OCA:Sqrt replicator rule: Difference between revisions
m Ian07 moved page Logarithmic replicator rule to OCA:Logarithmic replicator rule |
added W110 unit cell |
||
| Line 8: | Line 8: | ||
}}{{stub}} | }}{{stub}} | ||
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]]. | ||
On August 19, {{year|2020}}, [[Peter Naszvadi]] constructed a Rule 110 [[unit cell]] in B36/S245, proving the rule Turing-complete.<ref name="post102490" /> | |||
==Notable patterns== | ==Notable patterns== | ||
| Line 57: | Line 59: | ||
==References== | ==References== | ||
<references /> | <references> | ||
<ref name="post102490">{{LinkForumThread | |||
|format = ref | |||
|title = Re: List of the Turing-complete totalistic life-like CA | |||
|p = 102490 | |||
|author = Peter Naszvadi | |||
|date = August 19, 2020 | |||
}}</ref> | |||
</references> | |||
==External links== | ==External links== | ||
Revision as of 01:08, 20 August 2020
| Logarithmic replicator rule | |
| Rulestring | 245/36 B36/S245 |
|---|---|
| Rule integer | 26696 |
| Character | Stable |
| Black/white reversal | B012578/S0134678 |
|
This article is a stub. You can help LifeWiki by expanding it. |
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 |
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.[3]
| (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 |
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.
- ↑ David Eppstein. "B36/S245". Retrieved on June 2, 2019.
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