Engineered diehard

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x = 32, y = 32, rule = B3/S23 3b3obob3o$7b2o3b3o$b3obo2bo3bo$3b3o2b2o4bo$12b2o$2bo5b4obo2bobo2b3o$bo b4o3b3o3bobob2o2bo$5bo5bobo3bo2b2obo$22bo$16bo8b3o$6b2o8b3o6b2ob2o$2b 2obo2bo7bo2bo6bobob2o$2b2ob2obo8b2o6b2o3b2o$6bob2o7b2o6b2obob2o$6bo2bo 3b2o12b3o$3b2ob2o5b2o10bo$3bo2bo10b2o5b2o$bobo2bobo7bobo2bo4bo$b2o4b2o 3bo3b2o3bo4b2o$11bobo8b5o$12bo12bo3$12b2o4bo2bo2bobo2bo$12bobo2bobo2bo bob3o$14bo3bo2b3o5b2o$ob2ob3o6b2o3b2obo3b2o$o2b2ob2o10bo2b2ob3ob3o$2b 5o12bo2bobo4b2o$3o3bo6b2ob2obob6ob4o$obo2b2o6b2ob4obo2b3o2b2o$2b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]] 30,273-tick diehard with bounding box 32 × 32 by Hickerson (click above to open LifeViewer) RLE: here Plaintext: here

Main article: Die hard#"Die hard" as a general term

Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, Dean Hickerson shared a 9044-tick 32 × 32 diehard in a private email to Dave Greene. After a complex series of interactions between an active reaction and various still lifes, a single lightweight spaceship is produced which eventually catches up to and collides with 30P5H2V0, producing a single loaf. Finally, an even slower 25P3H1V0.1 eventually collides with the loaf, destroying both of them. On March 6, more optimized versions using different combinations of spaceships (including the especially slow copperhead) were shared, including a 14,010-tick diehard at 32 × 32 and an 18,477-tick diehard at 36 × 36.

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones. On March 31, Pavel Grankovskiy posted a 50,716-tick diehard in which a Simkin glider gun and pulse-dividing glider reflectors are used to slowly eat through a series of tubs. Although significantly larger than Hickerson's constructions at 90 × 86, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box. Jiahao Yu optimized the bounding box of both of these patterns to 87 × 86, as shown below.

x = 87, y = 86, rule = B3/S23 64bo9b2o$63bobo7bobo$44b2o18b2o7bo$44bo27b2o2$53bo25b2o$51b3o24bo2bo$ 50bo28bobo$42b2o6b2o28bo2b3o$42bobo38bo$43bo40bo2$49bo$48b2o5b2o$56bo$ 51bo$50bobo$38b2o11bo$39bo8bo10bo$47bobo9bo$48bo4b2o4bo$45bo7bobo3bo$ 44bobo8bo$45bo9b2o$42bo$34bo6bobo$34b2o6bo7bo$39bo10b2o$38bobo13bo30bo $39bo13bobo29b2o$36bo17bo$35bobo19bo$25b2o9bo11b2o6bobo$26bo6bo15b2o6b o23bo$32bobo15bo9bo3b4o13b2o$15b4o14bo19b2o4bobo$30bo22bo6bo$29bobo19b obo18bo$10b2o8bo9bo20b2o10b2o7b2o$10bo7b3o6bo6bo28bobo14bobo3bo$17bo8b obo4bo30b2o14b2o3bo$2b2o13b2o8bo5b3o3bo40bo4b2o$3bo9bo9b2o13bobo27bo 11b2o3b2o$3bobo6bobo9bo14bo14bo6bo5bobo9bobo4bo$4b2o7bo40b2o5b2o5bo12b o4bo$9bo6bo25b2o6bo34b2o$9b2o4bobo23bobo6b2o5bo13bo13b2o$16bo21b2o2bo 14b2o11bobo4bo7bo$o18bo17b2o32bo5b2o7bo$2o16bobo18bo23bo10bo7b2o$2o4bo 12bo34bo8b2o8bobo6bobo$o4bobo14bo11bo19b2o18bo9bo$5b2o14bobo10b2o25bo 7b2o13b2o$22bo37bobo7bo$30bo6bo12b2o9bo5b3o6bo$14b2o9bo4b2o5b2o12bo6bo 8bo8b2o$14bo9bobo30bobo$25bo32bo$20bo24bo9bo13b4o$19b2o7b2o15b2o7bobo$ 28bobo24bo5b2o$29b2o9b2o10bo9bo14bo$39bobo6bo2bobo23b3o$39b2o6b2o3bo 27bo$25b2o9bo42b2o$26bo8bobo$22bo3bobo7bo16b2o$22bo4b2o4bo20bo19bo$22b o9bobo38bobo$22bo10bo8b2o28bo2bo$30bo12bo4b2o23b2o$29bobo17b2o$30bo19b o20b2o$25b2o43bobo$26bo5bo39bo$32b2o$49bo$38bo10b2o$37bobo10b2o$30b2o 6b2o$31bo$28b3o13bo$28bo14bobo$43b2o$36b2o$37bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]

