo3b2o$20bo15bobo5b2o
13bobo14bo2bo4bo5b2ob2o$7b2o8bo5bo7b2o4bobo20bo15bobo3b2o5bobobo$8bo7b
obo3bobo7bo5bobo36bo6bo2b2o3bo$8bobo6bo5bo5b3o7bobo22bo20bo2bobo2b2o$
9b2o3bo14bo4b2o4bobo19b3o22b2o2b2o$13bobo17bo2bo4bobo5b2o10bo14b2o6bo
2b2obo$14bo18bo2bo5bobo3bobo10b2o12bo2bo3bob2o3bo2bo$b2o8bo5b2o4b2o9b
2o7bobo2bo26bobo5b2obobob2o$2bo7bobo4b2o4b2o13bo5bo2b2o27bo12bo3bo$2bo
bo6bo25bobo$3b2o3bo5bo22b2o46b2o$7bobo3bobo10b2o28b2o7b2o5b2o11b2o$8bo
5bo11b2o14b2o21b2o5b2o$5bo5bo30b2o11bobo$4bobo3bobo10b2o28bo14b2o$5bo
5bo11b2o24b2obob2o12b2o$8bo6b2o33bob2o$o6bobo6bo23bo10bo$2o6bo7bobo21b
o$2o3bo11b2o21bo4b2o$o3bobo38b2o$5bo$13b3o25b2o5b2o21b2o7b2o$9bo31b2o
5b2o21b2o7bobo$3b2o4b3o69bo$3b2o7bo$11b2o70b2o$33b3o30bo16bobo$33bo2bo
16b2o6bo3bobo4b2o10b2o$33bob2o16b2o5bobo3bo4bo2bo$18b2o2b2o26bo10bo10b
2o$2o5b2o8b3o29bobo$2o5b2o15bo25bo31b2o$15bobo14b2o22bo25bo$4b2o10b4ob
o2bo7bo2bo18b3o6b2o9bo9bo$4b2o11b3ob3o9b3o17bo10bo8bobo7b2o$53b2o9bobo
5bobo6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o17b2o7bobo3b2o6bob2o$27b
2o5b2o24bo2bo5bobo4b2o3b2obobo$27b2o10bo11bo8bo2bo4bobo10b2obobo$38bob
o10bo9b2o4bobo14bob2o$24b2o5b2o6bo10bobo13bobo15bo$24b2o5b2o16b2ob2o
11bobo14bobo$35b2o11bo5bo11bo15b2o$34bobo14bo11bo11b2o$34b2o12b2o3b2o
7bobo11bo$63bo7b2o3bob2o$ob3o66b2o2b2obo2bo$ob4o24b2o13b2o11b2o7b2o9bo
b2o$o5bo22bobo13b2o11b2o7b2o2b2o5bo$bobobo2b3o18b2o31b2o7bo5b2o$2bobob
4o15bo30bo5bo10bo$3bo2bob2o16b2o20b2o5bobo5bo8b2o6bo$3bo3b3obo13b2o22b
o6bo5b2o15bobo$4b3o2b2obo27bo5b3o4bo5bo20bo$10bo11b2o15bobo4bo5bobo3bo
bo5b2o$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo$13b2o3bo21bo8bob
o3bobo$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$15bobo22b2o3bobo
4bobo7bo$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$14bo2bo2b2o54bo$
15b2obob2o$17bo2b2o30bo$18bo10bo17b3o3bo3b2o$19b3o6bobo16bo6bo2b2o$28b
2o17bo5bo18bo$48b2ob2o19bo$64bo7bo$24b2o37bobo$23bobo36bo2bo$24bo21bo
5b3o8b2o$30b2o12bo4bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b3o2b2o$20bo5b
2o5b2o9bo2bo6b2o$26b2o5b2o10b3o6bo!

[Pavgran]

And that allows to push the bounding box in the other direction by moving the last quadri-Snark 1fd away and opening up space for more efficient glider-eating reactions. Additionally, I was able to postpone self-destruction-launching glider and fit more SLs here. Totail improvement is 69 more eating reactions.
Bounding box 98*102 and lifespan 1.273e1320

Code: Select all

x = 98, y = 102, rule = B3/S23
16b3o12b2o2bo41b3o3b2o$16bo2bo10bob4o33bo7b3o2bo2bo$16bo2bo10bo37bobo
12b2o$20bo7b2ob7o30bo2bo$18bobo5bo2bobo6bo30b2o$19b2o5b2o3bob2o2b2o$
17b3o10b2ob2o7b2o4bo23b2o$17b2o24bo3bobo21bo2bo$17bobo21bo6bo10b2o11bo
bo$17bobo21b5o12bo2bo11bo9bo$17b2o13b2o11bo13b2o23bo4bo2bobo$32b2o5b4o
20b2o4bo12b3o4bo3b2o$29bo9bo2bo19bobo3bobo19bo3b2o$23bo4bobo32bo5b2o
16b3o4bo$22bobo4bobo14b2o34b2o3bo9bo$12b2o8bobo5bobo8b2obo2bo34bo13b2o
$13bo9bo7bobo7b2ob2o21b2o14b3o8bob2o$13bobo16bobo32bobo15bo10b2o$14b2o
3bo13bobo32bo25bo2bo$18bobo13bobo6b2o14b2o33b2o$19bo15bobo5b2o13bo2bo
15b2o12bo$6b2o8bo5bo7b2o4bobo20bobo14bo2bo10bobo$5bobo7bobo3bobo7bo5bo
bo20bo15bobo12bo$4bo2bobo6bo5bo5b3o7bobo36bo$4b2o2b2o3bo5bo8bo4b2o4bob
o5bo16bo20b2o$12bobo3bobo11bo2bo4bobo3bobo13b3o19bobo$13bo5bo12bo2bo5b
o5bo13bo14b2o7bo$2o8bo5bo16b2o9bo16b2o12bo2bo$bo7bobo3bobo5b2o18bobo
29bobo$bobo6bo5bo6b2o13bo5bo31bo$2b2o3bo5bo23bobo$6bobo3bobo22b2o46b2o
$7bo5bo12b2o23bob3o9b2o5b2o11b2o$4bo5bo15b2o14b2o5b2obo3bo8b2o5b2o$3bo
bo3bobo30b2o6bo4b2o$4bo5bo12b2o26b4obo11b2o$o6bo15b2o43b2o$2o4bobo6b2o
$2o5bo8bo$o15bobo20b3o$17b2o26b2o$45b2o$14bo$3b2o9bo26b2o5b2o21b2o7b2o
$3b2o4bo4bo26b2o5b2o21b2o7bobo$9b3o69bo$12bo$11b2o70b2o$66bo16bobo$53b
2o6bo3bobo4b2o10b2o$53b2o5bobo3bo4bo2bo$18bo2bo11b3o14bo10bo10b2o$2o5b
2o9bo3bo10b3o13bobo$2o5b2o8bo4bo9bo3bo13bo31b2o$17bo4bo8b5o20bo25bo$4b
2o11bo3bo9b4o19b3o6b2o9bo9bo$4b2o12bobo32bo10bo8bobo7b2o$53b2o9bobo5bo
bo6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o17b2o7bobo3b2o6bob2o$27b2o5b
2o24bo2bo5bobo4b2o3b2obobo$27b2o10bo20bo2bo4bobo10b2obobo$38bobo20b2o
4bobo14bob2o$24b2o5b2o6bo26bobo15bo$24b2o5b2o32bobo14bobo$35b2o13b3o
13bo15b2o$34bobo12bo3bo9bo11b2o$34b2o12bo5bo7bobo11bo$48bo5bo8bo7b2o3b
ob2o$ob3o46bo19b2o2b2obo2bo$ob4o24b2o13b2o2bo3bo4b2o7b2o9bob2o$o5bo17b
o4bobo13b2o3b3o5b2o7b2o2b2o5bo$bobobo2b3o14bo3b2o20bo10b2o7bo5b2o$2bob
ob4o13b3o30bo5bo10bo$3bo2bob2o38b2o5bobo5bo8b2o6bo$3bo3b3obo37bo6bo5b
2o15bobo$4b3o2b2obo27bo5b3o4bo5bo20bo$10bo11b2o15bobo4bo5bobo3bobo5b2o
$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo$13b2o3bo21bo8bobo3bobo
$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$15bobo22b2o3bobo4bobo7b
o$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$14bo2bo2b2o54bo$15b2obob
2o$17bo2b2o$18bo10bo21bo5b2o$19b3o6bobo19b3o4b2o$28b2o18b2o2bo$48b2o
21b3o$49bob2o11bo$24b2o22b5o10bobo$23bobo20b5o11bo2bo$24bo21bo4b4o8b2o
$30b2o17bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b3o2b2o$20bo5b2o5b2o9bo2b
o6b2o$26b2o5b2o10b3o6bo!

Dave Greene calls it "pointless optimization game", right?

[squareroot12621]

[…]Bounding box 98*102 and lifespan 1.273e1320[…]

Honestly, when I (coincidentally) made this thread, I was thinking that the maximum would be 50,000. Maybe 100,000. And yet we've come so far. I want to see which popular challenge comes next!

That's one small step for [a] man, one giant leap for mankind.

I can apply that here.

[ihatecorderships]

Since we've gotten so high with diehards, how much more higher could we go if we instead removed the population=0 limit, and investigated engineered methuselahs?

[Rocknlol]

Dave Greene calls it "pointless optimization game", right?

Speaking of! Here's a bounding-box reduction to 94x96:

Code: Select all

x = 94, y = 96, rule = B3/S23
9bo2b9o3bo3b5ob3o2bo2bo24b2obo3b8ob3o$8bo4bo2b2o3bo4bo2b2o2bob2ob2o24b
ob2o2b3o5b3o2bob2o$10b3o3bo7bo8bo4bobob2o21bo3b2o3bo8b2o$12b2o4bobo5b
3o2bobo2b2o2bo3b2o19bobob2o4bo8bo$13bob2o2b2o4bob3o2bo2b2ob3o2bo3b2o
15bo6bobo13bo3b2o$24b2o2bo2bobob5ob3o3bo10b2o3bobo2bo3bo14b2o4bo$13b2o
3b2o6bo3bo9b2o2b2o11bo2bo5bo5bo15bo2bo$15bo3bobo10b2o12bo11b2o11bo16bo
3bo$17bob2o3b2o5bo6b7o2bo14b2o4bo20bo3bo$15b2o11bo9bo2bo19bobo3bobo20b
o2bo$16bo5bo4bobo32bo5b2o16b2o3b3o$21bobo4bobo14b2o34b2o3bobobob2o$11b
2o8bobo5bobo8b2obo2bo34bo7bo3bo$12bo9bo7bobo7b2ob2o21b2o14b3o2b2o4bo$
12bobo16bobo32bobo15bo5b2obo$13b2o3bo13bobo32bo19b3o3bo$5bo11bobo13bob
o6b2o14b2o33bo$2bobo13bo15bobo5b2o13bo2bo15b2o11bo3bo$2bobobo8bo5bo7b
2o4bobo20bobo14bo2bo11bob2o$7bo6bobo3bobo7bo5bobo20bo15bobo10bobo$4bo
3bo6bo5bo5b3o7bobo36bo12bo$4bo2b2o3bo5bo8bo4b2o4bobo5bo16bo20b2o$3bo7b
obo3bobo11bo2bo4bobo3bobo13b3o19bobo$o3bo7bo5bo12bo2bo5bo5bo13bo14b2o
7bo$3o5b2o5bo16b2o9bo16b2o12bo2bo$2bo7bo3bobo5b2o18bobo29bobo$bo3bo3bo
5bo6b2o13bo5bo31bo$bo2bo3bo3bo23bobo$2b5o4bobo22b2o13bo2bo29b2o$ob2o4b
o3bo12b2o23bo3bo9b2o5b2o11b2o$o4bo3bo15b2o14b2o7bo4bo8b2o5b2o$bobobo4b
o30b2o7bo4bo$2o3bob2obo11b2o27bo3bo11b2o$bo3bo16b2o28bobo12b2o$2bobo9b
2o$3o3bob2o5bo23bo$bo5bo7bobo21bo$5b5o6b2o21bo4b2o$2obo3bo36b2o$2bo2b
2o$12b3o25b2o5b2o21b2o7b2o$bobo4bo31b2o5b2o21b2o7bobo$3bo4b3o69bo$2bo
8bo$10b2o70b2o$65bo16bobo$52b2o6bo3bobo4b2o10b2o$2bo49b2o5bobo3bo4bo2b
o$o48bo10bo10b2o$obo3b2o10b3o12b2o13bobo$o5b2o8b2ob2o8b3obobo13bo31b2o
$o15b2ob2o11bo2bo19bo25bo$3b2o12b2o9bo24b3o6b2o9bo9bo$3b2o47bo10bo8bob
o7b2o$52b2o9bobo5bobo6bo3b2o$41b2o21b2o4bobo7b4o2bo$33b2o6b2o17b2o7bob
o3b2o6bob2o$26b2o5b2o24bo2bo5bobo4b2o3b2obobo$26b2o10bo20bo2bo4bobo10b
2obobo$37bobo20b2o4bobo14bob2o$23b2o5b2o6bo26bobo15bo$23b2o5b2o32bobo
14bobo$34b2o29bo15b2o$3bo29bobo26bo11b2o$33b2o13b5o8bobo11bo$2ob3o41bo
b3obo8bo7b2o3bob2o$2o2bo2bo40bo3bo17b2o2b2obo2bo$o6bo21b2o13b2o3b3o5b
2o7b2o9bob2o$2o2bo2bobo11bobo4bobo13b2o4bo6b2o7b2o2b2o5bo$2bo4bo14b2o
4b2o31b2o7bo5b2o$3bo2bobo13bo32bo5bo10bo$5bo41b2o5bobo5bo8b2o6bo$2bob
3o3bo37bo6bo5b2o15bobo$4bo5bo28bo5b3o4bo5bo20bo$3bo3bo2b2o9b2o15bobo4b
o5bobo3bobo5b2o$12bo7bobo16bo12bo5bo6b2o$12b3o5b2o27bo5bo$39bo8bobo3bo
bo$38bobo8bo5bo3b2o$15bo22bo2bo3bo6bo6bobo$14bob5o18b2o3bobo4bobo7bo$
13b2o5bo23b2o6bo8b2o12b2o$13b2o3bo2bo52bobo$21bo53bo$15b2obo2bo26bo$
18bo2bo25b2o2bo$19b2o7bo20bo3bo2b2o$19b2o6bobo15b2o4bo4b2o$27b2o20b2o
20bo$46b2o5bo17bo$44bo4bo3bo9bo7bo$17b2o7b2obo18b2ob2obo7bobo$18bo4b2o
2b4o16b2ob2o2bo6bo2bo$17bobo2bo8bobo13bo6b2o6b2o$17bo2b2obo2bo3bo2bo8b
o2b2o5b2o$18b3obo2b3ob7o5b9ob5o!

[Dean Hickerson]

And that allows to push the bounding box in the other direction by moving the last quadri-Snark 1fd away and opening up space for more efficient glider-eating reactions. Additionally, I was able to postpone self-destruction-launching glider and fit more SLs here. Totail improvement is 69 more eating reactions.
Bounding box 98*102 and lifespan 1.273e1320

I don't think that's right. I ran my simulated version of the pattern and concluded that it would only be about 1.7e1295. I wasn't sure that I'd computed correctly, so I ran the original using Hyperspeed in Golly and it died around gen 1.7705e1295.

After much experimentation, I've found a way to slow down the deletions of both quadri-snarks.

For the one on the north edge, I replaced the 2-block reflector on the west edge by 2 blinkers, which consume 2 southwestward gliders before sending a glider northeast. That gives another factor of 121^16. (It also makes room for another tub to be deleted, gaining another factor of 121^32.) We gain some more because the reflected glider doesn't do much of the deletion of the quadri-snark; it just deletes a beehive. Subsequent gliders on the northwestward path handle the rest.

That modification doesn't work for the quadri-snark on the east edge. Instead, I kept the 2-block reflector, but changed the extra stuff near the quadri-snark. Now it consumes several more gliders before being deleted completely. Of course, that doesn't give as much of an improvement as changing the one on the north edge.

This dies about generation 1.33616e1443. No doubt it can be improved further using Rocknlol's bounding-box reduction.

