LifeWiki - User contributions [en]

Roteightor

2026-01-23T20:13:59Z

77551enpassant:

{{Oscillator
|name = Roteightor
|pname = roteightor
|c = 35
|bx = 14
|by = 14
|p = 8
|m = 2
|h = 11.0
|v = 0.63
|sv = 0.63
|symmetry = nrk
|discoverer = Robert Wainwright
|discoveryear = 1972
|rulemin = B3/S23
|rulemax = B368/S02378
|isorulemin = B3aijq/S2-in3ijnr
|isorulemax = B2cik34-ajn5-aq67e8/S0234-ajw5-nqy6-k78
|plaintext = true
|rle = true
|synthesis = 27
|synthesisRLE = true
|animated = yes
|viewerconfig = #C [[ GPS 2 LOOP 8 THUMBSIZE 3 ZOOM 27 WIDTH 480 HEIGHT 480 ]]
|apgcode = xp8_032acy1oge2zwggseb6z4701y1354c
|pentadecathlonid = 35P8.1
}}
'''Roteightor''' is a {{period|8}} [[oscillator]] with 35 [[cell]]s. It was discovered by [[Robert Wainwright]] in {{year|1972}}.<ref>{{CiteLifeline|vol=6|pages=page 3}}</ref> It consists of four [[eater 1]]s [[hassle|hassling]] a [[fleet]] [[predecessor]] that resembles a standard spaceship of length 3, sometimes called an ''underweight spaceship'' (UWSS). It can also be extended as an [[agar]], as noted by [[Dean Hickerson]] in January {{year|1990}}, to make a family of oscillators called '''multiple roteightors'''.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> The eater 1s can individually be replaced with [[eater 2]]s.

{{EmbedViewer
|pname = multipleroteightors
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 Z 12 HEIGHT 480 GPS 2 AUTOSTART LOOP 8 ]]
}}

== Etymology ==
The roteightor is period eight, the rotor appears to rotate, and in an extended roteightor with the underweight spaceships in their dense phases the UWSSs that touch resemble black eights.

== See also ==
* [[Four eaters hassling lumps of muck]]
* [[Dinner table]]
* [[Honey thieves]]

== References ==
<references />

== External links ==
{{LinkLexicon|lex_r.htm#roteightor}}
{{LinkLexicon|filename=lex_m.htm#multipleroteightors|patternname=Multiple roteightors}}
{{LinkCatagolue|xp8_032acy1oge2zwggseb6z4701y1354c}}
{{LinkPentadecathlonObject|35P8.1}}

__NOTOC__

[[Category:Agars]]

Roteightor

2026-01-23T20:13:39Z

77551enpassant:

{{Oscillator
|name = Roteightor
|pname = roteightor
|c = 35
|bx = 14
|by = 14
|p = 8
|m = 2
|h = 11.0
|v = 0.63
|sv = 0.63
|symmetry = nrk
|discoverer = Robert Wainwright
|discoveryear = 1972
|rulemin = B3/S23
|rulemax = B368/S02378
|isorulemin = B3aijq/S2-in3ijnr
|isorulemax = B2cik34-ajn5-aq67e8/S0234-ajw5-nqy6-k78
|plaintext = true
|rle = true
|synthesis = 27
|synthesisRLE = true
|animated = yes
|viewerconfig = #C [[ GPS 2 LOOP 8 THUMBSIZE 3 ZOOM 27 WIDTH 480 HEIGHT 480 ]]
|apgcode = xp8_032acy1oge2zwggseb6z4701y1354c
|pentadecathlonid = 35P8.1
}}
'''Roteightor''' is a {{period|8}} [[oscillator]] with 35 [[cell]]s. It was discovered by [[Robert Wainwright]] in {{year|1972}}.<ref>{{CiteLifeline|vol=6|pages=page 3}}</ref> It consists of four [[eater 1]]s [[hassle|hassling]] a [[fleet]] [[predecessor]] that resembles a standard spaceship of length 3, sometimes called an ''underweight spaceship'' (UWSS). It can also be extended as an [[agar]], as noted by [[Dean Hickerson]] in January {{year|1990}}, to make a family of oscillators called '''multiple roteightors'''.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> The eater 1s can indivitually be replaced with [[eater 2]]s.

{{EmbedViewer
|pname = multipleroteightors
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 Z 12 HEIGHT 480 GPS 2 AUTOSTART LOOP 8 ]]
}}

== Etymology ==
The roteightor is period eight, the rotor appears to rotate, and in an extended roteightor with the underweight spaceships in their dense phases the UWSSs that touch resemble black eights.

== See also ==
* [[Four eaters hassling lumps of muck]]
* [[Dinner table]]
* [[Honey thieves]]

== References ==
<references />

== External links ==
{{LinkLexicon|lex_r.htm#roteightor}}
{{LinkLexicon|filename=lex_m.htm#multipleroteightors|patternname=Multiple roteightors}}
{{LinkCatagolue|xp8_032acy1oge2zwggseb6z4701y1354c}}
{{LinkPentadecathlonObject|35P8.1}}

__NOTOC__

[[Category:Agars]]

Ikpx

2025-12-15T18:36:09Z

77551enpassant: /* Quotient lattice */

{{Software
|name = ikpx
|image = true
|url = https://gitlab.com/apgoucher/metasat
|purpose = Searching for [[knightship]]s
|createdby = [[Adam P. Goucher]]
|platform = Platform-independent (Python)
}}
'''ikpx (incremental knightship partial extender)''' is a tool for finding [[spaceship]]s by extending [[partial result|partial]]s, written by [[Adam P. Goucher]] in {{year|2018}}. It was used to find [[Sir Robin]], the first [[elementary]] [[knightship]] in [[Conway's Game of Life]].

In particular, the search program can find spaceships which move ''a'' cells left and ''b'' cells upwards every ''p'' generations, provided that the parameters are coprime. Without loss of generality, ''b'' is assumed to be nonzero and at least as large as ''a''.

==Quotient lattice==

Inspired by [[gfind]], the internal representation of patterns interleaves the phases of the pattern. This is slightly more complex in the case of oblique spaceships, where one cannot simply interleave the rows of the phases. As such, ikpx uses the more general idea of a quotient lattice.

Specifically, the history of the pattern can be considered as a subset of the three-dimensional integer lattice, where (x, y, t) indicates the cell at coordinates (x, y) at generation t. Oscillators and spaceships correspond to singly-periodic subsets of this lattice. If the parameters are coprime, then quotienting the integer lattice by the periodicity direction (-a, -b, p) gives a quotient lattice. In the case of orthogonal spaceships, where a = 0, this coincides exactly with the representation used in gfind.

For convenience, a pair of [[Golly]] scripts called '''golly2ikpx.py''' and '''ikpx2golly.py''' are included for converting between the quotient lattice representation and the phases of the pattern.

The choice of coordinates of the quotient lattice is designed so that the front of the spaceship corresponds to the top of the representation, and the back of the spaceship corresponds to the bottom of the representation.

==iglucose==

The search tree is substantially pruned by using a lookahead: we only consider partials that can be extended by another k rows at the current search width. This is accomplished by the use of an incremental [[SAT solver]] called ''iglucose'', modified by [[Marijn Heule]] and [[Tomas Rokicki]] from the ''Glucose'' SAT solver, itself a descendent of ''MiniSAT''. The modifications mean that ''iglucose'' can be operated interactively by ikpx, which feeds constraints to ''iglucose'' and awaits partial results in return.

