OCA:HighLife/Replicator: Difference between revisions
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The '''HighLife replicator''' is by far the most well-known [[replicator]] in any [[Life-like cellular automaton]] | The '''HighLife replicator''' is by far the most well-known [[replicator]] in any [[Life-like cellular automaton]]. | ||
Because of the way | This replicator is a [[parity rule replicator]] which remains bounded within a diagonal line. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2<sup>n</sup> copies of the replicator at generation {{nowrap|12(2<sup>n</sup> - 1)}} and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a simplified [[speed]] of c/6. Because of the way it duplicates itself, much like other parity replicators, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. | ||
As the replicator is so small, it often occurs naturally from [[soup]] (the Life equivalent is [[butterfly]]). This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns. | |||
A natural [[period]] 96 [[oscillator]] based on the replicator and a pair of [[block]]s functioning as [[eater]]s exists. The oscillator is adjustable; moving the bottom block 16n cells down and 16n cells right yields an oscillator with a period of 96 times the (n+1)th term of the sequence {{OEIS|id=A086839}}. | A natural [[period]] 96 [[oscillator]] based on the replicator and a pair of [[block]]s functioning as [[eater]]s exists. The oscillator is adjustable; moving the bottom block 16n cells down and 16n cells right yields an oscillator with a period of 96 times the (n+1)th term of the sequence {{OEIS|id=A086839}}. | ||
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All linear growth patterns for HighLife on the Catagolue feature the replicator in a major way. | |||
== Bomber == | |||
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}} | {{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}} | ||
{{main|OCA:HighLife/Bomber}} | {{main|OCA:HighLife/Bomber}} | ||
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==References== | == References == | ||
<references /> | <references /> | ||
[[Category:Alien patterns]] | [[Category:Alien patterns]] | ||
Latest revision as of 10:45, 13 September 2025
- Main article: OCA:HighLife
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The HighLife replicator is by far the most well-known replicator in any Life-like cellular automaton.
This replicator is a parity rule replicator which remains bounded within a diagonal line. It copies itself the first time after 12 generations, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a simplified speed of c/6. Because of the way it duplicates itself, much like other parity replicators, it can be considered a sawtooth with expansion factor 2 and a minimum repeating population of 22.
As the replicator is so small, it often occurs naturally from soup (the Life equivalent is butterfly). This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.
A natural period 96 oscillator based on the replicator and a pair of blocks functioning as eaters exists. The oscillator is adjustable; moving the bottom block 16n cells down and 16n cells right yields an oscillator with a period of 96 times the (n+1)th term of the sequence 
A086839.
| The period 96 replicator oscillator (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
All linear growth patterns for HighLife on the Catagolue feature the replicator in a major way.
Bomber
- For other uses of the term 'bomber', see Bomber (disambiguation).
- Main article: OCA:HighLife/Bomber
The bomber is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a blinker in the path of the replicator as shown below. The spaceship itself has a period 48 and travels diagonally at speed c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a glide symmetric spaceship with mod equal to 24. It is the 3rd most common spaceship in HighLife, being slightly more common than the middleweight spaceship.[1]
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References
- ↑ Adam P. Goucher. "/census/b36s23/C1". Catagolue. Retrieved on July 3, 2019.