Code: Select all

x = 98, y = 102, rule = B3/S23
16b3o12b2o2bo5bo3b2o30b3o3b2o$16bo2bo10bob4o5bo4bo22bo7b3o2bo2bo$16bo
2bo10bo10bo4bob2o18bobo12b2o$20bo7b2ob7o9bobo18bo2bo$18bobo5bo2bobo6bo
30b2o$19b2o5b2o3bob2o2b2o$17b3o10b2ob2o7b2o28b2o$17b2o24bo27bo2bo$17bo
bo21bo17b2o11bobo$17bobo21b5o12bo2bo11bo9bo$17b2o13b2o11bo13b2o23bo4bo
2bobo$32b2o5b4o20b2o4bo12b3o4bo3b2o$29bo9bo2bo19bobo3bobo19bo3b2o$23bo
4bobo32bo5b2o16b3o4bo$22bobo4bobo14b2o34b2o3bo9bo$12b2o8bobo5bobo8b2ob
o2bo34bo13b2o$13bo9bo7bobo7b2ob2o21b2o14b3o8bob2o$13bobo16bobo32bobo
15bo10b2o$14b2o3bo13bobo32bo25bo2bo$18bobo13bobo6b2o14b2o33b2o$19bo15b
obo5b2o13bo2bo15b2o12bo$6b2o8bo5bo7b2o4bobo20bobo14bo2bo10bobo$5bobo7b
obo3bobo7bo5bobo20bo15bobo12bo$4bo2bobo6bo5bo5b3o7bobo36bo$4b2o2b2o3bo
5bo8bo10bobo5bo16bo20b2o$12bobo3bobo19bobo3bobo13b3o19bobo$13bo5bo21bo
5bo13bo14b2o7bo$2o8bo5bo27bo16b2o12bo2bo$bo7bobo3bobo5b2o18bobo29bobo$
bobo6bo5bo6b2o13bo5bo31bo$2b2o3bo5bo23bobo$6bobo3bobo22b2o46b2o$7bo5bo
12b2o23bob3o9b2o5b2o11b2o$4bo5bo15b2o14b2o5b2obo3bo8b2o5b2o$3bobo3bobo
30b2o6bo4b2o$4bo5bo12b2o26b4obo11b2o$o6bo15b2o43b2o$o5bobo6b2o$o6bo8bo
$4bo11bobo20b3o$3bobo11b2o26b2o$4bo40b2o$14bo$14bo26b2o5b2o21b2o7b2o$
9bo4bo26b2o5b2o21b2o7bobo$2b3o4b3o69bo$12bo$11b2o70b2o$66bo16bobo$53b
2o6bo3bobo4b2o10b2o$53b2o5bobo3bo4bo2bo$18bo2bo11b3o14bo10bo10b2o$2o5b
2o9bo3bo10b3o13bobo$2o5b2o8bo4bo9bo3bo13bo31b2o$17bo4bo8b5o20bo25bo$4b
2o11bo3bo9b4o19b3o6b2o9bo9bo$4b2o12bobo32bo10bo8bobo7b2o$53b2o9bobo5bo
bo6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o17b2o7bobo3b2o6bob2o$27b2o5b
2o24bo2bo5bobo4b2o3b2obobo$27b2o10bo20bo2bo4bobo10b2obobo$38bobo20b2o
4bobo14bob2o$24b2o5b2o6bo26bobo15bo$24b2o5b2o32bobo14bobo$35b2o13b3o
13bo15b2o$34bobo12bo3bo9bo11b2o9b2o$34b2o12bo5bo7bobo11bo9bo$48bo5bo8b
o7b2o3bob2o4bobo$ob3o46bo19b2o2b2obo2bo2b2o$ob4o24b2o13b2o2bo3bo4b2o7b
2o9bob2o$o5bo17bo4bobo13b2o3b3o5b2o7b2o2b2o5bo5b4o$bobobo2b3o14bo3b2o
20bo10b2o7bo5b2o4bo3bo$2bobob4o13b3o30bo5bo10bo8bobo$3bo2bob2o38b2o5bo
bo5bo8b2o9b2o$3bo3b3obo37bo6bo5b2o$4b3o2b2obo27bo5b3o4bo5bo$10bo11b2o
15bobo4bo5bobo3bobo5b2o$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo
$13b2o3bo21bo8bobo3bobo$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$
15bobo22b2o3bobo4bobo7bo$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$
14bo2bo2b2o54bo$15b2obob2o$17bo2b2o$18bo10bo21bo5b2o$19b3o6bobo19b3o4b
2o$28b2o18b2o2bo$48b2o21b3o$49bob2o11bo$24b2o22b5o10bobo$23bobo20b5o
11bo2bo$24bo21bo4b4o8b2o$30b2o17bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b
3o2b2o$20bo5b2o5b2o9bo2bo6b2o$26b2o5b2o10b3o6bo!

Here's a fast simulator for it; at gen 499321 it produces the last 3 gliders that help to delete the c/5 spaceship:

Code: Select all

x = 131, y = 143, rule = B3/S23
49b3o12b2o2bo5bo3b2o30b3o3b2o$49bo2bo10bob4o5bo4bo22bo7b3o2bo2bo$49bo
2bo10bo10bo4bob2o18bobo12b2o$53bo7b2ob7o9bobo18bo2bo$51bobo5bo2bobo6bo
30b2o$52b2o5b2o3bob2o2b2o$50b3o10b2ob2o7b2o28b2o$50b2o24bo27bo2bo$50bo
bo21bo17b2o11bobo$50bobo21b5o12bo2bo11bo9bo$50b2o13b2o11bo13b2o23bo4bo
2bobo$65b2o5b4o20b2o4bo12b3o4bo3b2o$62bo9bo2bo19bobo3bobo19bo3b2o$56bo
4bobo32bo5b2o16b3o4bo$55bobo4bobo14b2o34b2o3bo9bo$45b2o8bobo5bobo8b2ob
o2bo34bo13b2o$46bo9bo7bobo7b2ob2o21b2o14b3o8bob2o$46bobo16bobo32bobo
15bo10b2o$47b2o3bo13bobo32bo25bo2bo$51bobo13bobo6b2o14b2o33b2o$52bo15b
obo5b2o13bo2bo15b2o12bo$39b2o8bo5bo7b2o4bobo20bobo14bo2bo10bobo$38bobo
7bobo3bobo7bo5bobo20bo15bobo12bo$37bo2bobo6bo5bo5b3o7bobo36bo$37b2o2b
2o3bo5bo8bo10bobo5bo16bo20b2o$45bobo3bobo19bobo3bobo13b3o19bobo$46bo5b
o21bo5bo13bo14b2o7bo$33b2o8bo5bo27bo16b2o12bo2bo$34bo7bobo3bobo5b2o18b
obo29bobo$34bobo6bo5bo6b2o13bo5bo31bo$35b2o3bo5bo23bobo$39bobo3bobo22b
2o46b2o$40bo5bo12b2o23bob3o9b2o5b2o11b2o$37bo5bo15b2o14b2o5b2obo3bo8b
2o5b2o$36bobo3bobo30b2o6bo4b2o$37bo5bo12b2o26b4obo11b2o$33bo6bo15b2o
43b2o$33bo5bobo6b2o$33bo6bo8bo$37bo11bobo20b3o$36bobo11b2o26b2o$37bo
40b2o$47bo$47bo26b2o5b2o21b2o7b2o$42bo4bo26b2o5b2o21b2o7bobo$35b3o4b3o
69bo$45bo$44b2o70b2o$99bo16bobo$86b2o6bo3bobo4b2o10b2o$86b2o5bobo3bo4b
o2bo$51bo2bo11b3o14bo10bo10b2o$33b2o5b2o9bo3bo10b3o13bobo$33b2o5b2o8bo
4bo9bo3bo13bo31b2o$50bo4bo8b5o20bo25bo$37b2o11bo3bo9b4o19b3o6b2o9bo9bo
$37b2o12bobo32bo10bo8bobo7b2o$86b2o9bobo5bobo6bo3b2o$75b2o21b2o4bobo7b
4o2bo$67b2o6b2o17b2o7bobo3b2o6bob2o$60b2o5b2o24bo2bo5bobo4b2o3b2obobo$
60b2o10bo20bo2bo4bobo10b2obobo$71bobo20b2o4bobo14bob2o$57b2o5b2o6bo26b
obo15bo$57b2o5b2o32bobo14bobo$68b2o13b3o13bo15b2o$67bobo12bo3bo9bo11b
2o9b2o$67b2o12bo5bo7bobo11bo9bo$81bo5bo8bo7b2o3bob2o4bobo$33bob3o46bo
19b2o2b2obo2bo2b2o$33bob4o24b2o13b2o2bo3bo4b2o7b2o9bob2o$33bo5bo17bo4b
obo13b2o3b3o5b2o7b2o2b2o5bo5b4o$34bobobo2b3o14bo3b2o20bo10b2o7bo5b2o4b
o3bo$35bobob4o13b3o30bo5bo10bo8bobo$36bo2bob2o38b2o5bobo5bo8b2o9b2o$
36bo3b3obo37bo6bo5b2o$37b3o2b2obo27bo5b3o4bo5bo$43bo11b2o15bobo4bo5bob
o3bobo5b2o$44bo2bo6bobo16bo12bo5bo6b2o$45bo2bo5b2o27bo5bo$46b2o3bo21bo
8bobo3bobo$47b5o20bobo8bo5bo3b2o$48b4o20bo2bo3bo6bo6bobo$48bobo22b2o3b
obo4bobo7bo$37b2o8bob2obo25b2o6bo8b2o12b2o$36bo2bo7bo3bobo54bobo$35bob
obo7bo2bo2b2o54bo$36bobo9b2obob2o$37bo12bo2b2o$51bo10bo21bo5b2o$52b3o
6bobo19b3o4b2o$61b2o18b2o2bo$81b2o21b3o$82bob2o11bo$57b2o22b5o10bobo$
56bobo20b5o11bo2bo$57bo21bo4b4o8b2o$63b2o17bo2b3o$53b2o8b2o11bo5b3o2b
2o$52bobo27b3o2b2o$53bo5b2o5b2o9bo2bo6b2o$32b2o25b2o5b2o10b3o6bo$31bob
o$31bo5b2o4b3o$30b2o6bo$35b3o$35bo5bo$39b3o$4b2o32bo$5bo32b2o$3bo19b2o
3b2o$3b2o18bo4b2o$b2o3bo14bobo$o2b4o14b2o$2obo6b2o19b2o$bobob2o3b2o19b
2o$bobob2o$2obo24b2o$3bo24b2o$3bobo$4b2o2b2o$8b2o$13b2o$14bo$11b3o12b
2o$11bo13b2o$21bo5bo$20bob2o$19bo3bo$19bo5bo$16bo2bo5bo$15bobo7bo13bo$
16b2o2b4o14b3o$37b2obo$16b2o2b4o14b2o6b2o$15bobo7bo12b3o6bo$16bo2bo5bo
12b2obo4bo$19bo5bo12bobo5b2o$19bo3bo4b2o9bo$20bob2o4b2o$21bo$39b2o$39b
2o!

[squareroot12621]

Since we've gotten so high with diehards, how much more higher could we go if we instead removed the population=0 limit, and investigated engineered methuselahs?

I never would have expected that change in direction, but what can go wrong?

Here's as far as I got:

Code: Select all

x = 103, y = 71, rule = LifeHistory
81.2A$22.A2.2A54.2A$22.4A.A$27.A$20.7A.2A$19.A6.A.A2.A37.2A22.2A$19.2A
2.2A.A3.2A38.A8.2A12.A$23.2A.2A42.A.A7.A10.A.A$66.A4.2A7.A10.2A4.A$66.
3A10.A15.3A$69.A24.A$26.A41.2A24.2A$15.A9.A.A$13.2A.A8.A.A$12.A13.A$11.
A.A2.A$11.A2.A5.A$12.2A5.A.A9.D$19.A.A10.D34.A2.A$20.A9.3D34.3A$61.2A
38.2A$61.2A38.2A$18.2D6.2A8.A57.3A$17.D.D6.A8.A.A55.A2.A$4.2A13.D7.3A
6.A.A$5.A23.A7.A.A$3.A19.2A13.A.A$3.2A18.A15.A.A$.2A3.A4.2A8.A.A16.A.
A$A2.4A3.A2.A7.2A18.A.A$2A.A7.2A29.A.A22.2A25.2A$.A.A.2A36.A.A21.2A25.
A$.A.A.2A37.A.A18.2A17.A10.3A$2A.A26.2A13.A.A17.2A4.2A10.A7.2A4.A$3.A
12.2A11.A2.A13.A.A4.D2C14.A.A10.A7.A.A$3.A.A9.A2.A11.2A15.A.A4.A7.2A6.
A12.2A8.A$4.2A10.2A3.3D24.A3.A.A7.2A5.2A22.2A$21.D30.2A6.2A$22.D10.2A
13.A11.2A$12.A20.A13.A.A$11.A.2A10.2A7.3A10.A.A31.2A$15.A9.A.A8.A11.A
17.2A2.A10.2A$11.A2.A.A9.2A34.2A2.2A3.A$13.A2.A13.A31.2A7.A$14.2A13.A
.A35.4A$28.A2.A$29.2A9.A10.D$32.3D5.3A7.D$32.D10.A6.3D21.2A$33.D8.2A30.
A.A$71.2D2.A$70.D.D$49.A22.D$48.A.A$48.A.A5.2A$49.A5.A2.A10.D$53.A2.A
.A11.D$43.A13.A10.3D$42.A.A8.A.2A$42.A.A9.A16.2A$43.A26.A.A$71.A3$42.
2A.2A$38.2A3.A.2A2.2A$38.A2.A.A6.A$40.2A.7A$42.A$42.A.4A$43.2A2.A!
[[ ZOOM 5 AUTOSTART STEP 64 T 0 PAUSE 1 T 325450 STEP 64 ]]
[[ T 326000 STEP 1 ZOOM 11/3 X 15 Y 0 LOOP 326400 ]]

(It will take 1:25.5 to get to the interesting part.)

[calcyman]

This dies about generation 1.33616e1443. No doubt it can be improved further using Rocknlol's bounding-box reduction.

Here's a 94-by-99 version. Generation 35 of my pattern is equal to generation 32 of your pattern:

Code: Select all

x = 94, y = 99, rule = B3/S23
15b3o12b2o2bo9b2o$15bo2bo10bob4o4b3o3bo$15bo2bo10bo15bob2o$19bo7b2ob7o
9bobo18b2obo3b8ob3o$17bobo5bo2bobo6bo26bob2o2b3o5b3o2bob2o$18b2o5b2o3b
ob2o2b2o27bo3b2o3bo8b2o$16b3o10b2ob2o7b2o22bobob2o4bo8bo$16b2o24bo21bo
6bobo13bo3b2o$16bobo21bo17b2o3bobo2bo3bo14b2o4bo$16bobo21b5o12bo2bo5bo
5bo7bobo5bo2bo$16b2o13b2o11bo13b2o11bo9b2o5bo3bo$31b2o5b4o20b2o4bo12bo
7bo3bo$28bo9bo2bo19bobo3bobo20bo2bo$22bo4bobo32bo5b2o16b2o3b3o$21bobo
4bobo14b2o34b2o3bobobob2o$11b2o8bobo5bobo8b2obo2bo34bo7bo3bo$12bo9bo7b
obo7b2ob2o21b2o14b3o2b2o4bo$12bobo16bobo32bobo15bo5b2obo$13b2o3bo13bob
o32bo19b3o3bo$2b2o3b2o8bobo13bobo6b2o14b2o33bo$2b3ob3o9bo15bobo5b2o13b
o2bo15b2o11bo3bo$3b2ob2o7bo5bo7b2o4bobo20bobo14bo2bo11bob2o$14bobo3bob
o7bo5bobo20bo15bobo10bobo$o2b3o2bo6bo5bo5b3o7bobo36bo12bo$2bo4b2o3bo5b
o8bo10bobo5bo16bo20b2o$ob2ob3o3bobo3bobo19bobo3bobo13b3o19bobo$ob2ob4o
3bo5bo21bo5bo13bo14b2o7bo$obo3b2obo5bo27bo16b2o12bo2bo$4bo3bobo3bobo5b
2o18bobo29bobo$2ob4o2bo5bo6b2o13bo5bo31bo$bo10bo23bobo$2o4bo4bobo22b2o
13bo2bo29b2o$3obobobo3bo12b2o23bo3bo9b2o5b2o11b2o$bo3b2o2bo15b2o14b2o
7bo4bo8b2o5b2o$bo2b5obo30b2o7bo4bo$3o2b2o2bo12b2o27bo3bo11b2o$2o2bo3bo
13b2o28bobo12b2o$ob4o8b2o$4o2bobo6bo23bo$2o3bo9bobo21bo$b2o13b2o21bo4b
2o$o2bobo2bo35b2o$2bo3bo$12b3o25b2o5b2o21b2o7b2o$2bo5bo31b2o5b2o21b2o
7bobo$2bo5b3o69bo$2bo8bo$10b2o70b2o$65bo16bobo$52b2o6bo3bobo4b2o10b2o$
2bo49b2o5bobo3bo4bo2bo$o48bo10bo10b2o$obo3b2o10b3o12b2o13bobo$o5b2o8b
2ob2o8b3obobo13bo31b2o$o15b2ob2o11bo2bo19bo25bo$3b2o12b2o9bo24b3o6b2o
9bo9bo$3b2o47bo10bo8bobo7b2o$52b2o9bobo5bobo6bo3b2o$41b2o21b2o4bobo7b
4o2bo$33b2o6b2o17b2o7bobo3b2o6bob2o$26b2o5b2o24bo2bo5bobo4b2o3b2obobo$
26b2o10bo20bo2bo4bobo10b2obobo$37bobo20b2o4bobo14bob2o$23b2o5b2o6bo26b
obo15bo$23b2o5b2o32bobo14bobo$34b2o29bo15b2o$3bo29bobo26bo11b2o9b2o$
33b2o13b5o8bobo11bo9bo$2ob3o41bob3obo8bo7b2o3bob2o4bobo$2o2bo2bo40bo3b
o17b2o2b2obo2bo2b2o$o6bo21b2o13b2o3b3o5b2o7b2o9bob2o$2o2bo2bobo11bobo
4bobo13b2o4bo6b2o7b2o2b2o5bo5b4o$2bo4bo14b2o4b2o31b2o7bo5b2o4bo3bo$3bo
2bobo13bo32bo5bo10bo8bobo$5bo41b2o5bobo5bo8b2o9b2o$2bob3o3bo37bo6bo5b
2o$4bo5bo28bo5b3o4bo5bo$3bo3bo2b2o9b2o15bobo4bo5bobo3bobo5b2o$12bo7bob
o16bo12bo5bo6b2o$12b3o5b2o27bo5bo$39bo8bobo3bobo$38bobo8bo5bo3b2o$15bo
22bo2bo3bo6bo6bobo$14bob5o18b2o3bobo4bobo7bo$13b2o5bo23b2o6bo8b2o12b2o
$13b2o3bo2bo52bobo$21bo53bo$15b2obo2bo26bo$18bo2bo25b2o2bo$19b2o7bo20b
o3bo2b2o$19b2o6bobo15b2o4bo4b2o$27b2o20b2o20bo$46b2o5bo17bo$44bo4bo3bo
9bo7bo$17b2o7b2obo18b2ob2obo7bobo$18bo4b2o2b4o16b2ob2o2bo6bo2bo$17bobo
2bo8bobo13bo6b2o6b2o$17bo2b2obo2bo3bo2bo8bo2b2o5b2o$18b3obo2b3ob7o5b9o
b5o!