50,716-tick diehard with bounding box 87 × 86 by Grankovskiy and Yu (click above to open LifeViewer) RLE: here Plaintext: here

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]

518,476-tick diehard with bounding box 87 × 86 by Grankovskiy and Yu (click above to open LifeViewer) RLE: here Plaintext: here

Sawtooth-based designs

Using a sawtooth allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an expansion factor of 121. The pattern fits within a bounding box of 99 × 101 (just barely meeting the 10,000-cell restriction specified in the original post) and lasts approximately 2.280624 × 10⁸⁷⁰ generations. Further optimizations, with the help of toroidalet, Dean Hickerson, EvinZL, Rocknlol, and Adam P. Goucher increased its lifespan to ~1.33616 × 10¹⁴⁴³ ticks and decreased its bounding box to 94 × 98.

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]

94 × 98 exponential diehard by Grankovskiy et al. (click above to open LifeViewer) RLE: here Plaintext: here

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via tetration, the next hyperoperator after exponentiation. Originally posted in the form of a methuselah, the diehard version was completed on April 11. With optimization by Tanner Jacobi and toroidalet, its lifespan is somewhere between ¹⁵10 and ¹⁶10 ticks.

x = 111, y = 90, rule = B3/S23 21b6o23b8obo$19b10o21b2obobo4b3o24b2o15bo$21bo4bo26bo3b2o28b2o8bo6bo$ 43b2o13b2o2bo34b2o5bo$44bo12bo40bo8b2o$44bobo6b2o3bobobo21b2o21bobo$ 45b2o6bobo28b2o22bo$56bo7b2o$39b3o11bo2bo7b2o21b2o8bo$30b2o6b3o15bo30b 2o6b3o4b2o$30b2o13bo7bobo38bo7b2o$44bobo6b2o39b2o$45bo$23b2o17bo5bo50b 2o7b3o$23b2o6bo9bobo3bobo18bo30b2o6bobo$31b2o7bobo5bo3b2o13bobo37bo$ 31b2o6bobo3bo6b2o14b2o32bo2bobob2o$32bo5bobo3bobo9bo5b2o22bobo13b2o3b 2obo$37bobo5bo9bobo3bo2bo23bo17bobobo$36bobo17bobo3b2o20bobo21b2o$35bo bo19bobo24bo23bo$34bobo21bo24bobo$33bobo6b2o5b2o4bo27b2o$21b2o3b2o4bob o7b2o5bo4bobo3b2o20bo$22b5o6bo13bobo5bo4bobo20b2o$22b2ob2o20b2o12b2o 13b2o6bo$22b2ob2o10b2o37b2o$23b3o4b2o5b2o$30b2o23b2o22b2o$55bo23b2o$ 42bo10bobo13b2o$41bobo9b2o14bobo13b2o$21b2o4b2o5b2o4bob2o26b2o4b2o6bob o4b3o$22bo4bobo4b2o3b2ob2o22bo9b2o6b2o5b3o$19b3o6b2o10bob2o21bobo13bo 8bo3bo$19bo21bobo22bo6bo6bobo8b5o10bobo$31bo10bo29bobo4bobo10b4o11b4o$ 30bobo39bobo3bobo24bob2o$25b2o4bobo39bo5bo6bo18bo4bo$27bo4bobo25b2o8bo 5bo7b3o18b3ob2o$24bo8bo25bobo7bobo3bobo5bo7b2o13b3obo$25b2o31bo2bobo6b o5bo6b2o6b2o12bo3b2o$43bo14b2o2b2o3bo5bo33bobo$20bo16b2o3bobo10bo10bob o3bobo12bo17bo2bobo$20b3o8bo5b2o4bo10bobo10bo5bo7bo5bo18bobo$23bo7b2o 22bo8bo5bo9b3o4bo$13bo8b2o7b2o9bo20bobo3bobo7bo3bo8bo$12bo6bo12bo9bobo 19bo5bo7bob3obo7bo$12b3o3bobo6bo14b2o17bo5bo11b5o8bo$17bo2bo6b2o31bobo 