The effect is that the vast majority of CPU usage is by the optimised ''iglucose'' code, rather than the Python script orchestrating the search.

==Features==

As the Python script is not a performance bottleneck, it is free to include many features and optimisations.

===Floating rows===

Most spaceship search programs mandate that the spaceship fits entirely within a rectangle of width ''w''. Instead, ikpx only requires the spaceship to locally have a width of ''w'', so the shape of the partial is permitted to drift arbitrarily in a horizontal direction. An effect of this is that a shifted copy of a partial is considered equivalent to the original partial, eliminating any redundancy in the search tree.

===Adaptive widening===

When completing a search in [[gfind]] without any results, it is common for the operator to attempt a search at the next width up. This discards all of the time spent searching, starting completely afresh. As an alternative, ikpx increments the width whenever the search completes, and retains the existing search tree so that the work need not be repeated.

===Saving and restoring===

Every hour, ikpx periodically dumps its search tree(s) in compressed pickled files. Also, a SIGINT (operating system interrupt) causes the program to similarly save its progress before exiting. A subsequent run of ikpx with the same target directory will resume its progress from the backup, allowing a search to persist even if the program is terminated. When restoring, it is perfectly possible to use different hyperparameters (i.e. change ''w'' and ''k''), allowing one to find spaceships with sections of different widths. This idea, albeit with a different search program, allowed [[Tim Coe]] to discover the [[spaghetti monster]].

===Importing partials===

An RLE saved by Golly after running '''golly2ikpx.py''' can be opened by ikpx and included in the search tree. [[Sir Robin]] was found by importing a partial discovered by [[Tomas Rokicki]] using a separate search program and running at a lower width.

===Meet-in-the-middle===

It is possible to run ikpx to extend partial front-ends of spaceships, partial back-ends of spaceships, or both simultaneously. In the latter case, it uses a hashtable lookup to see whether a front-end can be joined to a back-end to yield a complete result. This same methodology is used in cryptanalysis, where it can give a quadratic speedup over brute force.

In any case, when extending front-ends it also looks for a direct completion, which was the methodology that found [[Sir Robin]]. This was somewhat surprising, as both the author and [[Tomas Rokicki]] expected the meet-in-the-middle approach to find a solution long before the direct completion approach.

===Parallelism===

The script is designed to run on multicore computers, running many simultaneous instances of iglucose to take advantage of the number of processors. This gives ikpx an advantage over single-threaded search programs.

==ikpx2==

There is a new version of ikpx called ikpx2. This version is written entirely in C++ and uses a new SAT solver (Armin Biere's kissat), and is able to support [[symmetry]] and arbitrary [[isotropic non-totalistic]] rules.<ref name="post101925" /> The [https://gitlab.com/apgoucher/ikpx2 GitLab repository] was made public on August 24, 2020.<ref name="message747441492041400321" />

ikpx 2.2 was released in October 2020, with further speed improvements as well as the ability to upload results to [[Catagolue]] by simulating partials in an integrated [[apgsearch]].<ref name="post106483" />

===Limitations===
It is unable to search for period-multiplied spaceships (though they sometimes arise in the decay of partials in true-period searches in Catagolue censuses), and whereas even-period diagonal spaceships can utilise symmetry (as well as glide symmetry, which is exclusive to them), odd-period ones cannot.

==References==
<references>
<ref name="post101925">{{LinkForumThread
|format = ref
|title = Re: Ikpx and grills
|p = 101925
|author = Adam P. Goucher
|date = August 8, 2020
}}</ref>
<ref name="post106483">{{LinkForumThread
|format = ref
|title = Re: ikpx 2.2
|p = 106483
|author = Adam P. Goucher
|date = October 12, 2020
}}</ref>
<ref name="message747441492041400321">{{CiteDiscord
|author = Adam P. Goucher
|date = August 24, 2020
|channel = tools
|id = 747441492041400321
}}</ref>
</references>

==External links==
* [https://gitlab.com/apgoucher/metasat metasat] on Gitlab
** [https://gitlab.com/apgoucher/metasat/blob/master/ikpx.py ikpx.py] on Gitlab
* [https://gitlab.com/apgoucher/ikpx2 ikpx2] on GitLab
* {{LinkForumThread|f=9|t=3318|title=Ikpx and grills}}
* {{LinkForumThread|f=9|t=4782|title=ikpx 2.2}}

{{CatagolueNavbox}}

{{DISPLAYTITLE:ikpx}}
[[Category:Search software]]

Lake

2022-05-21T21:33:34Z

77551enpassant: /* Semilakes */

{{Glossary}}
A '''lake''' is a [[still life]] that is a simple closed curve made from diagonally connected dominoes. The smallest example is the [[pond]] and the next smallest is [[lake 2]]. The seven smallest lakes are shown below. The number of [[cell]]s in a lake is always divisible by 8, and for any multiple of 8 other than 16 there is a lake with that many cells. The number of distinct lakes with 8n cells for n = 1, 2, 3, ... is given by the sequence 1, 0, 1, 1, 4, 7, 31, 98, 446, 1894, 9049, 43151, ... (Sloane's {{OEIS|A156228}}).

== Examples ==
The sequence of L's and R's notate which direction the edge of the still life turns, starting from the leftmost top domino and moving counterclockwise.
<gallery>
Pond.png|Pond/Lake 1 (8 cells) (LLLL)
Lake2.png|Lake 2 (24 cells) (LLRLLRLLRLLR)
Lake3.png|The 32-cell lake (LLRLLRLRLLRLLRLR)
Lake6.png|Lake 3 (40 cells) (LLRLRLLRLRLLRLRLLRLR)
Lake7.png|A 40-cell lake (LLRLLRLRLRLLRLLRLRLR)
Lake4.png|A 40-cell lake (LLRLRLLRRLLRLRLRLLRR)
Lake5.png|A 40-cell lake (LLRLLRLRLLRLRLLRLLRR)
</gallery>

== Semilakes ==
Smaller still lifes can be based on lakes by contracting their extremal dominoes into single cells, two at a time. Contracting the pond creates the [[beehive]] and the [[tub]]. The [[small lake]] is a twice contracted lake 2. Larger lakes with complex outlines may be contracted several times, e.g. the 6th lake listed above yields 16 different semilakes.

== See also ==
* [[Bi-pond]]
* [[Marshland agar]]

== External links ==
{{LinkLexicon|lex_l.htm#lake}}

__NOTOC__

RLE:P84honeyfarmhassler

2022-05-12T16:21:26Z

77551enpassant: Changed RLE to minpop version

x = 35, y = 20, rule = B3/S23
31bo$29b3o$28bo$2o26b2o$bo$bobo17bo$2b2o15b2obo$18bobo$18bo3$16bo$14b
obo$12bob2o15b2o$13bo17bobo$33bo$5b2o26b2o$6bo$3b3o$3bo!

Period-14 glider gun

2022-04-21T16:39:08Z

77551enpassant: My first time using a reference template, so I hope I did it right.