Potentially the top three rows can be shaved off.

[Pavgran]

And that allows to push the bounding box in the other direction by moving the last quadri-Snark 1fd away and opening up space for more efficient glider-eating reactions. Additionally, I was able to postpone self-destruction-launching glider and fit more SLs here. Totail improvement is 69 more eating reactions.
Bounding box 98*102 and lifespan 1.273e1320

I don't think that's right. I ran my simulated version of the pattern and concluded that it would only be about 1.7e1295. I wasn't sure that I'd computed correctly, so I ran the original using Hyperspeed in Golly and it died around gen 1.7705e1295.

Hmm. It looks like I posted the wrong version, without the last optimization I described.
Here is the correct one:

Code: Select all

x = 98, y = 102, rule = B3/S23
16b3o12b2o2bo41b3o3b2o$16bo2bo10bob4o33bo7b3o2bo2bo$16bo2bo10bo37bobo
12b2o$20bo7b2ob7o30bo2bo$18bobo5bo2bobo6bo30b2o$19b2o5b2o3bob2o2b2o$
17b3o10b2ob2o7b2o4bo23b2o$17b2o24bo3bobo21bo2bo$17bobo21bo6bo10b2o11bo
bo$17bobo21b5o12bo2bo11bo9bo$17b2o13b2o11bo13b2o23bo4bo2bobo$32b2o5b4o
20b2o4bo12b3o4bo3b2o$29bo9bo2bo19bobo3bobo19bo3b2o$23bo4bobo32bo5b2o
16b3o4bo$22bobo4bobo14b2o34b2o3bo9bo$12b2o8bobo5bobo8b2obo2bo34bo13b2o
$13bo9bo7bobo7b2ob2o21b2o14b3o8bob2o$13bobo16bobo32bobo15bo10b2o$14b2o
3bo13bobo32bo25bo2bo$18bobo13bobo6b2o14b2o33b2o$19bo15bobo5b2o13bo2bo
15b2o12bo$6b2o8bo5bo7b2o4bobo20bobo14bo2bo10bobo$5bobo7bobo3bobo7bo5bo
bo20bo15bobo12bo$4bo2bobo6bo5bo5b3o7bobo36bo$4b2o2b2o3bo5bo8bo4b2o4bob
o5bo16bo20b2o$12bobo3bobo11bo2bo4bobo3bobo13b3o19bobo$13bo5bo12bo2bo5b
o5bo13bo14b2o7bo$2o8bo5bo16b2o9bo16b2o12bo2bo$bo7bobo3bobo5b2o18bobo
29bobo$bobo6bo5bo6b2o13bo5bo31bo$2b2o3bo5bo23bobo$6bobo3bobo22b2o46b2o
$7bo5bo12b2o23bob3o9b2o5b2o11b2o$4bo5bo15b2o14b2o5b2obo3bo8b2o5b2o$3bo
bo3bobo30b2o6bo4b2o$4bo5bo12b2o26b4obo11b2o$o6bo15b2o43b2o17b2o$2o4bob
o6b2o70bobo$2o5bo8bo71bo$o15bobo20b3o$17b2o26b2o43b2o$45b2o43bobo$14bo
72bo3b2o$3b2o9bo26b2o5b2o21b2o13bobo$3b2o4bo4bo26b2o5b2o21b2o14bo$9b3o
72bo5bo$12bo70bobo3bobo$11b2o71bo5bo$66bo14bo5bo$53b2o6bo3bobo4b2o6bob
o3bobo$53b2o5bobo3bo4bo2bo6bo5bo$18bo2bo11b3o14bo10bo10b2o$2o5b2o9bo3b
o10b3o13bobo$2o5b2o8bo4bo9bo3bo13bo31b2o4b2o2b2o$17bo4bo8b5o20bo25bo5b
obo2bo$4b2o11bo3bo9b4o19b3o6b2o9bo9bo5bobo$4b2o12bobo32bo10bo8bobo7b2o
5b2o$53b2o9bobo5bobo6bo3b2o$42b2o21b2o4bobo7b4o2bo$34b2o6b2o17b2o7bobo
3b2o6bob2o$27b2o5b2o24bo2bo5bobo4b2o3b2obobo$27b2o10bo20bo2bo4bobo10b
2obobo$38bobo20b2o4bobo14bob2o$24b2o5b2o6bo26bobo15bo$24b2o5b2o32bobo
14bobo$35b2o13b3o13bo15b2o$34bobo12bo3bo9bo11b2o$34b2o12bo5bo7bobo11bo
$48bo5bo8bo7b2o3bob2o$ob3o46bo19b2o2b2obo2bo$ob4o24b2o13b2o2bo3bo4b2o
7b2o9bob2o$o5bo17bo4bobo13b2o3b3o5b2o7b2o2b2o5bo$bobobo2b3o14bo3b2o20b
o10b2o7bo5b2o$2bobob4o13b3o30bo5bo10bo$3bo2bob2o38b2o5bobo5bo8b2o6bo$
3bo3b3obo37bo6bo5b2o15bobo$4b3o2b2obo27bo5b3o4bo5bo20bo$10bo11b2o15bob
o4bo5bobo3bobo5b2o$11bo2bo6bobo16bo12bo5bo6b2o$12bo2bo5b2o27bo5bo$13b
2o3bo21bo8bobo3bobo$14b5o20bobo8bo5bo3b2o$15b4o20bo2bo3bo6bo6bobo$15bo
bo22b2o3bobo4bobo7bo$14bob2obo25b2o6bo8b2o12b2o$14bo3bobo54bobo$14bo2b
o2b2o54bo$15b2obob2o$17bo2b2o$18bo10bo21bo5b2o$19b3o6bobo19b3o4b2o$28b
2o18b2o2bo$48b2o21b3o$49bob2o11bo$24b2o22b5o10bobo$23bobo20b5o11bo2bo$
24bo21bo4b4o8b2o$30b2o17bo2b3o$20b2o8b2o11bo5b3o2b2o$19bobo27b3o2b2o$
20bo5b2o5b2o9bo2bo6b2o$26b2o5b2o10b3o6bo!

And including your last modifications (edit: and bounding box reduction):

Code: Select all

x = 94, y = 99, rule = B3/S23
15b3o12b2o2bo9b2o$15bo2bo10bob4o4b3o3bo$15bo2bo10bo15bob2o$19bo7b2ob7o
9bobo18b2obo3b8ob3o$17bobo5bo2bobo6bo26bob2o2b3o5b3o2bob2o$18b2o5b2o3b
ob2o2b2o27bo3b2o3bo8b2o$16b3o10b2ob2o7b2o22bobob2o4bo8bo$16b2o24bo21bo
6bobo13bo3b2o$16bobo21bo17b2o3bobo2bo3bo14b2o4bo$16bobo21b5o12bo2bo5bo
5bo7bobo5bo2bo$16b2o13b2o11bo13b2o11bo9b2o5bo3bo$31b2o5b4o20b2o4bo12bo
7bo3bo$28bo9bo2bo19bobo3bobo20bo2bo$22bo4bobo32bo5b2o16b2o3b3o$21bobo
4bobo14b2o34b2o3bobobob2o$11b2o8bobo5bobo8b2obo2bo34bo7bo3bo$12bo9bo7b
obo7b2ob2o21b2o14b3o2b2o4bo$12bobo16bobo32bobo15bo5b2obo$13b2o3bo13bob
o32bo19b3o3bo$2b2o3b2o8bobo13bobo6b2o14b2o33bo$2b3ob3o9bo15bobo5b2o13b
o2bo15b2o11bo3bo$3b2ob2o7bo5bo7b2o4bobo20bobo14bo2bo11bob2o$14bobo3bob
o7bo5bobo20bo15bobo10bobo$o2b3o2bo6bo5bo5b3o7bobo36bo12bo$2bo4b2o3bo5b
o8bo10bobo5bo16bo20b2o$ob2ob3o3bobo3bobo19bobo3bobo13b3o19bobo$ob2ob4o
3bo5bo21bo5bo13bo14b2o7bo$obo3b2obo5bo27bo16b2o12bo2bo$4bo3bobo3bobo5b
2o18bobo29bobo$2ob4o2bo5bo6b2o13bo5bo31bo$bo10bo23bobo$2o4bo4bobo22b2o
13bo2bo29b2o$3obobobo3bo12b2o23bo3bo9b2o5b2o11b2o$bo3b2o2bo15b2o14b2o
7bo4bo8b2o5b2o$bo2b5obo30b2o7bo4bo$3o2b2o2bo12b2o27bo3bo11b2o$2o2bo3bo
13b2o28bobo12b2o17b2o$ob4o8b2o70bobo$4o2bobo6bo23bo47bo$2o3bo9bobo21bo
$b2o13b2o21bo4b2o43b2o$o2bobo2bo35b2o43bobo$2bo3bo79bo3b2o$12b3o25b2o
5b2o21b2o13bobo$2bo5bo31b2o5b2o21b2o14bo$2bo5b3o72bo5bo$2bo8bo70bobo3b
obo$10b2o71bo5bo$65bo20bo$52b2o6bo3bobo4b2o12bobo$2bo49b2o5bobo3bo4bo
2bo12bo$o48bo10bo10b2o$obo3b2o10b3o12b2o13bobo$o5b2o8b2ob2o8b3obobo13b
o31b2o4b2o2b2o$o15b2ob2o11bo2bo19bo25bo5bobo2bo$3b2o12b2o9bo24b3o6b2o
9bo9bo5bobo$3b2o47bo10bo8bobo7b2o5b2o$52b2o9bobo5bobo6bo3b2o$41b2o21b
2o4bobo7b4o2bo$33b2o6b2o17b2o7bobo3b2o6bob2o$26b2o5b2o24bo2bo5bobo4b2o
3b2obobo$26b2o10bo20bo2bo4bobo10b2obobo$37bobo20b2o4bobo14bob2o$23b2o
5b2o6bo26bobo15bo$23b2o5b2o32bobo14bobo$34b2o29bo15b2o$3bo29bobo26bo
11b2o9b2o$33b2o13b5o8bobo11bo9bo$2ob3o41bob3obo8bo7b2o3bob2o4bobo$2o2b
o2bo40bo3bo17b2o2b2obo2bo2b2o$o6bo21b2o13b2o3b3o5b2o7b2o9bob2o$2o2bo2b
obo11bobo4bobo13b2o4bo6b2o7b2o2b2o5bo5b4o$2bo4bo14b2o4b2o31b2o7bo5b2o
4bo3bo$3bo2bobo13bo32bo5bo10bo8bobo$5bo41b2o5bobo5bo8b2o9b2o$2bob3o3bo
37bo6bo5b2o$4bo5bo28bo5b3o4bo5bo$3bo3bo2b2o9b2o15bobo4bo5bobo3bobo5b2o
$12bo7bobo16bo12bo5bo6b2o$12b3o5b2o27bo5bo$39bo8bobo3bobo$38bobo8bo5bo
3b2o$15bo22bo2bo3bo6bo6bobo$14bob5o18b2o3bobo4bobo7bo$13b2o5bo23b2o6bo
8b2o12b2o$13b2o3bo2bo52bobo$21bo53bo$15b2obo2bo26bo$18bo2bo25b2o2bo$
19b2o7bo20bo3bo2b2o$19b2o6bobo15b2o4bo4b2o$27b2o20b2o20bo$46b2o5bo17bo
$44bo4bo3bo9bo7bo$17b2o7b2obo18b2ob2obo7bobo$18bo4b2o2b4o16b2ob2o2bo6b
o2bo$17bobo2bo8bobo13bo6b2o6b2o$17bo2b2obo2bo3bo2bo8bo2b2o5b2o$18b3obo
2b3ob7o5b9ob5o!

Since we've gotten so high with diehards, how much more higher could we go if we instead removed the population=0 limit, and investigated engineered methuselahs?

This goes pretty has as a methuselah. Lifespan is proportional to 121^^n, where ^^ is a tetration, and n is the number of snake-plus-aircraft-carriers to the NW of c/5 ship. I'm currently working on making a diehard out of it.

Code: Select all

x = 107, y = 89, rule = B3/S23
82b2o$82b2o$38b2o$39bo$39bobo6b2o29b2o$40b2o6bobo28b2o$51bo7b2o$48bo2b
o7b2o21b2o8bo$51bo30b2o6b3o4b2o$48bobo38bo7b2o$48b2o39b2o2$18b2o74b2o$
18b2o74b2o2$97b2o$81bobo13b2o$83bo$79bobo$79bo$78bobo$78b2o$16b2o3b2o
54bo$17b5o56b2o$17b2ob2o49b2o6bo$17b2ob2o49b2o$18b3o76bo$50b2o22b2o22b
o$50bo23b2o22bo$37bo10bobo46b2o$36bobo9b2o$16b2o11b2o4bob2o32b2o13b3o
5b3o$17bo11b2o3b2ob2o32b2o13b3o6b2o$14b3o18bob2o46bo3bo5b2o$14bo21bobo
47b5o2b2o$37bo14bo34b4o2b2o$50b2o43b4o$51b2o28bo13b3o$79b3o11b2o$78bo
7b2o6bo$78b2o6b2o6bo$24b2o$24bo$26bo49bo$25b2o48b3o$20b2o3bo48bo3bo$
20bo5bo46bob3obo$22bo2b2o47b5o$21b2o$16b2o3bo$16bo5bo$18bo2b2o$17b2o$
12b2o3bo$12bo5bo$14bo2b2o$13b2o71b2o$8b2o3bo64b2o6b2o$8bo5bo63bo$10bo
2b2o64b3o$9b2o70bo7b2o$4b2o3bo6bob3o68b2o$4bo5bo5bob4o26bobo$6bo2b2o5b
o5bo25b2o36b2o$5b2o10bobobo2b3o22bo36b2o$2o3bo12bobob4o$o5bo12bo2bob2o
$2bo2b2o12bo3b3obo$b2o17b3o2b2obo$bo24bo$2bo24bo2bo$b2o25bo2bo$29b2o3b
o$30b5o$31b4o33bo$31bobo24b2o3bo4b2o$30bob2obo22b2o2b2o5b2o$30bo3bobo
26b2o4bo26b3o4b2o$30bo2bo2b2o26bo3bo26bo2bo4bo$31b2obob2o57bo2bo5b3o$
33bo2b2o68bo$34bo60bo$35b3o22bo2b2o30bo3bo$58b3o2b2o2bo17b2o9bobo$61b
2o2b3o17b2o10bo$61b2o2b3o$61b2o6bo2bo9b2o5b2o$62bo6b3o10b2o5b2o6b2o$
97b2o!

[toroidalet]

Another row shaved off the top reduces it to 94*98:

Code: Select all

x = 94, y = 98, rule = B3/S23
15b2o12b3o2b4ob3o3bo3b2o$14bo2bo11bob2o2bo8b2ob3o$14bo3bo7bo3bo2b2o8b
3o21b2obo3b8ob3o$15bo3bo7b2obo6bo6b2o4bo13bob2o2b3o5b3o2bob2o$16b4o5b
2obo5b2obo6bobobobo14bo3b2o3bo8b2o$16bo9bo3b2o9b2ob4o17bobob2o4bo8bo$
16b2o8bo4bob2obo5bob3o17bo6bobo13bo3b2o$18bo6bo3bo10bo3bo13b2o3bobo2bo
3bo14b2o4bo$15bobo22b5o12bo2bo5bo5bo7bobo5bo2bo$16bo14b2o25b2o11bo9b2o
5bo3bo$31b2o5b4o2bo17b2o4bo12bo7bo3bo$28bo9bo2bo19bobo3bobo20bo2bo$22b
o4bobo32bo5b2o16b2o3b3o$21bobo4bobo14b2o34b2o3bobobob2o$11b2o8bobo5bob
o8b2obo2bo34bo7bo3bo$12bo9bo7bobo7b2ob2o21b2o14b3o2b2o4bo$12bobo16bobo
32bobo15bo5b2obo$13b2o3bo13bobo32bo19b3o3bo$2b2o3b2o8bobo13bobo6b2o14b
2o33bo$2b3ob3o9bo15bobo5b2o13bo2bo15b2o11bo3bo$3b2ob2o7bo5bo7b2o4bobo
20bobo14bo2bo11bob2o$14bobo3bobo7bo5bobo20bo15bobo10bobo$o2b3o2bo6bo5b
o5b3o7bobo36bo12bo$2bo4b2o3bo5bo8bo10bobo5bo16bo20b2o$ob2ob3o3bobo3bob
o19bobo3bobo13b3o19bobo$ob2ob4o3bo5bo21bo5bo13bo14b2o7bo$obo3b2obo5bo
27bo16b2o12bo2bo$4bo3bobo3bobo5b2o18bobo29bobo$2ob4o2bo5bo6b2o13bo5bo
31bo$bo10bo23bobo$2o4bo4bobo22b2o13bo2bo29b2o$3obobobo3bo12b2o23bo3bo
9b2o5b2o11b2o$bo3b2o2bo15b2o14b2o7bo4bo8b2o5b2o$bo2b5obo30b2o7bo4bo$3o
2b2o2bo12b2o27bo3bo11b2o$2o2bo3bo13b2o28bobo12b2o17b2o$ob4o8b2o70bobo$
4o2bobo6bo23bo47bo$2o3bo9bobo21bo$b2o13b2o21bo4b2o43b2o$o2bobo2bo35b2o
43bobo$2bo3bo79bo3b2o$12b3o25b2o5b2o21b2o13bobo$2bo5bo31b2o5b2o21b2o
14bo$2bo5b3o72bo5bo$2bo8bo70bobo3bobo$10b2o71bo5bo$65bo20bo$52b2o6bo3b
obo4b2o12bobo$2bo49b2o5bobo3bo4bo2bo12bo$o48bo10bo10b2o$obo3b2o10b3o
12b2o13bobo$o5b2o8b2ob2o8b3obobo13bo31b2o4b2o2b2o$o15b2ob2o11bo2bo19bo
25bo5bobo2bo$3b2o12b2o9bo24b3o6b2o9bo9bo5bobo$3b2o47bo10bo8bobo7b2o5b
2o$52b2o9bobo5bobo6bo3b2o$41b2o21b2o4bobo7b4o2bo$33b2o6b2o17b2o7bobo3b
2o6bob2o$26b2o5b2o24bo2bo5bobo4b2o3b2obobo$26b2o10bo20bo2bo4bobo10b2ob
obo$37bobo20b2o4bobo14bob2o$23b2o5b2o6bo26bobo15bo$23b2o5b2o32bobo14bo
bo$34b2o29bo15b2o$3bo29bobo26bo11b2o9b2o$33b2o13b5o8bobo11bo9bo$2ob3o
41bob3obo8bo7b2o3bob2o4bobo$2o2bo2bo40bo3bo17b2o2b2obo2bo2b2o$o6bo21b
2o13b2o3b3o5b2o7b2o9bob2o$2o2bo2bobo11bobo4bobo13b2o4bo6b2o7b2o2b2o5bo
5b4o$2bo4bo14b2o4b2o31b2o7bo5b2o4bo3bo$3bo2bobo13bo32bo5bo10bo8bobo$5b
o41b2o5bobo5bo8b2o9b2o$2bob3o3bo37bo6bo5b2o$4bo5bo28bo5b3o4bo5bo$3bo3b
o2b2o9b2o15bobo4bo5bobo3bobo5b2o$12bo7bobo16bo12bo5bo6b2o$12b3o5b2o27b
o5bo$39bo8bobo3bobo$38bobo8bo5bo3b2o$15bo22bo2bo3bo6bo6bobo$14bob5o18b
2o3bobo4bobo7bo$13b2o5bo23b2o6bo8b2o12b2o$13b2o3bo2bo52bobo$21bo53bo$
15b2obo2bo26bo$18bo2bo25b2o2bo$19b2o7bo20bo3bo2b2o$19b2o6bobo15b2o4bo
4b2o$27b2o20b2o20bo$46b2o5bo17bo$44bo4bo3bo9bo7bo$17b2o7b2obo18b2ob2ob
o7bobo$18bo4b2o2b4o16b2ob2o2bo6bo2bo$17bobo2bo8bobo13bo6b2o6b2o$17bo2b
2obo2bo3bo2bo8bo2b2o5b2o$18b3obo2b3ob7o5b9ob5o!