3bobo$17bobo7b2o32bo5bo$18bo3bo5bo35bo$21bobo39bobo$21bo2bo39bo$22bobo 47bo25bo$12bo10bo22bo25b3o23b2o$12bobo4bo25bobo27bo23b2o$5bo6b2o5b2o 24b2o5bo21b2o15b2o$4bo14b2o30bobo29b2o6b2o$4b3o13bo31bo3b2o25bo$15bo9b o29bobo26b3o$15b2o7bo2bo14bo12b2o29bo7b2o$15b2o4b2obo2bo14b2o7bo42b2o 9bo2bobo$16bo5bo5bo13b2o6bobo53bobobo$11bo11b5o15bo7b2o38b2o14bo$11b2o 11bobobo62b2o17bo$11b2o11b5o79bo$o11bo12bo7bo72b2o2bo$obo4bo18b4o75b3o b2o$2o5b2o18bo3b2o19bo7b2o5bo37b2o3bo$7b2o4bobo17bo17bobo5bobo4bobo36b obob2o$8bo4b2o19bo2bo14bo6bo6b2o38bo$o13bo20bo13bo8b2o45b3o2bo$b3obo 29bo12bobo54b2obobo$bo2b2o43bo5bo$4bo31bo17bo2bo15bo$ob2obo30bob2obo4b 2o6bo2bo5b2o3bo4b2o$2o33b2obobob2o2b2o8bo6b2o2b2o5b2o$o35bob3o27b2o4bo 26b3o4bo$bobo33b2obo3bo6b2o16bo3bo26bo2bo4b2o$38b3ob2o6bo2bo46bo2bo2bo bobo$40bo10bo2bo52b2obo$41b2o4bo4b2o51bobob2o$9b4o29bo3bo2bo6b2o7bo2b 2o23bo13bo$9bo3bo2b2o2b2o3bo20bo2bo5bo2bo4b3o2b2o2bo16bob5o3b2o5b2obo$ 9bo6b3o4bo10b2obobo2bo5bo5bo2bo8b2o2b3o18b2ob2o4bo4bob2obo$10bo4b4obo 2bo11bobo3bo13b2o9b2o2b3o19b2o2b2o11bo$15b2obobobobo10bo4b2o3b2o19b2o 6bo2bo9b2o2b2obo14bo$16b10o10b3o2b2obo22bo6b3o10bo3b2ob6o2bo$35b9o2bo 41bo2bo3b5o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]

111 × 90 tetrational diehard by Grankovskiy et al. (click above to open LifeViewer) RLE: here Plaintext: here

On July 9, 2023, EvinZL proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length, based on the original idea of Tanner Jacobi. In a flurry of activity that followed after, toroidalet, Adam P. Goucher, Pavel Grankovskiy and EvinZL pushed the number of loaves from 15 to approximately 3.52 × 10⁴⁸, with the latter improvement based on idea by Adam P. Goucher to use gliders from exponential part of diehard to ignite the fuse. This was subsequently improved to 1.1 × 10¹⁰⁴⁶.

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109 × 91 tetrational diehard with a lifespan exceeding 10104610. (click above to open LifeViewer) RLE: here Plaintext: here

Double-tetrational designs

On 15th September 2023, Tim Coe and b3s23love increased the height of the tetrational tower from 1.1 × 10¹⁰⁴⁶ to 121^{8.46 × 101059}. The following day, Tim Coe further improved this height to 121^121121121498, so the height of the tetrational tower is itself a tetrational tower. This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121^{1211211211211211211211211356648129958673823266622201465466300} as of the 28th September 2023. The overall lifespan of the diehard exceeds ¹¹¹¹11, or 11^^^3 in Knuth's up-arrow notation.

External links

• Pavel Grankovskiy (April 12, 2022). Re: (Engineered) diehards (discussion thread) at the ConwayLife.com forums (analysis of the tetrational diehard's total runtime)