OCA:Sqrt replicator rule: Difference between revisions
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The '''logarithmic replicator rule''' is a [[Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have 2, 4, or 5 [[Moore neighbourhood|neighbours]] and are born if they have 3 or 6 neighbours. It is extremely similar to [[Move]], differing only by the <tt>B8</tt> transition. The time required to stabilize is generally much shorter than in [[Conway's Game of Life]]. | The '''logarithmic replicator rule''' is a [[Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have 2, 4, or 5 [[Moore neighbourhood|neighbours]] and are born if they have 3 or 6 neighbours. It is extremely similar to [[Move]], differing only by the <tt>B8</tt> transition. The time required to stabilize is generally much shorter than in [[Conway's Game of Life]]. | ||
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|caption = The namesake logarithmic replicator. | |caption = The namesake logarithmic replicator. | ||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ]] | ||
}} | |||
Its behaviour can be emulated by the following pattern, discovered by AforAmpere on April 11, 2020 in an [[isotropic non-totalistic]] rule:<ref name="post94136" /> | |||
{{EmbedViewer | |||
|rle = x = 3, y = 2, rule = B2a3eny4at/S01c2ci3i4e5e | |||
bo$obo! | |||
|position = center | |||
|caption = A small replicator that emulates the one above<br> | |||
}} | }} | ||
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|pname = b36s245gun | |pname = b36s245gun | ||
|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 ]] | ||
}} | }} | ||
On May 28, 2021, [[Luka Okanishi]] constructed the following period-408 4c/23 spaceship gun without synthesizing from smaller ships.<ref name="post131028" /> | |||
{{EmbedViewer | {{EmbedViewer | ||
|rle = x = 110, y = 64, rule = B36/S245 | |rle = x = 110, y = 64, rule = B36/S245 | ||
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36b2o! | 36b2o! | ||
|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 ]] | ||
}} | }} | ||
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|author = Peter Naszvadi | |author = Peter Naszvadi | ||
|date = August 19, 2020 | |date = August 19, 2020 | ||
}}</ref> | |||
<ref name="post94136">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Miscellaneous Discoveries in Other Cellular Automata | |||
|p = 94136 | |||
|author = AforAmpere | |||
|date = April 11, 2020 | |||
}}</ref> | |||
<ref name="post131028">{{LinkForumThread | |||
|format = ref | |||
|title = Re: B36/S245 | |||
|p = 131028 | |||
|author = Luka Okanishi | |||
|date = May 28, 2021 | |||
}}</ref> | }}</ref> | ||
</references> | </references> | ||
Revision as of 03:25, 15 January 2022
| Logarithmic replicator rule | |
| Rulestring | 245/36 B36/S245 |
|---|---|
| Rule integer | 26696 |
| Character | Stable |
| Black/white reversal | B012578/S0134678 |
The logarithmic replicator rule is a Life-like cellular automaton in which cells survive from one generation to the next if they have 2, 4, or 5 neighbours and are born if they have 3 or 6 neighbours. It is extremely similar to Move, differing only by the B8 transition. The time required to stabilize is generally much shorter than in Conway's Game of Life.
On August 19, 2020, Peter Naszvadi constructed a Rule 110 unit cell in B36/S245, proving the rule Turing-complete.[1]
Notable patterns
The replicator
The name of this rule comes from an elementary replicator first discovered by Mark Niemiec. Unlike other replicators, (such as the one from HighLife) this one does not reproduce itself cleanly, instead leaving oscillators behind which result in a more chaotic growth pattern.[2]
| The namesake logarithmic replicator. (click above to open LifeViewer) RLE: here Plaintext: here |
Its behaviour can be emulated by the following pattern, discovered by AforAmpere on April 11, 2020 in an isotropic non-totalistic rule:[3]
| A small replicator that emulates the one above (click above to open LifeViewer) |
Spaceships
The rule has several known elementary spaceships, the smallest ones having speeds of c/4 orthogonal, 4c/23 orthogonal, and c/7 diagonal, shown below. Other known elementary spaceship speeds include c/2 orthogonal, c/3 orthogonal, c/5 orthogonal, 2c/5 orthogonal, c/6 orthogonal, c/7 orthogonal, c/3 diagonal, and c/4 diagonal.[4]
| (click above to open LifeViewer) RLE: here Plaintext: here |
In 1997, Dean Hickerson discovered two replicator-based spaceships traveling at 7c/150 orthogonal and 7c/300 orthogonal respectively:
|
|
Linear growth
Replicators can also be used to create a gun for the c/7 diagonal ship:
| (click above to open LifeViewer) RLE: here Plaintext: here |
On May 28, 2021, Luka Okanishi constructed the following period-408 4c/23 spaceship gun without synthesizing from smaller ships.[5]
| (click above to open LifeViewer) |
References
- ↑ Peter Naszvadi (August 19, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
- ↑ David Eppstein. "Replicators: B36/S245". Replicators. Retrieved on June 2, 2019.
- ↑ AforAmpere (April 11, 2020). Re: Miscellaneous Discoveries in Other Cellular Automata (discussion thread) at the ConwayLife.com forums
- ↑ David Eppstein. "B36/S245". Retrieved on June 2, 2019.
- ↑ Luka Okanishi (May 28, 2021). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
External links
Sqrt replicator rule at Adam P. Goucher's Catagolue Sqrt replicator rule at David Eppstein's Glider Database
- B36/S245 (discussion thread) at the ConwayLife.com forums