{{Gun
|name = Period-14 glider gun
|pname = period14glidergun
|c = 8519
|bx = 385
|by = 337
|p = 70
|b = 1
|discoverer = Karel Suhajda
|discoveryear = 2004
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S234c
|rle = true
|viewerconfig = #C [[ ZOOM -1.5 AUTOSTART OFF ]]
}}
'''Period-14 glider gun''' refers to any glider gun which emits a period 14 glider stream, which is the smallest possible period for a glider gun since successive gliders cannot be closer than 14 generations apart. There is no known [[true]]-period p14 glider gun, and finding an example using a direct search is well beyond current search algorithms' abilities. One possible way to create a true-period 14 gun would be to find a p14 [[pi]] [[factory]], which can be converted to a glider using the same mechanism as the [[period-21 glider gun]].

The first pseudo-period 14 gun was built by [[Dietrich Leithner]] on 26th November 1994, which interleaved 15 streams of period 210 by means of [[glider injection gate]]s. Leithner subsequently optimised the gun in both 1995 and 1996, the latter of which has a bounding box of 695-by-689. [[Dean Hickerson]] moved several of the period-210 guns to shrink the bounding box to 528-by-522. [[Jason Summers]] reduced this to 440-by-307 on 28th November 2001 by injecting the gliders in a different order and bending the gun in the middle by means of p7 [[bouncer]]s:
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 14 HEIGHT 640 WIDTH 960 LOOP 210 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 2 ]]
|position = center
|caption = Jason Summers' p14 gun 
|pname = p14summers
}}

Further improvements followed by redesigning the gun with a different base period. [[Karel Suhajda]] built a smaller gun in February 2004, shown in the infobox, which operates at a base period of 70 and uses [[Herschel]] sources to manufacture the [[lightweight spaceship]]s for the injection gates. [[Chris Cain]] discovered a period-84 [[Herschel]] source in April 2016 that facilitated a smaller gun of base period 84. Several incremental improvements followed, for example by the use of the [[34P14 shuttle]] or the [[period-28 glider gun]]<ref name="post115938" />. The final version at this base period was 236-by-213, built by [[Adam P. Goucher]] in December 2020:
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 14 HEIGHT 880 WIDTH 960 LOOP 84 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 4 ]]
|position = center
|caption = pseudo-period-14 gun with a base period of 84 
|pname = p14orbital
}}

[[Tanner Jacobi]] created a slightly smaller (224-by-206) gun at a base period of 28, also in December 2020, using seven copies of the p28 glider gun in total (three to drive each of two LWSS guns which inject gliders into the stream produced by the first gun):
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 14 HEIGHT 840 WIDTH 960 LOOP 28 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 4 ]]
|position = center
|caption = Tanner Jacobi's p14 gun 
|pname = p14jacobi
}}

A smaller period-14 gun was discovered by Jacobi and reduced by Goucher on August 18, {{year|2021}} using [[p21 B-heptomino hassler]]s both as a period-21 gun and as a sparker to convert gliders to [[LWSS]]es. The true period of that gun is 42<ref name="post135004" />:
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 14 HEIGHT 640 WIDTH 640 LOOP 84 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 4 ]]
|position = center
|caption = Former smallest pseudo-period p14 gun 
|pname = pseudop14gun
}}

The smallest period-14 gun known to date was found by [[iNoMed]] (with slight improvements by Goucher and Jacobi) on February 14, {{year|2022}}, based on [[p4-assisted period-28 glider gun|a smaller p28 gun]] found by [[James Pascua]] the same day, and therefore has a true period of 28.<ref name="post141628" /><ref name="message942877372049403946" /> Further improvements were found on April 21, {{year|2022}}, by iNoMed.<ref name="post144541" /> iNoMed's version has a 116-by-95 bounding box and is shown below:
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 14 HEIGHT 640 WIDTH 720 LOOP 84 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 6 ]]
|position = center
|caption = Current smallest pseudo-period p14 gun 
|pname = p4assistedperiod14glidergun
}}

==References==
<references>
<ref name="post115938">{{LinkForumThread
|format = ref
|title = Re: Gun Discussion Thread
|p = 115938
|author = Tanner Jacobi
|date = December 16, 2020}}</ref>
<ref name="post135004">{{LinkForumThread
|format = ref
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|p = 135004
|author = Adam P. Goucher
|date = August 16, 2021}}</ref>
<ref name="post141628">{{LinkForumThread
|format = ref
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|p = 141628
|author = iNoMed
|date = February 14, 2022
}}</ref>
<ref name="message942877372049403946">{{CiteDiscord
|author = Tanner Jacobi
|date = February 14, 2022
|channel = cgol
|id = 942877372049403946
}}</ref>
<ref name="post144541">{{LinkForumThread
|f = 2
|t = 1657
|p = 144541
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|format = ref
|date = April 21, 2022
|author = iNoMed
}}</ref>
</references>
==External links==
{{LinkLexicon|lex_p.htm#p14gun|name=p14 gun}}