Likely at least 1 more row can be removed, so I probably will not be the victor of the Pointless Optimization Game.
Maybe it's time for a redesign which is slightly larger than 10k cells in its native state but can be shrunk.

[Dean Hickerson]

Hmm. It looks like I posted the wrong version, without the last optimization I described.

and

And including your last modifications (edit: and bounding box reduction):

That lasts 1.08767e1466 gens. But it turns out that, after each quadri-Snark is deleted, there's room for a short crystallization and decay event. My best attempt uses 62 more gliders, giving a lifespan of 1.47635e1595 gens. That could probably be improved.

And, thanks to the "pointless optimizations", there's still room to widen and/or lengthen the westmost glider path, which could give an even larger improvement.

Code: Select all

x = 94, y = 99, rule = B3/S23
14b2o14b2o2bo9b2o$13bobo13bob4o4b3o3bo$12bobo14bo15bob2o$12b2o13b2ob7o
9bobo18b2obo3b8ob3o$17b2o6bo2bobo6bo26bob2o2b3o5b3o2bob2o$18bo6b2o3bob
2o2b2o27bo3b2o3bo8b2o$17bo11b2ob2o7b2o22bobob2o4bo8bo$17b2o23bo21bo6bo
bo13bo3b2o$40bo17b2o3bobo2bo3bo14b2o4bo$40b5o12bo2bo5bo5bo7bobo5bo2bo$
31b2o11bo13b2o11bo9b2o5bo3bo$31b2o5b4o20b2o4bo12bo7bo3bo$28bo9bo2bo19b
obo3bobo20bo2bo$22bo4bobo32bo5b2o16b2o3b3o$21bobo4bobo14b2o34b2o3bobob
ob2o$11b2o8bobo5bobo8b2obo2bo34bo7bo3bo$12bo9bo7bobo7b2ob2o21b2o14b3o
2b2o4bo$12bobo16bobo32bobo15bo5b2obo$13b2o3bo13bobo32bo19b3o3bo$2b2o3b
2o8bobo13bobo6b2o14b2o33bo$2b3ob3o9bo15bobo5b2o13bo2bo15b2o11bo3bo$3b
2ob2o7bo5bo7b2o4bobo20bobo14bo2bo11bob2o$14bobo3bobo7bo5bobo20bo15bobo
10bobo$o2b3o2bo6bo5bo5b3o7bobo36bo12bo$2bo4b2o3bo5bo8bo10bobo5bo16bo
20b2o$ob2ob3o3bobo3bobo12b2o5bobo3bobo13b3o19bobo$ob2ob4o3bo5bo13b2o6b
o5bo13bo14b2o7bo$obo3b2obo5bo27bo16b2o12bo2bo$4bo3bobo3bobo5b2o18bobo
29bobo$2ob4o2bo5bo6b2o13bo5bo31bo$bo10bo23bobo$2o4bo4bobo22b2o13bo2bo
29b2o$3obobobo3bo12b2o23bo3bo9b2o5b2o11b2o$bo3b2o2bo15b2o14b2o7bo4bo8b
2o5b2o$bo2b5obo30b2o7bo4bo23b2o$3o2b2o2bo12b2o27bo3bo11b2o9bobo$2o2bo
3bo13b2o28bobo12b2o8bo8b2o$ob4o8b2o61b3o6bobo$4o2bobo6bo23bo40bo6bo$2o
3bo9bobo21bo39b2o3bo$b2o13b2o21bo4b2o37bobo3b2o$o2bobo2bo35b2o38bo4bob
o$2bo3bo83b2o$12b3o25b2o5b2o21b2o8bo$2bo5bo31b2o5b2o21b2o7bobo5b2o$2bo
5b3o69bo6bo$2bo8bo71bo4bo$10b2o70bobo2b2o$65bo17bo$52b2o6bo3bobo4b2o$
2bo49b2o5bobo3bo4bo2bo$o48bo10bo10b2o$obo3b2o10b3o12b2o13bobo$o5b2o8b
2ob2o8b3obobo13bo31b2o$o15b2ob2o11bo2bo19bo25bo$3b2o12b2o9bo24b3o6b2o
9bo9bo$3b2o47bo10bo8bobo7b2o$52b2o9bobo5bobo6bo3b2o$41b2o21b2o4bobo7b
4o2bo$33b2o6b2o17b2o7bobo3b2o6bob2o$26b2o5b2o24bo2bo5bobo4b2o3b2obobo$
26b2o10bo20bo2bo4bobo10b2obobo$37bobo20b2o4bobo14bob2o$23b2o5b2o6bo18b
o7bobo15bo$23b2o5b2o24bobo5bobo14bobo$34b2o21bo7bo15b2o$3bo29bobo26bo
11b2o9b2o$33b2o13b5o8bobo11bo9bo$2ob3o41bob3obo8bo7b2o3bob2o4bobo$2o2b
o2bo40bo3bo17b2o2b2obo2bo2b2o$o6bo21b2o13b2o3b3o5b2o7b2o9bob2o$2o2bo2b
obo11bobo4bobo13b2o4bo6b2o7b2o2b2o5bo5b4o$2bo4bo14b2o4b2o31b2o7bo5b2o
4bo3bo$3bo2bobo13bo32bo5bo10bo8bobo$5bo41b2o5bobo5bo8b2o9b2o$2bob3o3bo
37bo6bo5b2o$4bo5bo28bo5b3o4bo5bo$3bo3bo2b2o9b2o15bobo4bo5bobo3bobo5b2o
$12bo7bobo16bo12bo5bo6b2o$12b3o5b2o27bo5bo$39bo8bobo3bobo$38bobo8bo5bo
3b2o$15bo22bo2bo3bo6bo6bobo$14bob5o18b2o3bobo4bobo7bo$13b2o5bo23b2o6bo
8b2o12b2o$13b2o3bo2bo52bobo$21bo53bo$15b2obo2bo26bo$18bo2bo25b2o2bo$
19b2o7bo20bo3bo2b2o$19b2o6bobo15b2o4bo4b2o$27b2o20b2o20bo$46b2o5bo17bo
$44bo4bo3bo9bo7bo$17b2o7b2obo18b2ob2obo7bobo$18bo4b2o2b4o16b2ob2o2bo6b
o2bo$17bobo2bo8bobo13bo6b2o6b2o$17bo2b2obo2bo3bo2bo8bo2b2o5b2o$18b3obo
2b3ob7o5b9ob5o!

Here's a simulator for the above pattern. The first crystallization starts at gen 491319, the second one at 532195.

I couldn't find a way to destroy the p720 gun at the appropriate time for this, so to see the finish you'll need to delete it around gen 550400.

Code: Select all

x = 127, y = 142, rule = B3/S23
47b2o14b2o2bo9b2o$46bobo13bob4o4b3o3bo$45bobo14bo15bob2o$45b2o13b2ob7o
9bobo18b2obo3b8ob3o$50b2o6bo2bobo6bo26bob2o2b3o5b3o2bob2o$51bo6b2o3bob
2o2b2o27bo3b2o3bo8b2o$50bo11b2ob2o7b2o22bobob2o4bo8bo$50b2o23bo21bo6bo
bo13bo3b2o$73bo17b2o3bobo2bo3bo14b2o4bo$73b5o12bo2bo5bo5bo7bobo5bo2bo$
64b2o11bo13b2o11bo9b2o5bo3bo$64b2o5b4o20b2o4bo12bo7bo3bo$61bo9bo2bo19b
obo3bobo20bo2bo$55bo4bobo32bo5b2o16b2o3b3o$54bobo4bobo14b2o34b2o3bobob
ob2o$44b2o8bobo5bobo8b2obo2bo34bo7bo3bo$45bo9bo7bobo7b2ob2o21b2o14b3o
2b2o4bo$45bobo16bobo32bobo15bo5b2obo$46b2o3bo13bobo32bo19b3o3bo$35b2o
3b2o8bobo13bobo6b2o14b2o33bo$35b3ob3o9bo15bobo5b2o13bo2bo15b2o11bo3bo$
36b2ob2o7bo5bo7b2o4bobo20bobo14bo2bo11bob2o$47bobo3bobo7bo5bobo20bo15b
obo10bobo$33bo2b3o2bo6bo5bo5b3o7bobo36bo12bo$35bo4b2o3bo5bo8bo10bobo5b
o16bo20b2o$33bob2ob3o3bobo3bobo12b2o5bobo3bobo13b3o19bobo$33bob2ob4o3b
o5bo13b2o6bo5bo13bo14b2o7bo$33bobo3b2obo5bo27bo16b2o12bo2bo$37bo3bobo
3bobo5b2o18bobo29bobo$33b2ob4o2bo5bo6b2o13bo5bo31bo$34bo10bo23bobo$33b
2o4bo4bobo22b2o13bo2bo29b2o$33b3obobobo3bo12b2o23bo3bo9b2o5b2o11b2o$
34bo3b2o2bo15b2o14b2o7bo4bo8b2o5b2o$34bo2b5obo30b2o7bo4bo23b2o$33b3o2b
2o2bo12b2o27bo3bo11b2o9bobo$33b2o2bo3bo13b2o28bobo12b2o8bo8b2o$33bob4o
8b2o61b3o6bobo$33b4o2bobo6bo23bo40bo6bo$33b2o3bo9bobo21bo39b2o3bo$34b
2o13b2o21bo4b2o37bobo3b2o$33bo2bobo2bo35b2o38bo4bobo$35bo3bo83b2o$45b
3o25b2o5b2o21b2o8bo$35bo5bo31b2o5b2o21b2o7bobo5b2o$35bo5b3o69bo6bo$35b
o8bo71bo4bo$43b2o70bobo2b2o$98bo17bo$85b2o6bo3bobo4b2o$35bo49b2o5bobo
3bo4bo2bo$33bo48bo10bo10b2o$33bobo3b2o10b3o12b2o13bobo$33bo5b2o8b2ob2o
8b3obobo13bo31b2o$33bo15b2ob2o11bo2bo19bo25bo$36b2o12b2o9bo24b3o6b2o9b
o9bo$36b2o47bo10bo8bobo7b2o$85b2o9bobo5bobo6bo3b2o$74b2o21b2o4bobo7b4o
2bo$66b2o6b2o17b2o7bobo3b2o6bob2o$59b2o5b2o24bo2bo5bobo4b2o3b2obobo$
59b2o10bo20bo2bo4bobo10b2obobo$70bobo20b2o4bobo14bob2o$56b2o5b2o6bo18b
o7bobo15bo$56b2o5b2o24bobo5bobo14bobo$67b2o21bo7bo15b2o$36bo29bobo26bo
11b2o9b2o$66b2o13b5o8bobo11bo9bo$33b2ob3o41bob3obo8bo7b2o3bob2o4bobo$
33b2o2bo2bo40bo3bo17b2o2b2obo2bo2b2o$33bo6bo21b2o13b2o3b3o5b2o7b2o9bob
2o$33b2o2bo2bobo11bobo4bobo13b2o4bo6b2o7b2o2b2o5bo5b4o$35bo4bo14b2o4b
2o31b2o7bo5b2o4bo3bo$36bo2bobo13bo32bo5bo10bo8bobo$38bo41b2o5bobo5bo8b
2o9b2o$35bob3o3bo37bo6bo5b2o$37bo5bo28bo5b3o4bo5bo$36bo3bo2b2o9b2o15bo
bo4bo5bobo3bobo5b2o$45bo7bobo16bo12bo5bo6b2o$45b3o5b2o27bo5bo$72bo8bob
o3bobo$71bobo8bo5bo3b2o$48bo22bo2bo3bo6bo6bobo$37b2o8bob5o18b2o3bobo4b
obo7bo$36bo2bo6b2o5bo23b2o6bo8b2o12b2o$35bobobo6b2o3bo2bo52bobo$36bobo
15bo53bo$37bo10b2obo2bo26bo$51bo2bo25b2o2bo$52b2o7bo20bo3bo2b2o$52b2o
6bobo15b2o4bo4b2o$60b2o20b2o20bo$79b2o5bo17bo$77bo4bo3bo9bo7bo$50b2o7b
2obo18b2ob2obo7bobo$51bo4b2o2b4o16b2ob2o2bo6bo2bo$50bobo2bo8bobo13bo6b
2o6b2o$50bo2b2obo2bo3bo2bo8bo2b2o5b2o$51b3obo2b3ob7o5b9ob5o2$32b2o$31b
obo$31bo5b2o$30b2o6bo$35b3o$35bo5bo$39b3o$4b2o32bo$5bo32b2o$3bo19b2o3b
2o$3b2o18bo4b2o$b2o3bo14bobo$o2b4o14b2o$2obo6b2o19b2o$bobob2o3b2o19b2o
$bobob2o$2obo24b2o$3bo24b2o$3bobo$4b2o2b2o$8b2o$13b2o$14bo$11b3o$11bo$
17b2o8b3o$16b4o7bo$15b3ob2o7bo$15bo3b3o$13b3o5bobo$15bob3ob2obo10bo$
17b2o3b2o9b2o2bo$33b2ob3o$17b2o3b2o15bo6b2o$15bob3ob2obo7bo2bobobo7bo$
13b3o5bobo7bob3o2b2o6bo$15bo3b3o10b2o12b2o$15b3ob2o7b2o$16b4o8b2o$17b
2o$39b2o$39b2o!

