Die hard
| Die hard | |||||||||
| View static image | |||||||||
| Pattern type | Methuselah | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cells | 7 | ||||||||
| Bounding box | 8 × 3 | ||||||||
| MCPS | 11 | ||||||||
| Lifespan | 130 generations | ||||||||
| Final population | 0 | ||||||||
| L/I | 18.6 | ||||||||
| F/I | 0 | ||||||||
| F/L | 0 | ||||||||
| L/MCPS | 11.8 | ||||||||
| Static symmetry | C1 | ||||||||
| Discovered by | Unknown | ||||||||
| Year of discovery | Unknown | ||||||||
| |||||||||
| |||||||||
| |||||||||
Die hard is a 7-cell methuselah (essentially a collision between a block and the traffic light sequence) that vanishes after 130 generations, which is conjectured to be the limit for vanishing patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells, as eight cells suffice to have a glider heading towards an arbitrarily distant blinker or pre-block.
The diehard evolutionary sequence
Predecessors
The original diehard is a semi-common sequence. In addition to a traffic light hitting a block, a common blinker predecessor (called an angel) can hit the same block, turning it into the diehard sequence. This version lasts 137 generations.
| A variant that lasts 137 generations (click above to open LifeViewer) RLE: here Plaintext: here |
Furthermore, a traffic light predecessor hitting a pond yields this sequence after 22 generations. Using a pre-pond makes this require only 8 cells.
| An 8-cell variant that lasts 159 generations (click above to open LifeViewer) |
Descendants
Mitchell Riley found a way to turn the blinker into a block in the appropriate place to make a p42 diehard descendant hassler; this idea was first suggested in 2020 at latest,[1] but the sparker used, 42P14, was not discovered until 2022.
| Period-42 diehard hassler (Mitchell Riley, November 1, 2022) (click above to open LifeViewer) Catagolue: here |
"Die hard" as a general term
Alternatively, "die hard" or "diehard" may refer to any methuselah that eventually vanishes. Like with regular methuselahs, an arbitrarily long-lived diehard can be trivially constructed using only 8 cells from a single glider and either a blinker or a pre-block. Therefore, bounding box tends to be the preferred metric for the "size" of a diehard.
Natural diehards
Soups in Conway's Game of Life lasting at least 500 generations before disappearing completely are reported by apgsearch versions v4.69 and above and referred to as "messless methuselahs" on Catagolue.[2] As of October 2024, the longest-lasting known natural diehard lasts 1413 ticks, while the longest-lasting known semi-natural (i.e. symmetrical but still random) diehard has C4_4 symmetry and lasts 2500 ticks. Both soups were found by Charity Engine, the asymmetric soup on November 29, 2023,[3][4] and the symmetric one on April 6, 2023.[5]
| Asymmetric 1413-tick diehard (click above to open LifeViewer) RLE: here Plaintext: here |
| Symmetric 2500-tick diehard (click above to open LifeViewer) RLE: here Plaintext: here |
Engineered diehards
- Main article: Engineered diehard
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes.
In other rules
In HighLife, despite the instability of the traffic light sequence, the die hard still works, disappearing after 119 generations.
References
- ↑ Daniel Vargas (November 18, 2020). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Ian07 (December 11, 2018). Re: apgsearch v4.0 (discussion thread) at the ConwayLife.com forums
- ↑ Billabob (November 29, 2023). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ See also the attribute page
- ↑ the attribute page
External links
- Die hard at the Life Lexicon
- diehard1398 at Adam P. Goucher's Catagolue (long-lived pattern)
- diehard2474 at Adam P. Goucher's Catagolue (long-lived pattern)
- Thread for small diehards (discussion thread) at the ConwayLife.com forums