RLE:P4assistedperiod14glidergun

2022-04-21T16:28:25Z

77551enpassant: Improvements by INoMed

x = 116, y = 95, rule = B3/S23
73bo4bobo11bo$19b2o11b2o33bo5b2obobob2o11b2o$18bo2bo9bo2bo8bob2o15b2o
3bobobob2o5b2o9b2o$18bobo3b2ob2o3bobo8b2obo10b2o3bo2b2o2bo4bo6bobobob
o5bo8b2o$16b2o2bobo7bobo2b2o4b2o14bo6b2o19bob2o6b4o2bo2bo$17bobobo4bo
4bobobo4bo3b2o17b3o21b2o5b6o2b3o$16bo2b2o2b7o2b2o2bo3bob2obo3b2o18b2o
7bo9bobobob8o$16b2o5bobobobo5b2o4b2o5bobo17bo2bo6b3o11bo9bo$25bobo15b
o4bo20b2o10bo19b2o$21b3o5b3o11bo2bo3bo15b3o2b3o6b2o$20bobobo3bobobo10b
2obobo16bo4bo3bo11b2o$20b2o2b5o2b2o10bo4bo16b2obob2ob2o2bo5b2ob2o$15b
o22b2o2b3o4bo4b2o3bo6bo2bo2bo2b3o3bobo10bo$6b2o6bobo21bo4bo4bo4bobo3b
2o3bo5bo2b2o5bobo11b2o$6bo2bo3bobobo9bo8bobo4b2obobo3b4o3b4o3bo7bob2o
2bo24b2o$7b5o2bo2bo18b2o5bo2bo3bo3b2o3bobo4bo2bo4bobobobo6bo7b2o8b2o$
4b3o5b2o3bobo6bobobo12bo4bo6bo3b2o4bo2b2o3b2obobob2o5bobo6bo$3bo3bobo
bo6b2o7b3o11b2o5bobo15bo2bo4bobobo8b2o$3bobo3bo3b3o18bo5bob2obo3b2o15b
o7bobobo$4b2ob2ob2obo2bo10b3o5b2o3bo3b2o11bo6bo5bo2b2o2bo$15b2o9bobob
o3b2o5b2o15b2o6bo2bo2bo2b2o$4b4o3b4o28b2obo10b2o6b2obob2ob2o$4bo2bo3b
o2bo14bo13bob2o6b2o10bo4bo3bo5bo6b2ob7ob2o$6b3ob3o41bo11b3o2b3o6bobo3b
ob2o2b3o2b2obo$4bobo5bobo36b3o15b2o9b2o5b4o5b4o$4b2obo3bob2o13b5o8bo9b
o16bo2bo$4b3o5b3o9b2ob2o3b2ob2o5b2o20bo4b2o17b2o7b2o$23bo13bo3b2o22b2o
20bo3bo3bo3bo$3b4o5b4o7bo2bobo3bobo2bo26b2o22b4o3b4o$2bob2o2b3o2b2obo
3b2ob2obobo3bobob2obo33bo11bo2bobo5bobo2bobo2bo$3b2ob7ob2o3bo2bo15bob
o32bobo9b3obo7bob3ob4o$19b2obob3o2b3o2b3obobo32b2o2b2o9bobobobobobo$21b
obo13bobo8bo28bobo5b2obo2b2ob2o2bo2b2obo$21bobobo9bobo11b2o20bo5bo7bo
b2o9b4ob2o$10b2o7bobobo3bo2bo2bo3bo10b2o22b2o17b2ob4o9b2obo$10b3o6b2o
3b2ob7ob2o34b2o18bob2o2bo2b2ob2o2bob2o$9b5o12bo7bo62bobobobobobo$8b2o
3b2o11bob2ob2obo54b4ob3obo7bob3o$2o5b3o3b3o11bobobobo50b2o3bo2bobo2bo
bo5bobo2bo$2o6b2o3b2o40bo28bobo10b4o3b4o$9b5o42b2o26bo11bo3bo3bo3bo$10b
3o8bo33b2o40b2o7b2o$11b2o6bobo$20b2o51b2o21b4o5b4o$73b3o19bob2o2b3o2b
2obo$72bob2o5b2o8b2o3b2ob7ob2o$7b2ob7ob2o42bo9b3o6bobo7bobo$6bob2o2b3o
2b2obo42b2o8bo4b2obobo7bo$7b4o5b4o8bo33b2o14bobobo$26bobo51bo$8b2o7b2o
8b2o49bo2bo7bo11bo3bo4b2o$7bo3bo3bo3bo61bo6bobo8bo2b3obo2b3o$8b4o3b4o
58bo3bo5bobo2bo5bo4bo8b4o$2b2obo2bobo5bobo2bo47bo7bo3bo5bobob2o5bo4bo
bo5bob3o$2b2ob3obo7bob3o8bobo37b2o9bo4b2ob2o7bobo4bo5bo$8bobobobobobo
11bob2obo9b4o10b4o6b2o7bo2bo8bo11bob3o$2b2ob2obo2b2ob2o2bob2o13bo8bo3b
o9bo3bo18b2o6bob2o2b2o6bo3bo$3bobo2bo9b2obo10bo2bo12bo13bo9bobo6b3o3b
obobo2bobo$bobobobo25bo10bo2bo10bo2bo11b2o8b2ob2obobob2o$o2bobo2b3o62b
o12b2obobo2bo$o4bo4bo65bo9b2obobobo$2b3o18bo22bob2o9b2obo14b2o9b2obob
2o5b2ob7ob2o$23b2o21b2obo2b2ob2o2bob2o3b3o7b2o12bo8bob2o2b3o2b2obo$2b
5o2bob2o9bobo24bobobobobobo7bo32b4o5b4o$2obo2bo2b2obo14b2o17b3o2bobob
obo2b3o16bobo$5bo20bo2bo7bo8bo15bo2bob2o11b2o19b2o7b2o$3o3b6o15b2o7b2o
9bob3obobob3obo3bobob2o9bo19bo3bo3bo3bo$b2o5bo3bo11b3o2b3o4bobo11bobo
3bobo8b3obo11bo17b4o3b4o$2bo8b2o3bo6bo2bobo3bo14bo2bo7bo2bo2b2o5bo12b
2o12bo2bobo5bobo2bo$o2bo12b2o5bo4bobobo17bo7bo5b2o4bo12b2o13b3obo7bob
3o$3bo11bobo7b2obo4b2o12bo13bo7bo31bobobobobobo$bo21bo7b2o2bo11bob2ob
2ob2ob2obo8b3o13bobo9b2obo2b2ob2o2bob2o$3bobobo14b2ob2o5bobo9bo3b2o4b
o4b2o11bo14b2o9bob2o9b2obo$2b2o3bo14bo5bo3bob2o7b2o6bo5bo29bo$13bo3bo
4bo5bo2b2o10bobo44bo$4b2obo6bobo2bo2bo5bo3bob2o18bo36b2o$7b2o4b2ob2o4b
2ob2o5bobo55b2o$8bo2bo2bobo6bo7b2o2bo26bo$5bo2bo4bo3bo7b2obo4b2o17b3o
b3o3b2o29bobo$8bo14bo4bobobo7b2o9b3obob2o2bo2bob2o26b2o$7b2o14bo2bobo
3bo8bo8b4obobob5o2b2o26bo$4b2obo16b3o2b3o9bobo6bo3b2obob4o34bo$4b3o20b
2o13bobo9b3ob3o37b2o$26bo2bo14bo2b2o48b2o$3b3o21b2o12bo2bo2b2o$3b4ob2o
31bo16bo41bobo$3b3o4bo4b2o25bo17bob2o37b2o$6bo2bo5b2o22b3o6b2o2bo10bo
37bo$5b2obo30bo12bobo6b2o41bo$4bobobobo20b2o17bo4b6o2b3o39b2o$4b2o3b2o
21bob2o5b2o2bob3o12bo2bo38b2o$30bo7bo6bo7bo9b2o$30b2o2bobobo4bo9bobo$
35bo4b3o9bobo$54bo!

Wickstretcher 1

2022-04-11T16:02:24Z

77551enpassant:

{{Wickstretcher
|name = Wickstretcher 1
|pname = wickstretcher1
|c = 176
|bx = 49
|by = 16
|dir = Orthogonal
|p = 5
|s = c/4
|discoverer = Hartmut Holzwart
|discoverer2 = Dean Hickerson
|discoveryear = 1992
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B36cn7c8/S234ce5aky6in8
|plaintext = true
|rle = true
|animated = yes
}}
'''Wickstretcher 1''' is the first explicitly constructed [[wickstretcher]]. Its front end was constructed by [[Hartmut Holzwart]] and its back end was constructed by [[Dean Hickerson]]. It was found in October {{year|1992}}. On November 25, {{year|2003}} [[Paul Tooke]] found a slightly smaller antstretcher.<ref>{{CiteSummersPattern|name=jslife}}</ref>

It works by having its front end stretch [[ants]] at a speed of [[c/4 orthogonal|c/4]], while its back end stabilizes the ants. Its back end can also be seen stabilizing ants in [[electric fence]].

