OCA:HighLife/Replicator: Difference between revisions
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{{Sawtooth|patternname= | {{Sawtooth | ||
The HighLife Replicator is by far the most well-known replicator in any [[Life-like cellular automaton]]. It often referred to as "Replicator" or "Simple Replicator" It repeatedly copies itself along a diagonal line according to [[Rule 90]]. 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 [[speed]] of c/6. | |patternname = HighLife Replicator | ||
|e = 2 | |||
|rulespecial = HighLife | |||
|pname = replicator | |||
|name = Highlife Replicator | |||
}} | |||
The HighLife Replicator is by far the most well-known replicator in any [[Life-like cellular automaton]]. It often referred to as "Replicator"{{cn}} or "Simple Replicator"{{cn}}. It repeatedly copies itself along a diagonal line according to [[Rule 90]]. 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 [[speed]] of c/6. | |||
Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because 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. | Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because 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. | ||
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|pname = replicatorpredecessor | |pname = replicatorpredecessor | ||
|position = center | |position = center | ||
|caption = A 6-cell, 3-generation predecessor of the replicator | |caption = A 6-cell, 3-generation predecessor of the replicator | ||
|style = width:300px; | |||
}} | }} | ||
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 16 cells down and 16 cells right n times will yield an oscillator with a period of 96 times the nth-1 term of the sequence {{OEIS|id=A019473}} | 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 16 cells down and 16 cells right n times will yield an oscillator with a period of 96 times the nth-1 term of the sequence {{OEIS|id=A019473}} --> | ||
{{EmbedViewer | {{EmbedViewer | ||
Revision as of 00:02, 28 January 2023
| Highlife Replicator | |||||
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| Pattern type | Sawtooth | ||||
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| Expansion factor | 2 | ||||
| Discovered by | Unknown | ||||
| Year of discovery | Unknown | ||||
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The HighLife Replicator is by far the most well-known replicator in any Life-like cellular automaton. It often referred to as "Replicator"[citation needed] or "Simple Replicator"[citation needed]. It repeatedly copies itself along a diagonal line according to Rule 90. 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 speed of c/6.
Because of the way the replicator duplicates itself, it can be considered a sawtooth with expansion factor 2 and a minimum repeating population of 22. Because 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 6-cell, 3-generation predecessor of the replicator (click above to open LifeViewer) RLE: here Plaintext: here |
A natural period 96 oscillator based on the replicator and a pair of blocks functioning as eaters exists.
| The period 96 replicator oscillator (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
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". Catagolue. Retrieved on July 3, 2019.