[Pavgran]

Well, it's time to step up to the next function in the fast-growing hierarchy: tetration.
It's very tedious to accurately calculate lifespan. But a rough estimate is 4*121^(121^(121^(121^(121^(121^(121^(120*37*121^12)))))))
I think it's an underestimate, but I'm not sure. Maybe I'll derive the precise formula later.
Here is the diehard:

Code: Select all

x = 104, y = 96, rule = LifeSuper
44.2Q$44.Q.Q$14.2Q29.Q$13.Q2.Q33.Q$14.2Q33.Q.Q$49.Q2.Q25.2M15.Q$50.2Q
26.2M8.2Q5.Q$34.2M51.Q2.Q4.Q$35.M52.2Q8.2Q$35.M.M6.2M29.2M21.Q.Q$36.
2M6.M.M28.2M22.Q$47.M7.2M$30.3O11.M2.M7.2M21.2M8.M$21.2Q6.3O15.M30.2M
6.3M4.2M$21.2Q21.M.M38.M7.2M$44.2M39.2M2$14.2M74.2M$14.2M6.O36.Q30.2M
$22.2O34.Q.Q$22.2O35.2Q32.2M$23.O29.2Q22.M.M13.2M7.M$52.Q2.Q23.M20.3M
$53.2Q20.M.M21.M$75.M23.2M$74.M.M$33.2O5.2O32.2M$12.2M3.2M14.2O5.O32.
M$13.5M20.O.O33.2M$13.2M.2M20.2O27.2M6.M$13.2M.2M10.2O37.2M$14.3M11.
2O$46.2M22.2M$46.M23.2M$33.M10.M.M$32.M.M9.2M30.2S$12.2M11.2M4.M.2M
32.2M6.S.S4.3M$13.M11.2M3.2M.2M32.2M6.2S5.3M$10.3M18.M.2M37.S8.M3.M$
10.M21.M.M29.S6.S.S8.5M$33.M29.S.S4.S.S10.4M$63.S.S3.S.S29.Q$64.S5.S
6.M22.Q.Q$15.2O34.2S8.S5.S7.3M22.Q2.Q$17.O32.S.S7.S.S3.S.S5.M7.2M17.
2Q$14.O34.S2.S.S6.S5.S6.2M6.2M$15.2O3.2W27.2S2.2S3.S5.S33.Q$20.W25.O
10.S.S3.S.S12.Q18.Q.Q$10.O11.W22.O.O10.S5.S7.M5.Q19.2Q$10.3O8.2W23.O
8.S5.S9.3M4.Q$13.O2.2W3.W32.S.S3.S.S7.M3.M8.Q$12.2O2.W5.W32.S5.S7.M.
3M.M7.Q$18.W2.2W29.S5.S11.5M8.Q$17.2W16.U15.S.S3.S.S$12.2W3.W15.2U17.
S5.S$12.W5.W15.2U19.S$14.W2.2W35.S.S$13.2W40.S$8.2W3.W49.S25.2Q$8.W5.
W48.3S22.Q2.Q$10.W2.2W21.O29.S22.Q.Q$9.2W24.O.O5.S21.2S15.2M6.Q$4.2W
3.W25.2O5.S.S29.2M6.2M$4.W5.W32.S3.2S25.M$6.W2.2W35.S.S26.3M$5.2W39.
2S29.M7.2M$2W3.W26.O9.S42.2M11.Q$W5.W25.2O7.S.S53.Q.Q$2.W2.2W25.2O8.
2S38.2M14.2Q$.2W30.O48.2M$.W$2.W99.Q$.2W98.Q.Q$51.2S5.Q43.2Q$4.M.3M
41.S.S4.Q.Q$4.M.4M40.S6.2Q$4.M5.M38.2S$5.M.M.M2.3M$6.M.M.4M$7.M2.M.2M
31.2U.2U14.M$7.M3.3M.M15.U.U11.U.2U2.U2.2M3.M4.2M$8.3M2.2M.M14.2U17.
2U2.2M2.2M5.2M$14.M17.U26.2M4.M26.3M4.2M$15.M2.M22.2U.2U14.M3.M26.M2.
M4.M$16.M2.M21.U.2U2.U43.M2.M5.3M$17.2M3.M23.2U54.M$18.5M68.M$19.4M
14.2U.2U14.M2.2M30.M3.M$19.M.M15.U.2U2.U10.3M2.2M2.M17.2M9.M.M5.Q$18.
M.2M.M18.2U13.2M2.3M17.2M10.M5.Q.Q$18.M3.M.M32.2M2.3M36.2Q$18.M2.M2.
2M7.2U.2U19.2M6.M2.M9.2M5.2M$19.2M.M.2M7.U.2U2.U18.M6.3M10.2M5.2M6.2M
$21.M2.2M12.2U53.2M$22.M65.2Q$23.3M62.2Q!

I've color-coded different things according to their function.
White (state 13) cells is the core of the recursive filter.
Salmon (state 15) and orange (state 17) cells are needed for self-destruction. Salmon ones were placed by me to cleanly destroy the c/5 ship and start the destruction, and the orange ones were placed by GoL-destroy (with a little help from me to jump-start the process).
Cyan (state 19) cells postpone the first glider reaching the c/5 ship. It contributes to "120*37" term in the lifespan.
Yellow-green (state 21) cells postpone the first glider in the second part of the filter reaching the c/5 ship. It contributes to "^12" term in the lifespan.
Green (state 23) cells postpone the destruction of the diehard. Each broken snake allows for one more level in exponential tower.

Here is what happens near the end of the lifetime:

Code: Select all

x = 94, y = 101, rule = LifeSuper
34.2Q$34.Q.Q$4.2Q29.Q$3.Q2.Q33.Q$4.2Q33.Q.Q$39.Q2.Q25.2M15.Q$40.2Q26.
2M8.2Q5.Q$24.2M51.Q2.Q4.Q$25.M52.2Q8.2Q$25.M.M6.2M29.2M21.Q.Q$26.3M5.
M.M28.2M22.Q$28.3M6.M7.2M$20.3O5.M2.M2.M2.M7.2M21.2M8.M$11.2Q6.3O7.2M
6.M30.2M6.3M4.2M$11.2Q21.M.M38.M7.2M$34.2M39.2M2$4.2M74.2M$4.2M6.O36.
Q30.2M$12.2O20.M13.Q.Q$12.2O21.2M12.2Q32.2M$13.O20.2M7.2Q22.M.M13.2M
7.M$6.2M34.Q2.Q23.M20.3M$43.2Q20.M.M21.M$65.M23.2M$64.M.M$23.2O5.2O
32.2M$2.2M3.2M14.2O5.O32.M$3.5M20.O.O33.2M18.2M$3.2M.2M20.2O27.2M6.M
19.2M$3.2M.2M10.2O26.M10.2M25.M$4.3M11.2O25.M$36.2M7.3M12.2M$36.M23.
2M$23.M10.M.M$22.M.M9.2M$2.2M11.2M4.M.2M32.2M13.3M$3.M11.2M3.2M.2M32.
2M13.3M4.2M$3M8.M9.M.2M46.M3.M4.M$M9.2M10.M.M47.5M2.M.M$10.M.M10.M49.
4M$91.Q$67.M22.Q.Q$5.2O50.M7.3M22.Q2.Q$7.O47.2M7.M7.2M17.2Q$4.O34.3M
14.2M6.2M6.2M$5.2O32.M48.Q$36.O3.M27.Q18.Q.Q$O34.O.O24.M5.Q19.2Q$3O
33.O24.3M4.Q$3.O51.M4.M3.M8.Q$2.2O50.M4.M.3M.M7.Q$54.3M3.5M8.Q3$20.2pA
$20.2pA2$79.2Q$78.Q2.Q$26.O52.Q.Q$25.O.O44.2M6.Q$25.2O16.2M19.2M6.2M$
5.M.3M32.2M20.M$5.M.4M33.M20.3M$5.M5.M24.2pA29.M7.2M$6.M.M.M2.3M6.O
13.2pA37.2M11.Q$7.M.M.4M7.2O63.Q.Q$8.M2.M.2M7.2O48.2M14.2Q$8.M3.3M.M
6.O48.2M$9.3M2.2M.M$15.M76.Q$16.M2.M71.Q.Q$17.M2.M27.Q43.2Q$18.2M3.M
23.Q.Q$19.5M23.2Q20.3M$20.4M45.M$20.M.M47.M$19.M.2M.M$19.M3.M.M28.M$
19.M2.M2.2M17.2M3.M4.2M$20.2M.M.2M17.2M2.2M5.2M$22.M2.2M22.2M4.M26.3M
4.2M$23.M26.M3.M26.M2.M4.M$24.3M54.M2.M5.3M$92.M$81.M$81.M3.M$71.2M9.
M.M5.Q$71.2M10.M5.Q.Q$90.2Q$68.2M5.2M$68.2M5.2M6.2M$61.M21.2M$62.2M
14.2Q$61.2M15.2Q2$65.2M$65.M.M$67.M$67.2M!

Of course the c/5 ship is closer than it would otherwise be, but that's for the sake of demonstration.
Magenta (state 25) cells show the locations of two blocks pulled by the mechanism.

On the further improvements:
The most important thing is to reduce the rightmost (EDIT: any, actually) boundary by some multiple of 4, as that will allow for more broken snakes to fit and therefore to add more levels to exponential tower.
Next comes the number of gliders eaten in the second filter. Perhaps there is some other glider collision producing more delay. Or there could be another glider pair coexisting with the current one.
And finally there is the delay of the first glider and/or rewinding guns a few ticks, but that's the least important thing.

[yujh]

I have no chance winning, but i at least participated.

Code: Select all

x = 103, y = 95, rule = B3/S23
43b4o$14b2o$13bo2bo28bo4bo$14b2o33bobo$49bo2bo25b2o15bo$50b2o26b2o8b2o
5bo$34b2o51bo2bo4bo$35bo52b2o8b2o$35bobo6b2o29b2o21bobo$36b2o6bobo28b
2o22bo$47bo7b2o$30b3o11bo2bo7b2o21b2o8bo$21b2o6b3o15bo30b2o6b3o4b2o$
21b2o21bobo38bo7b2o$44b2o39b2o2$14b2o74b2o$14b2o6bo36bo30b2o$22b2o34bo
bo$22b2o35b2o32b2o$23bo29b2o22bobo13b2o7bo$52bo2bo23bo20b3o$53b2o20bob
o21bo$75bo23b2o$74bobo$33b2o5b2o32b2o$12b2o3b2o14b2o5bo32bo$13b5o20bob
o33b2o$13b2ob2o20b2o27b2o6bo$13b2ob2o10b2o37b2o$14b3o11b2o$46b2o22b2o$
46bo23b2o$33bo10bobo$32bobo9b2o30b2o$12b2o11b2o4bob2o32b2o6bobo4b3o$
13bo11b2o3b2ob2o32b2o6b2o5b3o$10b3o18bob2o37bo8bo3bo$10bo21bobo29bo6bo
bo8b5o$33bo29bobo4bobo10b4o$63bobo3bobo$64bo5bo6bo22b2o$15b2o34b2o8bo
5bo7b3o23b2o$17bo32bobo7bobo3bobo5bo7b2o18bo$14bo34bo2bobo6bo5bo6b2o6b
2o$15b2o3b2o27b2o2b2o3bo5bo33bo$20bo25bo10bobo3bobo12bo18bobo$10bo11bo
22bobo10bo5bo7bo5bo19b2o$10b3o8b2o23bo8bo5bo9b3o4bo$13bo2b2o3bo32bobo
3bobo7bo3bo8bo$12b2o2bo5bo32bo5bo7bob3obo7bo$18bo2b2o29bo5bo11b5o8bo$
17b2o16bo15bobo3bobo$12b2o3bo15b2o17bo5bo$12bo5bo15b2o19bo$14bo2b2o35b
obo$13b2o40bo$8b2o3bo49bo25b2o$8bo5bo48b3o22bo2bo$10bo2b2o21bo29bo22bo
bo$9b2o24bobo5bo21b2o15b2o6bo$4b2o3bo25b2o5bobo29b2o6b2o$4bo5bo32bo3b
2o25bo$6bo2b2o35bobo26b3o$5b2o39b2o29bo7b2o$2o3bo26bo9bo42b2o11bo$o5bo
25b2o7bobo53bobo$2bo2b2o25b2o8b2o38b2o14b2o$b2o30bo48b2o$bo$2bo99bo$b
2o97bobo$51b2o5bo43bo$4bob3o41bobo4bobo42bo$4bob4o40bo6b2o$4bo5bo38b2o
$5bobobo2b3o$6bobob4o$7bo2bob2o31b2ob2o14bo$7bo3b3obo15bobo11bob2o2bo
2b2o3bo4b2o$8b3o2b2obo14b2o17b2o2b2o2b2o5b2o$14bo17bo26b2o4bo26b3o4b2o
$15bo2bo22b2ob2o14bo3bo26bo2bo4bo$16bo2bo21bob2o2bo43bo2bo5b3o$17b2o3b
o23b2o54bo$18b5o68bo$19b4o14b2ob2o14bo2b2o30bo3bo$19bobo15bob2o2bo10b
3o2b2o2bo17b2o9bobo5bo$18bob2obo18b2o13b2o2b3o17b2o10bo5bobo$18bo3bobo
32b2o2b3o36b2o$18bo2bo2b2o7b2ob2o19b2o6bo2bo9b2o5b2o$19b2obob2o7bob2o
2bo18bo6b3o10b2o5b2o6b2o$21bo2b2o12b2o53b2o$22bo65b2o$23b3o62b2o!

[Pavgran]

Kazyan mentioned on the Discord that toads can eat block pulls. So, here goes the first exponential tower length improvement:

Code: Select all

x = 105, y = 95, rule = LifeSuper
45.4Q$16.2Q$15.Q2.Q28.Q4.Q$16.2Q33.Q.Q$51.Q2.Q25.2M15.Q$52.2Q26.2M8.
2Q5.Q$36.2M51.Q2.Q4.Q$37.M52.2Q8.2Q$37.M.M6.2M29.2M21.Q.Q$38.2M6.M.M
28.2M22.Q$49.M7.2M$32.3O11.M2.M7.2M21.2M8.M$23.2Q6.3O15.M30.2M6.3M4.
2M$23.2Q21.M.M38.M7.2M$46.2M39.2M2$16.2M74.2M$16.2M6.O36.Q30.2M$24.2O
34.Q.Q$24.2O35.2Q32.2M$25.O29.2Q22.M.M13.2M7.M$54.Q2.Q23.M20.3M$55.2Q
20.M.M21.M$77.M23.2M$76.M.M$35.2O5.2O32.2M$14.2M3.2M14.2O5.O32.M$15.
5M20.O.O33.2M$15.2M.2M20.2O27.2M6.M$15.2M.2M10.2O37.2M$16.3M11.2O$48.
2M22.2M$48.M23.2M$35.M10.M.M$34.M.M9.2M30.2S$14.2M11.2M4.M.2M32.2M6.S
.S4.3M$15.M11.2M3.2M.2M32.2M6.2S5.3M$12.3M18.M.2M37.S8.M3.M$12.M21.M.
M29.S6.S.S8.5M$35.M29.S.S4.S.S10.4M$65.S.S3.S.S$66.S5.S6.M22.2Q$17.2O
34.2S8.S5.S7.3M23.2Q$19.O32.S.S7.S.S3.S.S5.M7.2M18.Q$16.O34.S2.S.S6.S
5.S6.2M6.2M$17.2O32.2S2.2S3.S5.S33.Q$48.O10.S.S3.S.S12.Q18.Q.Q$12.O
11.W22.O.O10.S5.S7.M5.Q19.2Q$12.3O9.2W22.O8.S5.S9.3M4.Q$15.O8.2W30.S.
S3.S.S7.M3.M8.Q$14.2O9.W31.S5.S7.M.3M.M7.Q$20.W16.U16.S5.S11.5M8.Q$
20.2W14.U16.S.S3.S.S$20.2W14.3U15.S5.S$21.W35.S$16.W39.S.S$16.2W39.S$
16.2W47.S25.2Q$17.W47.3S22.Q2.Q$12.W25.O29.S22.Q.Q$12.2W23.O.O5.S21.
2S15.2M6.Q$12.2W23.2O5.S.S29.2M6.2M$13.W31.S3.2S25.M$8.W39.S.S26.3M$
8.2W38.2S29.M7.2M$8.2W24.O9.S42.2M11.Q$9.W24.2O7.S.S53.Q.Q$4.W29.2O8.
2S38.2M14.2Q$4.2W29.O48.2M$4.2W$5.W98.Q$W101.Q.Q$2W51.2S5.Q43.Q$2W4.M
.3M41.S.S4.Q.Q42.Q$.W4.M.4M40.S6.2Q$6.M5.M38.2S$7.M.M.M2.3M$8.M.M.4M$
9.M2.M.2M18.U12.2U.2U14.M$9.M3.3M.M16.U.U10.U.2U2.U2.2M3.M4.2M$10.3M
2.2M.M15.2U16.2U2.2M2.2M5.2M$16.M44.2M4.M26.3M4.2M$17.M2.M22.2U.2U14.
M3.M26.M2.M4.M$18.M2.M21.U.2U2.U43.M2.M5.3M$19.2M3.M23.2U54.M$20.5M
68.M$21.4M14.2U.2U14.M2.2M30.M3.M$21.M.M15.U.2U2.U10.3M2.2M2.M17.2M9.
M.M5.Q$20.M.2M.M18.2U13.2M2.3M17.2M10.M5.Q.Q$20.M3.M.M32.2M2.3M36.2Q$
20.M2.M2.2M7.2U.2U19.2M6.M2.M9.2M5.2M$21.2M.M.2M7.U.2U2.U18.M6.3M10.
2M5.2M6.2M$23.M2.2M12.2U53.2M$24.M65.2Q$25.3M62.2Q!

For the future improvers: please keep in mind that every repositioning of c/5 ship and every addition of block eaters would require adjustment in the initial gliders, as the reaction with a block has to not hit the block eaters.

[Dean Hickerson]

Well, it's time to step up to the next function in the fast-growing hierarchy: tetration.

Wow! I hadn't expected something like this to fit in area 10000. Nice work!

And once again lots of work done on optimizing a pattern becomes obsolete because of a new idea. That happens a lot.

[Pavgran]

Let's analyze diehard's running time thoroughly.

We'll work mostly with multiples of 120 as the gun's period is 120.
First, let's note that delaying or advancing a glider 1 tick results in moving the glider's interaction with the c/5 ship away or towards the guns, respectively. Similar reasoning applies to advancing/delaying the ship. There are 3 types of interaction with the c/5 ship: first sawtooth's block production, second sawtooth's block production and ship destruction.