==Gallery==
{|
|-
|{{EmbedViewer
|pname = wickstretcher1variant
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = A slightly smaller wickstretcher found by Paul Tooke 
}}
|}

==References==
<references/>

==External links==
{{LinkLexicon|lex_w.htm#wickstretcher}}

Raucci's p38

2022-04-04T17:52:27Z

77551enpassant:

{{Oscillator
|name = 44P38
|pname = 44p38
|c = 44
|bx = 44
|by = 13
|p = 38
|m = 38
|h = 52.7
|v = 0.96
|sv = 0.96
|discoverer = David Raucci
|discoveryear = 2022
|rulemin = B3/S23
|rulemax = B3/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B36i7c/S234c6i8
|synthesis = 14
|plaintext = true
|rle = true
|apgcode = xp38_32acywca23z0888xooxoa6ya6aoxoox888zy17ys7
|viewerconfig = #C [[ GPS 19 THUMBSIZE 2 ZOOM 10 ]]
}}
'''44P38''' is a {{period|38}} [[oscillator]] found by [[David Raucci]] on January 12, {{year|2022}}<ref name="post140183" />. It is the first finite oscillator of this period to be discovered. It consists of two [[wing]]s being [[hassle]]d by the [[three quarters traffic light catalyst]]. The period-38 wing reaction was originally found in the form of an infinite [[wick]] by [[Jason Summers]] on August 31, {{year|2000}}.

Its [[duoplet]] [[spark]] can reflect [[glider]]s in at least two ways, as shown by [[vivi]]<ref name="message930880731037728768" /> and [[Kalan Warusa]].<ref name="post140191" />

A {{gliders|14}} [[synthesis]] was found for this oscillator on the day of its discovery.<ref name="post140194" />

==Gallery==
<center>
{|
|-
| {{EmbedViewer
|pname = p38rpentominohassler
|caption = p38 [[R-pentomino]] hassler<ref name="message930895679725924352" /> 
|apgcode = xp38_w32acywca23zy0sy48kie4y84eik8y4szy3771y7gsyb177zyk33oy066zy9ggx2cy31zy1ggy211y1330s4y8ggzwsw332x8k4ogy8go4k8x233wszw8oy511ya11y5o8z311yy113
|position = center
}}[[Category:Pages using extended apgcodes]]
|| {{EmbedViewer
|pname = p38wicksupport
|caption = Extended form to show connectivity of the original wick
|apgcode = xp38_y2ca23yzyr32acz888xooxoa6ya6aoy0ogycgoy0oa6ya6aoxoox888zy07yr23ya32yr7
|position = center
}}
|| {{EmbedViewer
|pname = p38reflectglider
|caption = Two ways to reflect a glider with the duoplet spark Top is [[color-preserving]], bottom is [[color-changing]] 
|viewerconfig = #C [[ ZOOM 4 ]]
|position = center
}}
|-
|| {{EmbedViewer
|pname = p38blinkerhassler
|caption = p38 [[blinker]] hassler<ref name="message930896079707340830" /> 
|apgcode = xp38_y1ca23yi32aczsxgooxsq6ya6qsxoogxszw223y9geqcy9322zy5ggy311y1ggz4r4y233568r3kwk3r86533y24r4zxckggy41y01y4ggkczy21yi1
|position = center
}}
|| {{EmbedViewer
|pname = p76blockpusher
|caption = p76 [[block]] hassler<ref name="message930896228525416478" /><ref name="post140195" /> 
|apgcode = xp76_32acywca23z0888xooxoa6ya6aoxoox888zy17y8ok24soya7zy1sy8358473yasz0222x33x3acyaca3x33x222zo8a6yw6a8o
|position = center
}}
|| {{EmbedViewer
|pname = p38biblockhassler
|caption = p38 [[bi-block]] hassler<ref name="message930905780369100830" /> 
|apgcode = xp38_y1ca23yi32aczsy08owgga6ya6aggwo8y0szw222ydogy4gw222ydgzyiddy165110o4ec8gy4g8ce4o01156zym4e2cy1ba8cd3y23dc8aby1c2e4
|position = center
}}
|-
|| {{EmbedViewer
|pname = p38twopondandtwoblockreaction
|caption = p38 [[two pond and two block reaction|two pond and two block hassler]]<ref name="post140208" /> 
|apgcode = xp38_y311hgsz8e13y033ykoggy8ggozy26533y166y1gw676y18goosb59ewe95bsoog8y1676zy9a9p96w69995x6a8oy11y61y1o8a6zyh66zy2ckooz2egoy0oozy3ggh17
|position = center
}}
|| {{EmbedViewer
|pname = p38honeyfarmhassler
|caption = p38 [[honey farm hassler]]<ref name="post140225" /> 
|apgcode = xp38_yzy031e8zyzwo8b513xsczy2ca23yi32acy9lanxggg070ooxogycgoxoo070gggz888xooxoa6ya6aoxoox888x8k8w1y6ggy023ya32y0ggzy07ys7y3nq5y1ggoy11226yi6221zyzy211xmk56zyzy8346
|position = center
}}
|| {{EmbedViewer
|pname = moldon44p38
|caption = [[Mold]] on 44P38, the smallest known p76 oscillator<ref name="message930905878356459600" /> 
|apgcode = xp76_o4an7y1ca23yi32acz0110888xooxoa6ya6aoxoox888zy47ys7
|position = center
}}
|-
|| {{EmbedViewer
|pname = catereron44p38
|caption = [[Caterer]] on 44P38, the smallest known p114 oscillator<ref name="post140186" /> 
|apgcode = xp114_32acywca23z0888xooxoa6ya6aoxoox888zy17ys7zye4hh186zyf7
|position = center
}}
|| {{EmbedViewer
|pname = figureeighton44p38
|caption = [[Figure eight]] on 44P38, the smallest known p152 oscillator<ref name="post140193" /> 
|apgcode = xp152_32acywca23zwsy48kie4y84eik8y4szy1771yo177zybgggeeezyb333
|position = center
}}
|}
</center>

==References==
<references>
<ref name="post140183">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140183
|author = David Raucci
|date = January 12, 2022
}}</ref>
<ref name="message930880731037728768">{{CiteDiscord
|author = vivi
|date = January 12, 2022
|channel = cgol
|id = 930880731037728768
}}</ref>
<ref name="post140191">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140191
|author = Kalan Warusa
|date = January 12, 2022
}}</ref>
<ref name="post140194">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 140194
|author = Jeremy Tan
|date = January 12, 2022
}}</ref>
<ref name="message930895679725924352">{{CiteDiscord
|author = David Raucci
|date = January 12, 2022
|channel = cgol
|id = 930895679725924352
}}</ref>
<ref name="message930896079707340830">{{CiteDiscord
|author = iNoMed
|date = January 12, 2022
|channel = cgol
|id = 930896079707340830
}}</ref>
<ref name="message930896228525416478">{{CiteDiscord
|author = dani
|date = January 12, 2022
|channel = cgol
|id = 930896228525416478
}}</ref>
<ref name="post140195">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140195
|author = dani
|date = January 12, 2022
}}</ref>
<ref name="message930905780369100830">{{CiteDiscord
|author = dani
|date = January 12, 2022
|channel = cgol
|id = 930905780369100830
}}</ref>
<ref name="post140208">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140208
|author = cvojan
|date = January 12, 2022
}}</ref>
<ref name="post140225">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140225
|author = James Pascua
|date = January 13, 2022
}}</ref>
<ref name="message930905878356459600">{{CiteDiscord
|author = iNoMed
|date = January 12, 2022
|channel = cgol
|id = 930905878356459600
}}</ref>
<ref name="post140186">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140186
|author = C28
|date = January 12, 2022
}}</ref>
<ref name="post140193">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 140193
|author = Kalan Warusa
|date = January 12, 2022
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xp38_32acywca23z0888xooxoa6ya6aoxoox888zy17ys7}}
{{LinkCatagolue|xp38_32acysgsszwsy48kie4y84e952y47zy1771ys6a8o|patternname=46P38}} (''[[trans]]'' form; does not produce duoplet sparks)