First sawtooth analysis
Let's now analyze the first sawtooth, that is, when it finishes pulling nth block.
Consider the following configuration:

Code: Select all

x = 100, y = 101, rule = LifeSuper
40.2Q$40.Q.Q$10.2Q29.Q$9.Q2.Q33.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q
26.2M8.2Q5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.
3M5.M.M28.2M22.Q$34.3M6.M7.2M$26.3O5.M2.M2.M2.M7.2M21.2M8.M$17.2Q6.3O
7.2M6.M30.2M6.3M4.2M$17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M
6.O36.Q30.2M$18.2O20.M13.Q.Q$18.2O21.2M12.2Q32.2M$19.O20.2M7.2Q22.M.M
13.2M7.M$12.2M34.Q2.Q23.M20.3M$49.2Q20.M.M21.M$71.M23.2M$70.M.M$29.2O
5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O.O33.2M18.2M$9.2M.2M20.2O27.2M
6.M19.2M$9.2M.2M10.2O26.M10.2M25.M$10.3M11.2O25.M$42.2M7.3M12.2M$42.M
23.2M$29.M10.M.M$28.M.M9.2M$8.2M11.2M4.M.2M32.2M13.3M$9.M11.2M3.2M.2M
32.2M13.3M4.2M$6.3M8.M9.M.2M46.M3.M4.M$6.M9.2M10.M.M47.5M2.M.M$16.M.M
10.M49.4M$97.Q$73.M22.Q.Q$11.2O50.pA7.3M22.Q2.Q$13.O47.2pA7.M7.2M17.
2Q$10.O34.3M14.2pA6.2M6.2M$11.2O32.M48.Q$42.O3.M27.Q18.Q.Q$6.O34.O.O
24.M5.Q19.2Q$6.3O33.O24.3M4.Q$9.O51.pA4.M3.M8.Q$8.2O50.pA4.M.3M.M7.Q$
60.3pA3.5M8.Q6$85.2Q$84.Q2.Q$32.O52.Q.Q$31.O.O44.2M6.Q$31.2O16.2M19.
2M6.2M$48.2M20.M$50.M20.3M$73.M7.2M$28.O52.2M11.Q$28.2O63.Q.Q$28.2O
48.2M14.2Q$29.O48.2M2$98.Q$97.Q.Q$54.Q43.2Q$M.3M48.Q.Q$M.4M47.2Q20.3M
$M5.M68.M$.M.M.M2.3M65.M$2.M.M.4M$3.M2.M.2M50.M$3.M3.3M.M38.2M3.M4.2M
$4.3M2.2M.M37.2M2.2M5.2M$10.M44.2M4.M26.3M4.2M$11.M2.M41.M3.M26.M2.M
4.M$12.M2.M71.M2.M5.3M$13.2M3.M79.M$14.5M68.M$15.4M68.M3.M$15.M.M59.
2M9.M.M5.Q$14.M.2M.M57.2M10.M5.Q.Q$14.M3.M.M75.2Q$14.M2.M2.2M52.2M5.
2M$15.2M.M.2M52.2M5.2M6.2M$17.M2.2M45.M21.2M$18.M49.2M14.2Q$19.3M45.
2M15.2Q2$71.2M$71.M.M$73.M$73.2M!

It's the same as the starting configuration, except all the delaying objects are removed and the guns have fired the necessary amount of gliders to reach periodic configuration (basically that's when the glider from the bottomest gun has looped all around the way to it's position in first sawtooth's salvo.
I've marked that salvo with magenta (state 25) cells. I've also marked the location to which the block has to be pulled for the mechanism to delete it and fire a second sawtooth's salvo.
So, in this configuration, we can see that the salvo produces the block at a distance of 182fd (full diagonals) away from the marked position. Let's make it our first parameter, a. So a=182. It depends on the initial position of the ship and initial phase of the guns, but let's not complicate things for now.
Now, we need to calculate x_0 - the time at which the block will be pulled all the way to the marked position for the first time. We need for the first salvo to produce a block, and then for the next a salvos to make pulls, and each salvo needs 120 ticks, so x_0=120(a+1).
Next we need to calculate x_1 - the time at which the second block will be pulled all the way to the marked position. First, we have to note that each block-eating inroduces a gap of 4 salvos till the next salvo capable of producing a pullable block (that's because these 4 salvos first produce the block, then pull it two times, then kill the block, due to some gliders missing in the salvos). So the time at which the second block-producing salvo will be at the same position as the first one is x_0+4*120=120(a+5). At which distance the block will be this time? Well, the ship advanced 120(a+5) ticks from it's initial position, so the block will be that many fd away compared to the first one. That is, it'll be a+120(a+5)=121a+600 fd away. And then x_1=x_0+4*120+120+120*(121a+600). After the first block, we have to wait 4 salvos (which are cleanly eaten), then one salvo (to produce a block), then 121a+600 salvos (to pull the block).
Let's now derive the general formula.
If the ith block is at time x_i at a marked position, then x_(i+1)=x_i+120*4+120+120*(a+x_i+4*120)=121*x_i+120*(4*121+a+1)
We have a recurrent equation of the form x_(i+1)=Ax_i+B, and it has solution x'_n=x'_0*a^n, where x'_n=x_n+B/(A-1).
In this case, we have
A=121,
B=120*(4*121+a+1),
B/(A-1)=4*121+a+1,
x'_0=120(a+1)+4*121+a+1
=121*(a+5),
x'_n=(a+5)*121^(n+1),
x_n=(a+5)*121^(n+1)-121*4-a-1

Phew. That was only the first sawtooth without initial delay. Time to factor that in.
We now have this configuration:

Code: Select all

x = 99, y = 95, rule = LifeSuper
39.4Q$10.2Q$9.Q2.Q28.Q4.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q26.2M8.2Q
5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.2M6.M.M28.
2M22.Q$43.M7.2M$26.3O11.M2.M7.2M21.2M8.M$17.2Q6.3O15.M30.2M6.3M4.2M$
17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M6.O36.Q30.2M$18.2O34.
Q.Q$18.2O35.2Q32.2M$19.O29.2Q22.M.M13.2M7.M$48.Q2.Q23.M20.3M$49.2Q20.
M.M21.M$71.M23.2M$70.M.M$29.2O5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O
.O33.2M$9.2M.2M20.2O27.2M6.M$9.2M.2M10.2O37.2M$10.3M11.2O$42.2M22.2M$
42.M23.2M$29.M10.M.M$28.M.M9.2M30.2S$8.2M11.2M4.M.2M32.2M6.S.S4.3M$9.
M11.2M3.2M.2M32.2M6.2S5.3M$6.3M18.M.2M37.S8.M3.M$6.M21.M.M29.S6.S.S8.
5M$29.M29.S.S4.S.S10.4M$59.S.S3.S.S$60.S5.S6.M22.2Q$11.2O34.2S8.S5.S
7.3M23.2Q$13.O32.S.S7.S.S3.S.S5.M7.2M18.Q$10.O34.S2.S.S6.S5.S6.2M6.2M
$11.2O32.2S2.2S3.S5.S33.Q$42.O10.S.S3.S.S12.Q18.Q.Q$6.O34.O.O10.S5.S
7.M5.Q19.2Q$6.3O33.O8.S5.S9.3M4.Q$9.O40.S.S3.S.S7.M3.M8.Q$8.2O41.S5.S
7.M.3M.M7.Q$48.S5.S11.5M8.Q$47.S.S3.S.S$48.S5.S$51.S$50.S.S$51.S$59.S
25.2Q$59.3S22.Q2.Q$32.O29.S22.Q.Q$31.O.O5.S21.2S15.2M6.Q$31.2O5.S.S
29.2M6.2M$39.S3.SGH24.M$42.S.GH25.3M$42.2S29.M7.2M$28.O9.S42.2M11.Q$
28.2O7.S.S53.Q.Q$28.2O8.2S38.2M14.2Q$29.O48.2M2$98.Q$96.Q.Q$47.2S5.Q
43.Q$M.3M41.S.S4.Q.Q42.Q$M.4M40.S6.2Q$M5.M38.2S$.M.M.M2.3M$2.M.M.4M$
3.M2.M.2M50.M$3.M3.3M.M38.2M3.M4.2M$4.3M2.2M.M37.2M2.2M5.2M$10.M44.2M
4.M26.3M4.2M$11.M2.M41.M3.M26.M2.M4.M$12.M2.M71.M2.M5.3M$13.2M3.M79.M
$14.5M68.M$15.4M33.M2.2M30.M3.M$15.M.M32.3M2.2M2.M17.2M9.M.M5.Q$14.M.
2M.M33.2M2.3M17.2M10.M5.Q.Q$14.M3.M.M32.2M2.3M36.2Q$14.M2.M2.2M31.2M
6.M2.M9.2M5.2M$15.2M.M.2M32.M6.3M10.2M5.2M6.2M$17.M2.2M67.2M$18.M65.
2Q$19.3M62.2Q!

And we need to know when the nth block will be at the marked position in this configuration. Let's call it y_n. Basically we need to calculate a new a parameter, that is, the distance at which the first salvo produces the first block. To that end, we see that the first 32 gliders are eaten. Plus the next 4 salvos are missing one glider, and so they produce and then eat the block 2 times. That means that the first 36 salvos are doing nothing. And there is no salvo at tick 0, so that means 37 skipped salvos (comparing to the previous analysis). Let's make this our parameter b. So b=37. That means that after 120*b ticks we arrive at essentialy the situation in the first picture except the ship has now flew away. So we effectively increased our a parameter by 120b, so the first block is now at distance a+120b. Plus we have to offset the number of ticks by 120b, so we need to take that into account as well.
So now
y_n=(a+120b+5)*121^(n+1)-121*4-(a+120b)-1+120b
=(a+120b+5)*121^(n+1)-121*4-a-1.

Next, we have to consider what effect do the broken snakes have on the first sawtooth. Let's consider their effect in isolation of the initial delay.
Here is the picture:

Code: Select all

x = 100, y = 101, rule = LifeSuper
40.2Q$40.Q.Q$10.2Q29.Q$9.Q2.Q33.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q
26.2M8.2Q5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.
3M5.M.M28.2M22.Q$34.3M6.M7.2M$26.3O5.M2.M2.M2.M7.2M21.2M8.M$17.2Q6.3O
7.2M6.M30.2M6.3M4.2M$17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M
6.O36.Q30.2M$18.2O20.M13.Q.Q$18.2O21.2M12.2Q32.2M$19.O20.2M7.2Q22.M.M
13.2M7.M$12.2M34.Q2.Q23.M20.3M$49.2Q20.M.M21.M$71.M23.2M$70.M.M$29.2O
5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O.O33.2M18.2M$9.2M.2M20.2O27.2M
6.M19.2M$9.2M.2M10.2O26.M10.2M25.M$10.3M11.2O25.M$42.2M7.3M12.2M$42.M
23.2M$29.M10.M.M$28.M.M9.2M$8.2M11.2M4.M.2M32.2M13.3M$9.M11.2M3.2M.2M
32.2M13.3M4.2M$6.3M8.M9.M.2M46.M3.M4.M$6.M9.2M10.M.M47.5M2.M.M$16.M.M
10.M49.4M$97.Q$73.M22.Q.Q$11.2O50.pA7.3M22.Q2.Q$13.O47.2pA7.M7.2M17.
2Q$10.O34.3M14.2pA6.2M6.2M$11.2O32.M48.Q$42.O3.M27.Q18.Q.Q$6.O34.O.O
24.M5.Q19.2Q$6.3O33.O24.3M4.Q$9.O51.pA4.M3.M8.Q$8.2O50.pA4.M.3M.M7.Q$
60.3pA3.5M8.Q6$85.2Q$84.Q2.Q$32.O52.Q.Q$31.O.O44.2M6.Q$31.2O16.2M19.
2M6.2M$44.2H2.2M20.M$44.2H4.M20.3M$73.M7.2M$28.O52.2M11.Q$28.2O63.Q.Q
$28.2O48.2M14.2Q$29.O48.2M2$98.Q$97.Q.Q$54.Q43.2Q$M.3M48.Q.Q$M.4M26.
2H19.2Q20.3M$M5.M25.2H41.M$.M.M.M2.3M65.M$2.M.M.4M$3.M2.M.2M18.2H11.
2U.2U14.M$3.M3.3M.M16.2H11.U.2U2.U2.2M3.M4.2M$4.3M2.2M.M33.2U2.2M2.2M
5.2M$10.M44.2M4.M26.3M4.2M$11.M2.M9.2H11.2U.2U14.M3.M26.M2.M4.M$12.M
2.M8.2H11.U.2U2.U43.M2.M5.3M$13.2M3.M23.2U54.M$14.5M68.M$15.4M.2H11.
2U.2U49.M3.M$15.M.M2.2H11.U.2U2.U37.2M9.M.M5.Q$14.M.2M.M18.2U37.2M10.
M5.Q.Q$14.M3.M.M75.2Q$14.M2.M2.2M7.2U.2U40.2M5.2M$15.2M.M.2M7.U.2U2.U
38.2M5.2M6.2M$17.M2.2M12.2U31.M21.2M$18.M49.2M14.2Q$19.3M45.2M15.2Q2$
71.2M$71.M.M$73.M$73.2M!

Here there are 5 locations marked which the block should be pulled to to be eaten. One is the same as in the previous pictures, and there are 4 locations where the broken snakes eat the block. Note that the block only briefly appears on that location, as it's eaten almost immediately. We can immediately introduce two new parameters, c and d. c is the distance between the main block location and the closest broken snake block location. c=12. d is the number of broken snakes. d=4. There is also the distance between broken snakes, which is 4. I'll leave that as a number instead of making a new name, as I don't expect it to change.
Let's introduce a temporary sequence t_i, which shows when ith block is pulled to ith broken snake, counting from the outside.
So, what is t_0? Well, as we already know, the first salvo creates the block a fds away, and now it needs to be pulled only (a-c-4*(d-1))=a-c-4d+4 times. So t_0=120(a-c-4d+4+1), similar to x_0. What's the recurrence formula for t_i? It's similar to that one for x_i, but we need to account for the block having a new target location each cycle, and that there is no wastage in glider salvos. From the time t_i, we have to launch one salvo to produce a block, which will be at distance t_i+a from the main location, and then pull it t_i+a-c-4(d-1-(i+1)) times. So t_(i+1)=t_i+120+120*(t_i+a-c-4(d-i-2))=121*t_i+120*(a-c-4d+9+4i). This time we have a recurrent relation of the form t_(i+1)=A*t_i+B+C*i, and it has solution t'_n=t'_0*A^n, where t'_n=t_n+1/(A-1)*(C*n+B+C/(A-1)). We have
A=121,
B=120*(a-c-4d+9),
C=120*4,
B/(A-1)=a-c-4d+9,
C/(A-1)=4,
t'_0=120(a-c-4d+5)+a-c-4d+9+4/120
=121(a-c-4d+5+4/120),
t'_n=(a-c-4d+5+4/120)*121^(n+1),
t_n=(a-c-4d+5+4/120)*121^(n+1)-4n-(a-c-4d+9)-4/120
=(a-c-4d+5+4/120)*(121^(n+1)-1)-4(n+1)

Now let's finally calculate the timings of the first sawtooth. To that end, we would have to offset the a parameter in the equation for t by 120b to account for the first delay and offset the a parameter in equation for x by t_(d-1) to account for broken snake delay.

Code: Select all

x = 99, y = 95, rule = LifeSuper
39.4Q$10.2Q$9.Q2.Q28.Q4.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q26.2M8.2Q
5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.2M6.M.M28.
2M22.Q$43.M7.2M$26.3O11.M2.M7.2M21.2M8.M$17.2Q6.3O15.M30.2M6.3M4.2M$
17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M6.O36.Q30.2M$18.2O34.
Q.Q$18.2O35.2Q32.2M$19.O29.2Q22.M.M13.2M7.M$48.Q2.Q23.M20.3M$49.2Q20.
M.M21.M$71.M23.2M$70.M.M$29.2O5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O
.O33.2M$9.2M.2M20.2O27.2M6.M$9.2M.2M10.2O37.2M$10.3M11.2O$42.2M22.2M$
42.M23.2M$29.M10.M.M$28.M.M9.2M30.2S$8.2M11.2M4.M.2M32.2M6.S.S4.3M$9.
M11.2M3.2M.2M32.2M6.2S5.3M$6.3M18.M.2M37.S8.M3.M$6.M21.M.M29.S6.S.S8.
5M$29.M29.S.S4.S.S10.4M$59.S.S3.S.S$60.S5.S6.M22.2Q$11.2O34.2S8.S5.S
7.3M23.2Q$13.O32.S.S7.S.S3.S.S5.M7.2M18.Q$10.O34.S2.S.S6.S5.S6.2M6.2M
$11.2O32.2S2.2S3.S5.S33.Q$42.O10.S.S3.S.S12.Q18.Q.Q$6.O34.O.O10.S5.S
7.M5.Q19.2Q$6.3O33.O8.S5.S9.3M4.Q$9.O40.S.S3.S.S7.M3.M8.Q$8.2O41.S5.S
7.M.3M.M7.Q$48.S5.S11.5M8.Q$47.S.S3.S.S$48.S5.S$51.S$50.S.S$51.S$59.S
25.2Q$59.3S22.Q2.Q$32.O29.S22.Q.Q$31.O.O5.S21.2S15.2M6.Q$31.2O5.S.S
29.2M6.2M$39.S3.SGH24.M$42.S.GH25.3M$42.2S29.M7.2M$28.O9.S42.2M11.Q$
28.2O7.S.S53.Q.Q$28.2O8.2S38.2M14.2Q$29.O48.2M2$98.Q$96.Q.Q$47.2S5.Q
43.Q$M.3M41.S.S4.Q.Q42.Q$M.4M40.S6.2Q$M5.M38.2S$.M.M.M2.3M$2.M.M.4M$
3.M2.M.2M31.2U.2U14.M$3.M3.3M.M29.U.2U2.U2.2M3.M4.2M$4.3M2.2M.M33.2U
2.2M2.2M5.2M$10.M44.2M4.M26.3M4.2M$11.M2.M22.2U.2U14.M3.M26.M2.M4.M$
12.M2.M21.U.2U2.U43.M2.M5.3M$13.2M3.M23.2U54.M$14.5M68.M$15.4M14.2U.
2U14.M2.2M30.M3.M$15.M.M15.U.2U2.U10.3M2.2M2.M17.2M9.M.M5.Q$14.M.2M.M
18.2U13.2M2.3M17.2M10.M5.Q.Q$14.M3.M.M32.2M2.3M36.2Q$14.M2.M2.2M7.2U.
2U19.2M6.M2.M9.2M5.2M$15.2M.M.2M7.U.2U2.U18.M6.3M10.2M5.2M6.2M$17.M2.
2M12.2U53.2M$18.M65.2Q$19.3M62.2Q!

z_n=(a+5+(a+120b-c-4d+5+4/120)*(121^d-1)-4d+120b)*121^(n+1)-121*4-a-1
=((a+120b-c-4d+5+4/120)*121^d+c-4/120)*121^(n+1)-121*4-a-1
=((a+120b-4d+5)*121^d-(c-4/120)*(121^d-1))*121^(n+1)-121*4-a-1


Second sawtooth analysis
Now, it's time to switch to the second sawtooth.