{{Sparker|p=38|type=domino|strength=moderate|type2=reflecting duoplet|strength2=strong}}
{{Symmetry|orthogonal2}}
[[Category:Unnamed periodic objects]]
__NOTOC__

P5 diamond

2022-03-18T20:48:25Z

77551enpassant:

{{Oscillator
|name = p5 diamond
|pname = p5diamond
|f1 = Billiard table
|c = 56
|bx = 13
|by = 13
|p = 5
|m = 5
|h = 8.0
|v = 0.28
|sv = 0.28
|rulemin = B3/S23
|rulemax = B378/S0235678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3aeinq/S2aei3-ciky
|isorulemax = B2in34aejkw5aciky6-k78/S01c234-ny5678
|rle = true
|apgcode = xp5_ggmmgm41v0ccz1km0sw898b9cz01107413033
|viewerconfig = [[ GPS 5 HEIGHT 480 ]]
}}
'''p5 diamond''' is a {{period|5}} [[oscillator]] that frequently appears in 4-fold odd rotationally symmetric soups (C4_1). It has various seminatural stator variants. The form shown in the infobox is the most common form.

== Gallery ==
{|
|| {{EmbedViewer
|rle = x = 23, y = 23, rule = B3/S23
8b2ob2o$8b2obo$12bo$6b6o$5bo6b3o$5b2o3b2o3bob2o$12bo2bobobo$5b7obobo3b
o$4bo6bobobo3bob2o$4bo2b4ob2obo3bob2o$obobobo2bo3bobobobo$2obobob2o5b
2obobob2o$3bobobobo3bo2bobobobo$2obo3bob2ob4o2bo$2obo3bobobo6bo$3bo3bo
bob7o$3bobobo2bo$4b2obo3b2o3b2o$8b3o6bo$11b6o$10bo$11bob2o$10b2ob2o!
|position = center
|viewerconfig = #C [[ GPS 5 THUMBSIZE 2 ]]
|caption = A period-17 oscillator that [[phase shift]]s the p5 diamond 
}}
|| {{EmbedViewer
|rle = x = 29, y = 29, rule = B3/S23
9bo$7b5obo5b2o4b2o$bob2obo5b2o4bo2bo3bo$b2obobo2b2o3b2o2b2obo4bo$6bo4b
3o2bobo2b2o2b2o$5b2obo6bo2bobo2bo$4bobo2b6o3b2ob6o$2b3ob3o6b3o3bo5bo$b
o3bo3bo2b3o3b2obobo3bo$bobo2bobo6bo2bobobo2bob2o$2b5ob7obobo3bo2bobo$
7bo6bobobo3bobo2bo$4bo2bo2b5obobobobobobo$3bobobobo6bobobobobob2o$3bo
2bobob3o3b3obobo2bo$b2obobobobobo6bobobobo$2bobobobobobob5o2bo2bo$bo2b
obo3bobobo6bo$bobo2bo3bobob7ob5o$2obo2bobobo2bo6bobo2bobo$bo3bobob2o3b
3o2bo3bo3bo$bo5bo3b3o6b3ob3o$2b6ob2o3b6o2bobo$5bo2bobo2bo6bob2o$2b2o2b
2o2bobo2b3o4bo$2bo4bob2o2b2o3b2o2bobob2o$3bo3bo2bo4b2o5bob2obo$2b2o4b
2o5bob5o$19bo!
|position = center
|viewerconfig = #C [[ GPS 5 THUMBSIZE 2 ]]
|caption = A period-27 oscillator that phase shifts the p5 diamond 
}}
||{{EmbedViewer
|rle = x = 17, y = 17, rule = B3/S23
5b2ob2o$5b2ob2o2$5b7o$4bo7bo$3bob2o3b2obob2o$3bobo5bobob2o$2obo9bo$2o
bo9bob2o$3bo9bob2o$2obobo5bobo$2obob2o3b2obo$4bo7bo$5b7o2$7b2ob2o$7b2o
b2o!
|position = center
|viewerconfig = #C [[ GPS 5 THUMBSIZE 2 ]]
|caption = A different, much rarer p5 diamond 
}}
|}

==External links==
{{LinkCatagolue|xp5_ggmmgm41v0ccz1km0sw898b9cz01107413033}}
{{LinkCatagolue|xp17_y4gglb8bb88gzoo0u1f0v0s25kkll55oz6243s24b898ws0u1i1u1qrzy1dlllhhla9870743zy466065|patternname=p17 phase shifter}}
{{LinkCatagolue|xp27_0c84c0s22baikm88g0sa2sgwmqz0o4k69n4la222aal44raheib2i2sgzw1p59heh9lld1347gv0o0v0ehcbzgt3o70v0h0v0eic8baa9o7o9ap8gz03kk4dkn85t2ia5lkk45a2u96221zw56x3453w116245d44303213|patternname=p27 phase shifter}}

{{Symmetry|90degree}}
{{seminatural}}

Hydra

2022-03-12T01:37:16Z

77551enpassant:

{{Pattern
|name = Hydra
|pname = hydra
|c = 64226
|bx = 3999
|by = 3921
|rulemin = B3/S23
|rulemax = B3/S23
|discoverer = Oscar Cunningham
|discoveryear = 2017
|rle = true
|viewerconfig = #C [[ WIDTH 600 HEIGHT 600 ]]
}}

'''Hydra''' is a [[single-channel]] [[quadratic growth]] pattern, also called '''QGC1''', constructed by [[Oscar Cunningham]] with [[slmake]] in November {{year|2017}}.<ref name="post53089" />

Similar to the forerunner [[spiral growth]] pattern, the construction [[recipe]]s used by Hydra are stored in a compact double spiral of [[glider]]s and [[Snark]]s. However, instead of simply building a Snark at each corner, the pattern constructs a [[Scorbie Splitter]], a [[glider duplicator]] with one 0-degree and one 90-degree output. Both outputs are aimed at separate [[elbow]]s, so that each branch of the output constructs another splitter.

If there is no room at a particular location for a new splitter construction to be completed, the construction recipe is instead absorbed by guard structures at the appropriate locations near existing splitters. This allows the branching structure to be extended indefinitely, resulting in a quadratic population growth rate.