Code: Select all

x = 100, y = 101, rule = LifeSuper
40.2Q$40.Q.Q$10.2Q29.Q$9.Q2.Q33.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q
26.2M8.2Q5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.
3M5.M.M28.2M22.Q$34.3M6.M7.2M$26.3O5.M2.M2.M2.M7.2M21.2M8.M$17.2Q6.3O
7.2M6.M30.2M6.3M4.2M$17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M
6.O36.Q30.2M$18.2O20.M13.Q.Q$18.2O21.2M12.2Q32.2M$19.O20.2M7.2Q22.M.M
13.2M7.M$12.2M34.Q2.Q23.M20.3M$49.2Q20.M.M21.M$71.M23.2M$70.M.M$29.2O
5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O.O33.2M18.2M$9.2M.2M20.2O27.2M
6.M19.2M$9.2M.2M10.2O26.M10.2M25.M$10.3M11.2O25.M$42.2M7.3M12.2M$42.M
23.2M$29.M10.M.M$28.M.M9.2M$8.2M11.2M4.M.2M32.2M13.3M$9.M11.2M3.2M.2M
32.2M13.3M4.2M$6.3M8.M9.M.2M46.M3.M4.M$6.M9.2M10.M.M47.5M2.M.M$16.M.M
10.M49.4M$97.Q$73.M22.Q.Q$11.2O50.pA7.3M22.Q2.Q$13.O47.2pA7.M7.2M17.
2Q$10.O34.3M14.2pA6.2M6.2M$11.2O32.M48.Q$42.O3.M27.Q18.Q.Q$6.O34.O.O
24.M5.Q19.2Q$6.3O33.O24.3M4.Q$9.O51.pA4.M3.M8.Q$8.2O50.pA4.M.3M.M7.Q$
60.3pA3.5M8.Q3$26.2H$26.2H2$85.2Q$84.Q2.Q$32.O52.Q.Q$31.O.O44.2M6.Q$
31.2O16.2M19.2M6.2M$44.2H2.2M20.M$44.2H4.M20.3M$73.M7.2M$28.O52.2M11.
Q$28.2O63.Q.Q$28.2O48.2M14.2Q$29.O48.2M2$98.Q$97.Q.Q$54.Q43.2Q$M.3M
48.Q.Q$M.4M47.2Q20.3M$M5.M68.M$.M.M.M2.3M65.M$2.M.M.4M$3.M2.M.2M50.M$
3.M3.3M.M38.2M3.M4.2M$4.3M2.2M.M37.2M2.2M5.2M$10.M44.2M4.M26.3M4.2M$
11.M2.M41.M3.M26.M2.M4.M$12.M2.M71.M2.M5.3M$13.2M3.M79.M$14.5M68.M$
15.4M68.M3.M$15.M.M59.2M9.M.M5.Q$14.M.2M.M57.2M10.M5.Q.Q$14.M3.M.M75.
2Q$14.M2.M2.2M52.2M5.2M$15.2M.M.2M52.2M5.2M6.2M$17.M2.2M45.M21.2M$18.
M49.2M14.2Q$19.3M45.2M15.2Q2$71.2M$71.M.M$73.M$73.2M!

The blocks at marked locations is all that is needed to launch self-destruction. We have to introduce two new parameters. One is e, the distance from the marked location at which the block is produced by the second sawtooth if the block is eaten by the first sawtooth, so e=182 (it is a coincidence that it precisely equals a). And the second one is the time that is needed for the ship and its debris to be destroyed given the blocks at marked locations. f=4722.
Now, let's calculate when exactly does this pattern die out. For this one, we have sequence x_n governing the appearance of (n-1)th salvo in the second sawtooth. What does it take for the pattern to be destroyed? Well, the second sawtooth first has to produce a block. The salvo doing that appears at time x_0. The block itself will be at distance x_0+e. Then the second sawtooth has to do x_0+e pulls. That happens at x_(x_0+e) (x subscripted by x_0+e). Note that we need a total of x_0+e+1 gliders, but x sequence starts from 0. And then the destruction gliders would have to reach the c/5 ship and destroy it. If the ship has advanced t ticks compared to initial position, that would require 4t+f ticks. So the overall lifespan is given by 4*((a+5)*121^(120*(a+1)+e+1)-121*4-a-1)+f.

Let's as a quick excersise calculate the lifespan of this diehard (the initial pattern minus all the delaying cells):

Code: Select all

x = 99, y = 95, rule = LifeSuper
39.4Q$10.2Q$9.Q2.Q28.Q4.Q$10.2Q33.Q.Q$45.Q2.Q25.2M15.Q$46.2Q26.2M8.2Q
5.Q$30.2M51.Q2.Q4.Q$31.M52.2Q8.2Q$31.M.M6.2M29.2M21.Q.Q$32.2M6.M.M28.
2M22.Q$43.M7.2M$26.3O11.M2.M7.2M21.2M8.M$17.2Q6.3O15.M30.2M6.3M4.2M$
17.2Q21.M.M38.M7.2M$40.2M39.2M2$10.2M74.2M$10.2M6.O36.Q30.2M$18.2O34.
Q.Q$18.2O35.2Q32.2M$19.O29.2Q22.M.M13.2M7.M$48.Q2.Q23.M20.3M$49.2Q20.
M.M21.M$71.M23.2M$70.M.M$29.2O5.2O32.2M$8.2M3.2M14.2O5.O32.M$9.5M20.O
.O33.2M$9.2M.2M20.2O27.2M6.M$9.2M.2M10.2O37.2M$10.3M11.2O$42.2M22.2M$
42.M23.2M$29.M10.M.M$28.M.M9.2M$8.2M11.2M4.M.2M32.2M13.3M$9.M11.2M3.
2M.2M32.2M13.3M$6.3M18.M.2M46.M3.M$6.M21.M.M47.5M$29.M49.4M2$73.M22.
2Q$11.2O58.3M23.2Q$13.O56.M7.2M18.Q$10.O59.2M6.2M$11.2O81.Q$42.O31.Q
18.Q.Q$6.O34.O.O24.M5.Q19.2Q$6.3O33.O24.3M4.Q$9.O56.M3.M8.Q$8.2O55.M.
3M.M7.Q$66.5M8.Q6$85.2Q$84.Q2.Q$32.O52.Q.Q$31.O.O44.2M6.Q$31.2O37.2M
6.2M$70.M$71.3M$73.M7.2M$28.O52.2M11.Q$28.2O63.Q.Q$28.2O48.2M14.2Q$
29.O48.2M2$98.Q$96.Q.Q$54.Q43.Q$M.3M48.Q.Q42.Q$M.4M47.2Q$M5.M$.M.M.M
2.3M$2.M.M.4M$3.M2.M.2M50.M$3.M3.3M.M38.2M3.M4.2M$4.3M2.2M.M37.2M2.2M
5.2M$10.M44.2M4.M26.3M4.2M$11.M2.M41.M3.M26.M2.M4.M$12.M2.M71.M2.M5.
3M$13.2M3.M79.M$14.5M68.M$15.4M33.M2.2M30.M3.M$15.M.M32.3M2.2M2.M17.
2M9.M.M5.Q$14.M.2M.M33.2M2.3M17.2M10.M5.Q.Q$14.M3.M.M32.2M2.3M36.2Q$
14.M2.M2.2M31.2M6.M2.M9.2M5.2M$15.2M.M.2M32.M6.3M10.2M5.2M6.2M$17.M2.
2M67.2M$18.M65.2Q$19.3M62.2Q!

For this one, we have to use a sequence y with the parameter b=5, as the first 4 salvos do nothing, plus we have to account for there being no salvo at time 0.
We have to calculate 4*y_(y_0+e)+f.
y_0=(a+120b+5)*121-121*4-a-1=120*(a+1+121b)
4*y_(y_0+e)+f=4*((a+120b+5)*121^(120*(a+1+121b)+e+1)-121*4-a-1)+f
=4*(787*121^(788*120+183)-121*4-a-1)+4722
=3148*121^94743+2054

Now for the full diehard:

Code: Select all

x = 105, y = 95, rule = LifeSuper
45.4Q$16.2Q$15.Q2.Q28.Q4.Q$16.2Q33.Q.Q$51.Q2.Q25.2M15.Q$52.2Q26.2M8.
2Q5.Q$36.2M51.Q2.Q4.Q$37.M52.2Q8.2Q$37.M.M6.2M29.2M21.Q.Q$38.2M6.M.M
28.2M22.Q$49.M7.2M$32.3O11.M2.M7.2M21.2M8.M$23.2Q6.3O15.M30.2M6.3M4.
2M$23.2Q21.M.M38.M7.2M$46.2M39.2M2$16.2M74.2M$16.2M6.O36.Q30.2M$24.2O
34.Q.Q$24.2O35.2Q32.2M$25.O29.2Q22.M.M13.2M7.M$54.Q2.Q23.M20.3M$55.2Q
20.M.M21.M$77.M23.2M$76.M.M$35.2O5.2O32.2M$14.2M3.2M14.2O5.O32.M$15.
5M20.O.O33.2M$15.2M.2M20.2O27.2M6.M$15.2M.2M10.2O37.2M$16.3M11.2O$48.
2M22.2M$48.M23.2M$35.M10.M.M$34.M.M9.2M30.2S$14.2M11.2M4.M.2M32.2M6.S
.S4.3M$15.M11.2M3.2M.2M32.2M6.2S5.3M$12.3M18.M.2M37.S8.M3.M$12.M21.M.
M29.S6.S.S8.5M$35.M29.S.S4.S.S10.4M$65.S.S3.S.S$66.S5.S6.M22.2Q$17.2O
34.2S8.S5.S7.3M23.2Q$19.O32.S.S7.S.S3.S.S5.M7.2M18.Q$16.O34.S2.S.S6.S
5.S6.2M6.2M$17.2O32.2S2.2S3.S5.S33.Q$48.O10.S.S3.S.S12.Q18.Q.Q$12.O
11.W22.O.O10.S5.S7.M5.Q19.2Q$12.3O9.2W22.O8.S5.S9.3M4.Q$15.O8.2W30.S.
S3.S.S7.M3.M8.Q$14.2O9.W31.S5.S7.M.3M.M7.Q$20.W16.U16.S5.S11.5M8.Q$
20.2W14.U16.S.S3.S.S$20.2W14.3U15.S5.S$21.W35.S$16.W39.S.S$16.2W39.S$
16.2W47.S25.2Q$17.W47.3S22.Q2.Q$12.W25.O29.S22.Q.Q$12.2W23.O.O5.S21.
2S15.2M6.Q$12.2W23.2O5.S.S29.2M6.2M$13.W31.S3.2S25.M$8.W39.S.S26.3M$
8.2W38.2S29.M7.2M$8.2W24.O9.S42.2M11.Q$9.W24.2O7.S.S53.Q.Q$4.W29.2O8.
2S38.2M14.2Q$4.2W29.O48.2M$4.2W$5.W98.Q$W101.Q.Q$2W51.2S5.Q43.Q$2W4.M
.3M41.S.S4.Q.Q42.Q$.W4.M.4M40.S6.2Q$6.M5.M38.2S$7.M.M.M2.3M$8.M.M.4M$
9.M2.M.2M18.U12.2U.2U14.M$9.M3.3M.M16.U.U10.U.2U2.U2.2M3.M4.2M$10.3M
2.2M.M15.2U16.2U2.2M2.2M5.2M$16.M44.2M4.M26.3M4.2M$17.M2.M22.2U.2U14.
M3.M26.M2.M4.M$18.M2.M21.U.2U2.U43.M2.M5.3M$19.2M3.M23.2U54.M$20.5M
68.M$21.4M14.2U.2U14.M2.2M30.M3.M$21.M.M15.U.2U2.U10.3M2.2M2.M17.2M9.
M.M5.Q$20.M.2M.M18.2U13.2M2.3M17.2M10.M5.Q.Q$20.M3.M.M32.2M2.3M36.2Q$
20.M2.M2.2M7.2U.2U19.2M6.M2.M9.2M5.2M$21.2M.M.2M7.U.2U2.U18.M6.3M10.
2M5.2M6.2M$23.M2.2M12.2U53.2M$24.M65.2Q$25.3M62.2Q!

We have to introduce 3 more parameters: g, the number of times the second sawtooth's salvos are eaten before the first block-producing one (similar to b), h, the distance between the second main block location and the toad block location (similar to c), and j, the number of toads. g=7, h=4, j=7
Let's introduce u_i, which shows the number of salvos that need to be produced by the first sawtooth until ith block is killed by it's toad. So u_0=g, meaning that the 0th "virtual block" consumes g salvos. The next salvo, which produces a block, fires at z_(u_0). Next, sawtooth has to do z_(u_0)+e-h-4(j-1) pulls.
So u_1=u_0+1+z_(u_0)+e-h-4(j-1)). Next, in addition to the previous salvos, we have to produce a block and do z_(u_1)+e-h-4(j-2) pulls. So we obtain u_2=u_1+1+z_(u_1)+e-h-4(j-2)). And so on until u_j.
After that, the sawtooth has to produce a block and do z_(u_j)+e pulls, with the next salvo launching destruction. Let's name it v=u_j+1+z_(u_j)+e.
So the final answer is 4*z_v+f.

Now let's work with actual numbers.
We have
z_n=((a+120b-4d+5)*121^d-(c-4/120)*(121^d-1))*121^(n+1)-121*4-a-1
=119287080322267*121^n-667
u_0=g=7
u_(i+1)=u_i+z_(u_i)+1+e-h-4(j-i-1)
=u_i+119287080322267*121^(u_i)-512+4*i

Final answer
u_0=7
u_1=u_0+119287080322267*121^(u_0)-512
u_2=u_1+119287080322267*121^(u_1)-508
u_3=u_2+119287080322267*121^(u_2)-504
u_4=u_3+119287080322267*121^(u_3)-500
u_5=u_4+119287080322267*121^(u_4)-496
u_6=u_5+119287080322267*121^(u_5)-492
u_7=u_6+119287080322267*121^(u_6)-488
v=u_7+119287080322267*121^(u_7)-484
T=4*119287080322267*121^v+2054

If someone knows if that answer can be significantly simplified, please let me know.

[LLAMASKYWALKER]

I am almost done with my first (unimpressive) diehard, I just need a 1-time glider reflector that keeps the glider on the same lane.

[dvgrn]

I am almost done with my first (unimpressive) diehard, I just need a 1-time glider reflector that keeps the glider on the same lane.

Do you mean a 180-degree reflector? There are lots of those that send the glider right back the way it came, like

Code: Select all

x = 11, y = 12, rule = LifeHistory
.A$2.A$3A2$9.2A$3.2A4.2A$.A2.A$.2A3$5.2A$5.2A!

Two-object one-time reflectors can be found in this post. The 180-degree turners really need to be reclassified -- they're currently done by timing, in a weird way that groups different lane shifts together. But with a little looking through the files you can find various same-lane 180-degree turners.

[LLAMASKYWALKER]

I am almost done with my first (unimpressive) diehard, I just need a 1-time glider reflector that keeps the glider on the same lane.

Do you mean a 180-degree reflector? There are lots of those that send the glider right back the way it came, like

Code: Select all

x = 11, y = 12, rule = LifeHistory
.A$2.A$3A2$9.2A$3.2A4.2A$.A2.A$.2A3$5.2A$5.2A!

Two-object one-time reflectors can be found in this post. The 180-degree turners really need to be reclassified -- they're currently done by timing, in a weird way that groups different lane shifts together. But with a little looking through the files you can find various same-lane 180-degree turners.

Thanks, this is my first engineered diehard:

Code: Select all

 # You can save the pattern into this box with Settings/Pattern/Save or Ctrl-S.
x = 40, y = 40, rule = B3/S23
33b2o$33b2o4$25b2o$25b2o5bo$31b3o$32bo4$24b3o$24b3o2b3o$29b3o8$3bo24b
3o$4bo23b3o2b3o$o3bo23b3o2b3o2b2o$b4o28b3o2b2o2$26b2o$26b2o$30b3o$30b
3o2b3o$30b3o2b3o$b2o32b3o$b2o4b2o$7bo2bo$9b2o3$5b2o$5b2o!