==Image gallery==
[[File:Hydra_102760448gen.png|center|frame|Overview of Hydra at generation 102760448 (98 cycles), showing the central memory storage diamond and surrounding growth matrix]]

==References==
<references>
<ref name="post53089">{{LinkForumThread
|format = ref
|p = 53089
|title = Re: Single-Channel Quadratic Growth Challenge
|author = Dave Greene
|date = November 23, 2017
}}</ref>
</references>

==External links==
{{LinkForumThread|f=2|t=3124|title=Single-Channel Quadratic Growth Challenge}}
__NOTOC__

Demonoid

2022-03-10T21:29:43Z

77551enpassant: /* Design */ fixed typo

{{Spaceship
|name = Demonoid
|pname = demonoid
|c = 27250
|bx = 55010
|by = 54964
|dir = Diagonal
|p = 438852
|s = 65c/438852
|z = 65c/438852
|discoverer = Chris Cain
|discoverer2 = Dave Greene
|discoveryear = 2015
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|synthesis = 12016
|synthesisRLE = true
|mc = true
}}
'''Demonoid''' is the first type of self-constructing diagonal spaceship in the B3/S23 rule. A small "0hd Demonoid" was completed by [[Chris Cain]] in December 2015, shortly after a much larger 10hd version constructed in November<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&p=25716#p25702|title=Re: Demonoid (diagonal Geminoid) completed!|date=December 6, 2015|work=ConwayLife.com forums|author=Chris Cain|accessdate=December 7, 2015}}</ref> in collaboration with [[Dave Greene]]. The 0hd spaceship displaces itself by 65 cells diagonally every 438,852 generations. As of 2018 it is the only case where a spaceship gun pattern was completed before the actual spaceship -- the first 0hd Demonoid was fired by a gun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=175#p25716|title=
Re: Demonoid (diagonal Geminoid) completed!|date=December 7, 2015|work=ConwayLife.com forums|author=Chris Cain|accessdate=January 4, 2016}}</ref>

The name "Demonoid" is an accidental portmanteau of "diagonal" and "Geminoid" by [[Paul Chapman]] in February 2013. "0hd" and "10hd" refer to the number of half-diagonals separating the two glider lanes in the spaceships' construction arms.

{{POTY|name=The Demonoids|year=2015|rank=3|behind=the [[Simkin glider gun]] and the [[syringe]]}}

== Design ==
Similar to the original Gemini spaceship, the Demonoid consists of two identical halves. Where the Gemini's halves are simple translations of each other, each half of the Demonoid is a glide-reflected mirror image of the other. A ''tape'' of gliders continually relays between the two halves, instructing each to construct a daughter configuration.

In the 0hd Demonoid, each half is itself made up of two identical parts. Each part consists of a [[syringe]]-based 180-degree reflector combined with an [[edge shooter]], plus a scattering of self-destruct circuitry. A cycle is completed when one of these parts is constructed ahead of the spaceship and an identical reflector/edge shooter is destroyed at the back end as soon as its construction work is done.

== Self-destruct mechanism ==
The self-destruct sequence is triggered by a glider that follows the construction recipe on a slightly different lane. The only output of the cleanup reaction is another trigger glider, which appears in the exact same location as the original trigger glider, relative to the end of the recipe stream.

== Statistics ==
Demonoids are the smallest known self-constructing or self-supporting spaceships in terms of population, but the [[bounding box]] of the [[centipede]] is about half the size of the smallest Demonoid's bounding box, and the [[waterbear]] is considerably smaller in both longest diameter and bounding box.

Demonoid variants make up the nineteenth and twentieth explicitly-constructed spaceship velocities, but as with previous self-constructing spaceships they actually represent an infinite family of related velocities. If the two halves of the Demonoid are moved N cells farther away from each other, the 0hd Demonoid travels diagonally at a speed of 65c/(438852+8N).

== Speed limit ==
Theoretically speaking, a Demonoid spaceship using the 0hd elbow-move library could be designed with any velocity slower but not equal to 17c/792 diagonally, or roughly c/47 -- much faster than the old Gemini limit of c/580<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&p=2405#p2397 |title=Re: Universal Constructor Based Spaceship|work=ConwayLife.com forums|author=Adam P. Goucher|date=May 21, 2010|accessdate=December 9, 2015}}</ref>. A 0hd elbow can be programmed to move much faster than a Gemini elbow's speed limit of one diagonal cell per coded instruction, and signals in syringe-based Herschel circuitry can be compressed to within 90 ticks of each other. However, any speed faster than 65c/438852 would require the 0hd Demonoid's circuitry and construction recipes to be completely redesigned, with a much larger total size and population in most cases.

[[Single-channel]] Demonoids have since been created that move a block to the next construction site by creating and triggering a [[seed]] for a spaceship -- e.g., a [[Cordership]] or a [[58P5H1V1]] -- and then shooting it down later with a small [[salvo]] of gliders to produce a faraway target for the [[construction arm]]. Demonoids using Corderships to move a target can approach [[c/12 diagonal|c/12]] in speed, but never quite reach that limit, and 58P5H1V1-based Demonoids can be built with any rational speed below [[c/5 diagonal|c/5]]. A [[crab]]-based [[wickstretcher]] seed discovered by [[Tanner Jacobi]] allows a Demonoid to reach any rational speed slower than [[c/4 diagonal|c/4]], which is the absolute speed limit for any diagonal spaceship in Life.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=101555#p101555 |title= One Glider Seeds|work=ConwayLife.com forums|author=Tanner Jacobi|date=August 2, 2020|accessdate=August 12, 2020}} </ref> The first such "[[Speed Demonoid]]" to use the crabstretcher in this way was made on September 18, 2020 by Dave Greene and Pavel Grankovskiy.

== History ==
The first Demonoid designs were significantly larger and more complicated than the final 10hd or 0hd models. Some early designs required all elbow operations to be made from pairs of gliders, with no singleton gliders allowed.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1006#p7339|title=Re: Geminoid Challenge|date=December 22, 2012|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref>

This allowed the gliders in each pair to be coded on a single tape, one directly after the other. However, it greatly increased the amount of timing circuitry needed. It also cut the allowable signal density in half. The signal density was already low because in 2012 the repeat rate for stable Spartan circuitry was 497 ticks or more.

A sizable improvement involved moving to a design with the two halves of the recipe encoded in series instead of interleaved. This allowed for better signal density, and also any combination of singleton gliders and glider pairs.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1006#p7447|title=Re: Geminoid Challenge|date=February 15, 2013|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref>

These early designs were all 9hd -- the two construction lanes were separated by 9 half diagonals, and a block centered between the lanes served as the elbow. This allowed all elbow operations to be used either directly or in mirror-image, which meant that gliders could be fired either left or right from the elbow, and elbow moves could be mirrored if there was limited space available and the move recipe had a larger spark on one side than on the other.

After the 9hd [[linear propagator]] was completed, it became clear that 10hd was significantly more efficient, in part because it allowed for two block elbows in slightly different positions between the construction lanes.

The 10hd and 0hd Demonoid both use a much larger number of elbow locations. A library of thousands of elbow operations allows easy switching between different elbow types, and gliders can be output on any nearby lane by stringing recipes together.

The 10hd Demonoid was the first complete self-constructing diagonal spaceship.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=150#p25401|title=Re: Demonoid (diagonal Geminoid) completed!|date=November 25, 2015|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref> Its construction recipe encoded two complete 180-degree reflector/edge shooter components, which were mostly identical to each other but had significant differences near the construction lanes. It included complex machinery that blocked the construction lanes during the half of the Demonoid's cycle when the recipe gliders intended for one circuit were passing through the other circuit's reflector.

The 0hd Demonoid improved on the 10hd model by removing the blocking mechanisms and the resulting long pause in construction. Instead, the two reflector/edge shooter components were designed to be completely identical. Each newly constructed component would first produce the trailing halves of the glider pairs in the next construction recipe. Then the same edge shooter would fire the leading halves of the glider pairs for the following construction.