It is also adjustable, just move the reflector down and to the left

[toroidalet]

With the help of some overkill patches of space dust, I have cut off enough rows and columns to add another toad:

Code: Select all

x = 108, y = 92, rule = LifeSuper
20.2Q25.Q.4Q.Q.Q.Q$19.Q2.Q24.Q6.Q.Q$20.2Q27.Q6.Q$49.3Q2.Q.Q27.2M15.Q$
47.Q10.Q25.2M8.2Q5.Q$40.2M13.2Q36.Q2.Q4.Q$41.M52.2Q8.2Q$41.M.M6.2M29.
2M21.Q.Q$42.2M6.M.M28.2M22.Q$53.M7.2M$36.3O11.M2.M7.2M21.2M8.M$27.2Q
6.3O15.M30.2M6.3M4.2M$27.2Q13.pA7.M.M38.M7.2M$41.pA.pA6.2M39.2M$42.pA
$20.2M17.pA5.pA50.2M7.3M$20.2M6.O9.pA.pA3.pA.pA18.Q30.2M6.M.M$28.2O7.
pA.pA5.pA3.2pA13.Q.Q37.M$28.2O6.pA.pA3.pA6.2pA14.2Q32.M2.M.M.2M$29.O
5.pA.pA3.pA.pA9.pA5.2Q22.M.M13.2M3.2M.M$34.pA.pA5.pA9.pA.pA3.Q2.Q23.M
17.M.M.M$33.pA.pA17.pA.pA3.2Q20.M.M21.2M$32.pA.pA19.pA.pA24.M23.M$31.
pA.pA21.pA24.M.M$30.pA.pA6.2O5.2O4.pA27.2M$18.2M3.2M4.pA.pA7.2O5.O4.pA
.pA3.2pA20.M$19.5M6.pA13.O.O5.pA4.pA.pA20.2M$19.2M.2M20.2O12.2pA13.2M
6.M$19.2M.2M10.2O37.2M$20.3M4.2pA5.2O$27.2pA23.2M22.2M$52.M23.2M$39.M
10.M.M13.2pA$38.M.M9.2M14.pA.pA13.2S$18.2M4.2pA5.2M4.M.2M26.2pA4.2M6.
S.S4.3M$19.M4.pA.pA4.2M3.2M.2M22.pA9.2M6.2S5.3M$16.3M6.2pA10.M.2M21.pA
.pA13.S8.M3.M$16.M21.M.M22.pA6.S6.S.S8.5M10.Q.Q$28.pA10.M29.S.S4.S.S
10.4M11.4Q$27.pA.pA39.S.S3.S.S24.Q.2Q$28.pA.pA39.S5.S6.M18.Q4.Q$21.2O
6.pA.pA25.2S8.S5.S7.3M18.3Q.2Q$23.O6.pA25.S.S7.S.S3.S.S5.M7.2M13.3Q.Q
$20.O34.S2.S.S6.S5.S6.2M6.2M12.Q3.2Q$21.2O17.pA14.2S2.2S3.S5.S33.Q.Q$
34.2pA3.pA.pA10.O10.S.S3.S.S12.Q17.Q2.Q.Q$16.O11.W5.2pA4.pA10.O.O10.S
5.S7.M5.Q18.Q.Q$16.3O9.2W22.O8.S5.S9.3M4.Q$19.O8.2W13.U16.S.S3.S.S7.M
3.M8.Q$18.2O9.W13.U.U15.S5.S7.M.3M.M7.Q$24.W18.2U13.S5.S11.5M8.Q$24.
2W31.S.S3.S.S$24.2W32.S5.S$25.W35.S$20.W39.S.S$20.2W39.S$20.2W47.S25.
2Q$21.W47.3S22.Q2.Q$16.W25.O29.S22.Q.Q$16.2W23.O.O5.S21.2S15.2M6.Q$
16.2W23.2O5.S.S29.2M6.2M$17.W31.S3.2S25.M$12.W39.S.S26.3M$12.2W38.2S
29.M7.2M$12.2W24.O9.S42.2M9.Q2.Q.Q$13.W24.2O7.S.S53.Q.Q.Q$8.W29.2O8.
2S38.2M14.Q$8.2W29.O48.2M17.Q$8.2W95.Q$9.W93.2Q2.Q$4.W7.M.3M26.2pA57.
3Q.2Q$4.2W6.M.4M25.2pA4.pA7.2S5.Q37.2Q3.Q$4.2W6.M5.M29.pA.pA5.S.S4.Q.
Q36.Q.Q.2Q$5.W7.M.M.M2.3M26.pA6.S6.2Q38.Q$W13.M.M.4M19.U4.pA8.2S45.3Q
2.Q$2W13.M2.M.2M18.U4.pA.pA54.2Q.Q.Q$2W13.M3.3M.M16.3U3.pA$.W14.3M2.
2M.M26.2U.2U14.M$22.M28.U.2U2.U2.2M3.M4.2M$23.M2.M29.2U2.2M2.2M5.2M$
24.M2.M37.2M4.M26.3M4.M$25.2M3.M16.2U.2U14.M3.M26.M2.M4.2M$26.5M16.U.
2U2.U43.M2.M2.M.M.M$27.4M21.2U50.2M.M$27.M.M72.M.M.2M$26.M.2M.M11.2U.
2U14.M2.2M23.M13.M$26.M3.M.M10.U.2U2.U10.3M2.2M2.M16.M.5M3.2M5.2Q.Q$
26.M2.M2.2M14.2U13.2M2.3M18.2M.2M4.M4.Q.2Q.Q$27.2M.M.2M29.2M2.3M19.2M
2.2M11.Q$29.M2.2M5.2U.2U19.2M6.M2.M9.2M2.2M.M14.Q$30.M8.U.2U2.U18.M6.
3M10.M3.2M.6M2.2M$31.3M10.2U39.M2.M3.5Q2.2M!

I also added a bunch of obstacles in hot pink which have to be cleared before the pull salvo works.

[Pavgran]

With the help of some overkill patches of space dust, I have cut off enough rows and columns to add another toad:

Code: Select all

x = 108, y = 92, rule = LifeSuper
20.2Q25.Q.4Q.Q.Q.Q$19.Q2.Q24.Q6.Q.Q$20.2Q27.Q6.Q$49.3Q2.Q.Q27.2M15.Q$
47.Q10.Q25.2M8.2Q5.Q$40.2M13.2Q36.Q2.Q4.Q$41.M52.2Q8.2Q$41.M.M6.2M29.
2M21.Q.Q$42.2M6.M.M28.2M22.Q$53.M7.2M$36.3O11.M2.M7.2M21.2M8.M$27.2Q
6.3O15.M30.2M6.3M4.2M$27.2Q13.pA7.M.M38.M7.2M$41.pA.pA6.2M39.2M$42.pA
$20.2M17.pA5.pA50.2M7.3M$20.2M6.O9.pA.pA3.pA.pA18.Q30.2M6.M.M$28.2O7.
pA.pA5.pA3.2pA13.Q.Q37.M$28.2O6.pA.pA3.pA6.2pA14.2Q32.M2.M.M.2M$29.O
5.pA.pA3.pA.pA9.pA5.2Q22.M.M13.2M3.2M.M$34.pA.pA5.pA9.pA.pA3.Q2.Q23.M
17.M.M.M$33.pA.pA17.pA.pA3.2Q20.M.M21.2M$32.pA.pA19.pA.pA24.M23.M$31.
pA.pA21.pA24.M.M$30.pA.pA6.2O5.2O4.pA27.2M$18.2M3.2M4.pA.pA7.2O5.O4.pA
.pA3.2pA20.M$19.5M6.pA13.O.O5.pA4.pA.pA20.2M$19.2M.2M20.2O12.2pA13.2M
6.M$19.2M.2M10.2O37.2M$20.3M4.2pA5.2O$27.2pA23.2M22.2M$52.M23.2M$39.M
10.M.M13.2pA$38.M.M9.2M14.pA.pA13.2S$18.2M4.2pA5.2M4.M.2M26.2pA4.2M6.
S.S4.3M$19.M4.pA.pA4.2M3.2M.2M22.pA9.2M6.2S5.3M$16.3M6.2pA10.M.2M21.pA
.pA13.S8.M3.M$16.M21.M.M22.pA6.S6.S.S8.5M10.Q.Q$28.pA10.M29.S.S4.S.S
10.4M11.4Q$27.pA.pA39.S.S3.S.S24.Q.2Q$28.pA.pA39.S5.S6.M18.Q4.Q$21.2O
6.pA.pA25.2S8.S5.S7.3M18.3Q.2Q$23.O6.pA25.S.S7.S.S3.S.S5.M7.2M13.3Q.Q
$20.O34.S2.S.S6.S5.S6.2M6.2M12.Q3.2Q$21.2O17.pA14.2S2.2S3.S5.S33.Q.Q$
34.2pA3.pA.pA10.O10.S.S3.S.S12.Q17.Q2.Q.Q$16.O11.W5.2pA4.pA10.O.O10.S
5.S7.M5.Q18.Q.Q$16.3O9.2W22.O8.S5.S9.3M4.Q$19.O8.2W13.U16.S.S3.S.S7.M
3.M8.Q$18.2O9.W13.U.U15.S5.S7.M.3M.M7.Q$24.W18.2U13.S5.S11.5M8.Q$24.
2W31.S.S3.S.S$24.2W32.S5.S$25.W35.S$20.W39.S.S$20.2W39.S$20.2W47.S25.
2Q$21.W47.3S22.Q2.Q$16.W25.O29.S22.Q.Q$16.2W23.O.O5.S21.2S15.2M6.Q$
16.2W23.2O5.S.S29.2M6.2M$17.W31.S3.2S25.M$12.W39.S.S26.3M$12.2W38.2S
29.M7.2M$12.2W24.O9.S42.2M9.Q2.Q.Q$13.W24.2O7.S.S53.Q.Q.Q$8.W29.2O8.
2S38.2M14.Q$8.2W29.O48.2M17.Q$8.2W95.Q$9.W93.2Q2.Q$4.W7.M.3M26.2pA57.
3Q.2Q$4.2W6.M.4M25.2pA4.pA7.2S5.Q37.2Q3.Q$4.2W6.M5.M29.pA.pA5.S.S4.Q.
Q36.Q.Q.2Q$5.W7.M.M.M2.3M26.pA6.S6.2Q38.Q$W13.M.M.4M19.U4.pA8.2S45.3Q
2.Q$2W13.M2.M.2M18.U4.pA.pA54.2Q.Q.Q$2W13.M3.3M.M16.3U3.pA$.W14.3M2.
2M.M26.2U.2U14.M$22.M28.U.2U2.U2.2M3.M4.2M$23.M2.M29.2U2.2M2.2M5.2M$
24.M2.M37.2M4.M26.3M4.M$25.2M3.M16.2U.2U14.M3.M26.M2.M4.2M$26.5M16.U.
2U2.U43.M2.M2.M.M.M$27.4M21.2U50.2M.M$27.M.M72.M.M.2M$26.M.2M.M11.2U.
2U14.M2.2M23.M13.M$26.M3.M.M10.U.2U2.U10.3M2.2M2.M16.M.5M3.2M5.2Q.Q$
26.M2.M2.2M14.2U13.2M2.3M18.2M.2M4.M4.Q.2Q.Q$27.2M.M.2M29.2M2.3M19.2M
2.2M11.Q$29.M2.2M5.2U.2U19.2M6.M2.M9.2M2.2M.M14.Q$30.M8.U.2U2.U18.M6.
3M10.M3.2M.6M2.2M$31.3M10.2U39.M2.M3.5Q2.2M!

I also added a bunch of obstacles in hot pink which have to be cleared before the pull salvo works.

Nice! Hot pink obstacles raise the multiplier of the u sequence more than 2 times, and a new toad allows for a new level in exponential tower, which is huge.
Although I have to adjust this a bit. Right now, the gliders producing the delaying block produce it too close to the toads, so they have to be moved back 4 ticks:

Code: Select all

x = 108, y = 92, rule = LifeSuper
20.2Q25.Q.4Q.Q.Q.Q$19.Q2.Q24.Q6.Q.Q$20.2Q27.Q6.Q$49.3Q2.Q.Q27.2M15.Q$
47.Q10.Q25.2M8.2Q5.Q$40.2M13.2Q36.Q2.Q4.Q$41.M52.2Q8.2Q$41.M.M6.2M29.
2M21.Q.Q$42.2M6.M.M28.2M22.Q$53.M7.2M$36.3O11.M2.M7.2M21.2M8.M$27.2Q
6.3O15.M30.2M6.3M4.2M$27.2Q13.pA7.M.M38.M7.2M$41.pA.pA6.2M39.2M$42.pA
$20.2M17.pA5.pA50.2M7.3M$20.2M6.O9.pA.pA3.pA.pA18.Q30.2M6.M.M$28.2O7.
pA.pA5.pA3.2pA13.Q.Q37.M$28.2O6.pA.pA3.pA6.2pA14.2Q32.M2.M.M.2M$29.O
5.pA.pA3.pA.pA9.pA5.2Q22.M.M13.2M3.2M.M$34.pA.pA5.pA9.pA.pA3.Q2.Q23.M
17.M.M.M$33.pA.pA17.pA.pA3.2Q20.M.M21.2M$32.pA.pA19.pA.pA24.M23.M$31.
pA.pA21.pA24.M.M$30.pA.pA6.2O5.2O4.pA27.2M$18.2M3.2M4.pA.pA7.2O5.O4.pA
.pA3.2pA20.M$19.5M6.pA13.O.O5.pA4.pA.pA20.2M$19.2M.2M20.2O12.2pA13.2M
6.M$19.2M.2M10.2O37.2M$20.3M4.2pA5.2O$27.2pA23.2M22.2M$52.M23.2M$39.M
10.M.M13.2pA$38.M.M9.2M14.pA.pA13.2S$18.2M4.2pA5.2M4.M.2M26.2pA4.2M6.
S.S4.3M$19.M4.pA.pA4.2M3.2M.2M22.pA9.2M6.2S5.3M$16.3M6.2pA10.M.2M21.pA
.pA13.S8.M3.M$16.M21.M.M22.pA6.S6.S.S8.5M10.Q.Q$28.pA10.M29.S.S4.S.S
10.4M11.4Q$27.pA.pA39.S.S3.S.S24.Q.2Q$28.pA.pA39.S5.S6.M18.Q4.Q$21.2O
6.pA.pA25.2S8.S5.S7.3M18.3Q.2Q$23.O6.pA25.S.S7.S.S3.S.S5.M7.2M13.3Q.Q
$20.O34.S2.S.S6.S5.S6.2M6.2M12.Q3.2Q$21.2O17.pA14.2S2.2S3.S5.S33.Q.Q$
34.2pA3.pA.pA10.O10.S.S3.S.S12.Q17.Q2.Q.Q$16.O11.W5.2pA4.pA10.O.O10.S
5.S7.M5.Q18.Q.Q$16.3O9.2W14.U7.O8.S5.S9.3M4.Q$19.O8.2W14.U.U13.S.S3.S
.S7.M3.M8.Q$18.2O9.W14.2U15.S5.S7.M.3M.M7.Q$24.W33.S5.S11.5M8.Q$24.2W
31.S.S3.S.S$24.2W32.S5.S$25.W35.S$20.W39.S.S$20.2W39.S$20.2W47.S25.2Q
$21.W47.3S22.Q2.Q$16.W25.O29.S22.Q.Q$16.2W23.O.O5.S21.2S15.2M6.Q$16.
2W23.2O5.S.S29.2M6.2M$17.W31.S3.2S25.M$12.W39.S.S26.3M$12.2W38.2S29.M
7.2M$12.2W24.O9.S42.2M9.Q2.Q.Q$13.W24.2O7.S.S53.Q.Q.Q$8.W29.2O8.2S38.
2M14.Q$8.2W29.O48.2M17.Q$8.2W95.Q$9.W33.2pA58.2Q2.Q$4.W7.M.3M25.4pA
56.3Q.2Q$4.2W6.M.4M31.pA7.2S5.Q37.2Q3.Q$4.2W6.M5.M29.pA.pA5.S.S4.Q.Q
36.Q.Q.2Q$5.W7.M.M.M2.3M19.U6.pA6.S6.2Q38.Q$W13.M.M.4M19.U4.pA8.2S45.
3Q2.Q$2W13.M2.M.2M19.3U.pA.pA54.2Q.Q.Q$2W13.M3.3M.M22.pA$.W14.3M2.2M.
M26.2U.2U14.M$22.M28.U.2U2.U2.2M3.M4.2M$23.M2.M29.2U2.2M2.2M5.2M$24.M
2.M37.2M4.M26.3M4.M$25.2M3.M16.2U.2U14.M3.M26.M2.M4.2M$26.5M16.U.2U2.
U43.M2.M2.M.M.M$27.4M21.2U50.2M.M$27.M.M72.M.M.2M$26.M.2M.M11.2U.2U
14.M2.2M23.M13.M$26.M3.M.M10.U.2U2.U10.3M2.2M2.M16.M.5M3.2M5.2Q.Q$26.
M2.M2.2M14.2U13.2M2.3M18.2M.2M4.M4.Q.2Q.Q$27.2M.M.2M29.2M2.3M19.2M2.
2M11.Q$29.M2.2M5.2U.2U19.2M6.M2.M9.2M2.2M.M14.Q$30.M8.U.2U2.U18.M6.3M
10.M3.2M.6M2.2M$31.3M10.2U39.M2.M3.5Q2.2M!

For this one, the parameters are
a=172, b=81, c=12, d=4, e=172, f=4682, g=7, h=4, j=8
And the equations are

m=255977307969537
u_0=7
u_1=u_0+m*121^(u_0)-516
u_2=u_1+m*121^(u_1)-512
u_3=u_2+m*121^(u_2)-508
u_4=u_3+m*121^(u_3)-504
u_5=u_4+m*121^(u_4)-500
u_6=u_5+m*121^(u_5)-496
u_7=u_6+m*121^(u_6)-492
u_8=u_7+m*121^(u_7)-488
v=u_8+m*121^(u_8)-484
T=4*m*121^v+2054

[ihatecorderships]

And the equations are

m=255977307969537
u_0=7
u_1=u_0+m*121^(u_0)-516
u_2=u_1+m*121^(u_1)-512
u_3=u_2+m*121^(u_2)-508
u_4=u_3+m*121^(u_3)-504
u_5=u_4+m*121^(u_4)-500
u_6=u_5+m*121^(u_5)-496
u_7=u_6+m*121^(u_6)-492
u_8=u_7+m*121^(u_7)-488
v=u_8+m*121^(u_8)-484
T=4*m*121^v+2054

And how large is that in scientific notation? It's hard to get a good idea of how large something is when its expressed in recursive equations like that.

[Nathaniel]

And how large is that in scientific notation? It's hard to get a good idea of how large something is when its expressed in recursive equations like that.

The reason for using recursive equations or tetration notation is that you cannot effectively write the lifespan using scientific notation. It's bigger than 10^999999999999....9, where there are as many "9"s in that exponent as there are atoms in the observable universe.

In other words: if you want to use scientific notation to get an idea of how large this number is, then it's much, much larger than you're thinking it is.