In June 2017 Dave Greene completed a much simpler [[single-channel]] Demonoid using a temporary [[lossless elbow]], which displaces itself 79 cells diagonally every 1,183,842 ticks.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=45264#p45264|title=Re: Demonoid (diagonal Geminoid) completed!|date=June 26, 2017|work=ConwayLife.com forums|author=Dave Greene|accessdate=June 3, 2018}}</ref> This was an improvement in terms of design complexity, but not in terms of speed, population, or bounding box. However, all of these could be further optimized. "Scorbie's Demonoid", a single-channel Demonoid design with much more compact stable circuitry suggested by Dongook Lee, was completed in October 2018.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=60370#p64321|title=Re: Demonoid (diagonal Geminoid) completed!|date=October 3, 2018|work=ConwayLife.com forums|author=Dave Greene|accessdate=October 3, 2018}}</ref> A week later this was followed by a larger but more Hashlife-friendly version traveling 32 times faster, using somewhat different construction methods.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=64590#p64590|title=Re: Demonoid (diagonal Geminoid) completed!|date=October 10, 2018|work=ConwayLife.com forums|author=Dave Greene|accessdate=October 10, 2018}}</ref>

On September 18, {{year|2020}}, [[Pavel Grankovskiy]] constructed the [[Speed Demonoid]]. It goes at 3492022/17833792=1746011/8916896 ≈ 0.1958c, very close to [[c/5]], making it the fastest Demonoid. It uses double [[crabstretcher]]s to accelerate a self-constructing spaceship to the aforementioned speed. It can be changed to any rational speed below 2c/9. Eight days later, Speed Demonoid version 2 was completed, removing the 2c/9 barrier and enabling the creation of any Demonoid with a speed of less than c/4.

==Pattern files==
*[https://conwaylife.com/patterns/demonoid.mc Demonoid]
*[https://conwaylife.com/patterns/demonoid10hd.mc Demonoid 10hd]

== See also ==
* [[Orthogonoid]]
* [[Gemini]]
* [[Caterloopillar]]
* [[Centipede]]
* [[Waterbear]]
* [[Half-baked knightship]]
* [[Replicator]]

== References ==
<references />

==External links==
{{LinkLexicon|lex_d.htm#demonoid}}

[[Category:Glide symmetric spaceships]]
[[Category:Non-monotonic_spaceships]]

Block

2022-03-10T21:24:44Z

77551enpassant: /* Commonness */ added period

{{Stilllife
|name = Block
|pname = block
|c = 4
|bx = 2
|by = 2
|fc = 0.0
|discoverer = John Conway
|discoveryear = 1969
|rulemin = B/S3
|rulemax = B345678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]], [[Maze]]
|isorulemin = B/S3a
|isorulemax = B1e2-a345678/S012345678
|synthesis = 2
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs4_33
|pentadecathlonid = 4.1
}}
'''Block''' is an extremely well-known and common [[still life]] that was found by [[John Conway]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> In terms of its {{slcells|4}} [[cell]]s it is tied with [[tub]] as the smallest still life, and in terms of its 2×2 [[bounding box]] it is the outright smallest. It is also the only known still life that is a [[polyomino]], and the only finite [[strict still life]] where all living cells have three neighbors. Its small size, [[#Use as an eater|ability to act as an eater]], and simple [[glider syntheses]] make it extremely useful in the construction of larger patterns.

The block was one of the patterns described in the original 1970 article by [[Martin Gardner]] that introduced the [[Game of Life]] to the world.

== Use in higher still lifes ==
Blocks serve useful in the construction of larger still lifes. Due to its high density, orthogonal and diagonal connections (like those seen in [[ship-tie]]) would overpopulate any present cells, preventing any patterns with this arrangement from being useful in a still life (this reaction can instead be used for oscillators such as [[beacon]] and variants of [[star]]). As such, its uses are limited to acting as an [[induction coil]].

Given the high symmetry of the block (the highest a pattern can have on {4,4}), cis-, trans- and other isomeric variants only arise if the object the block is stabilising is itself of a sufficiently low symmetry.

Examples of known still lifes which use the block as an induction coil are as follows:
* [[Block on table]] (10)
* [[Block on cap]] (12)
* [[Block on cover]] (12)
* [[Cis-block on long bookend]] (12)
* [[Trans-block on long bookend]] (12)
* [[Block on dock]] (14)
* [[Eater 2]] (19)
* [[Mango with block on dock]] (19)

Blocks can also be used to stabilise certain oscillators in a non-catalytic fashion, with examples as follows:
* [[Block on griddle]] (p2)
* [[Blocks on griddle]] (p2)
* [[Candlefrobra]] (p3)
* [[Trans-block on long hook eating tub]] (p3)

== Uses in catalysis ==
The block sees a diverse array of uses in larger patterns. For example, [[glider-block cycle|it can work]] as a [[reflector]] for two gliders via the [[interchange]] synthesis, as can be seen in [[106P135]].

=== Use as an eater ===
There are multiple ways in which the block may act as an [[eater]]. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a [[rock]], except through induction, such as the [[p47 pre-pulsar shuttle]].). Oscillators such as [[blocker]], [[p56 B-heptomino shuttle]], [[queen bee shuttle]], [[twin bees shuttle]] and [[unix]] showcase mechanisms which leave a [[pre-block]] or a [[hook]], while the mechanisms seen in [[Coe's p8]], [[eater 5]] and [[octagon 4]] leave a [[grin]]. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in [[37P7.1]]. It has been seen eating [[mango]]s, [[boat]]s, [[loaf|loaves]], and [[beehive]]s.

Some more complex eaters can be based on the block as well. [[Eater 2]] is a construction allowing a block to eat [[glider]]s: while the collision would normally destroy both, the addition of further still life(s) or [[inductee]]s allows the remaining three-cell [[spark]] to regenerate into a block.

Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]], as described above. Several larger oscillators including [[p54 shuttle]], [[78P70]], [[two blockers hassling R-pentomino]] and [[Achim's p144]] are examples. A particular reaction with a [[B-heptomino]] is commonly used in the construction of [[Herschel track]]s.

== Blockic constellation ==
A '''blockic constellation''' is a [[constellation]] consisting entirely of blocks. It's possible to arrange blocks in [[seed|a way]] that can be triggered by a single glider to produce any glider constructible pattern.{{citation needed}}

== Block arrays ==
[[Pseudo still life]]s exist consisting of an arbitrary array of blocks placed next to each other, which may be referred to as '''block [[agar]]s'''. On December 3, {{year|2015}}, [[Martin Grant]] found a method of constructing a 3×''n'' array via [[glider synthesis]],<ref name="post25637" /> and on May 6, {{year|2020}}, [[Goldtiger997]] found a method of constructing a 4×''n'' array.<ref name="post96210" />

== Commonness ==
The block is the '''most common object''' in the [[Catagolue]] [[census]], comprising 30.9% of all object occurrences.

In [[Achim Flammenkamp's census]] it occurred almost twice as often as [[beehive]], the next most common still life. However, the blinker is slightly more common than the block in Achim's census, unlike on Catagolue. This can be explained by Herschels, which have a lot of empty space to evolve in 16×16 soups but not on a torus, leaving two blocks behind.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>

=== Occurrence ===
The block is the most common still life (and indeed object) that occurs as a result of [[soup|random starting patterns]].

The chance of a block in a specific location in an infinite random soup is approximately 1 in 473. This number is the frequency of on cells (0.0287) divided by the average object size (4.388) times the chance that a particular object will be a block (0.323). As blocks have 8-way symmetry, there is no symmetry factor to take into account. This number is helpful in determining how often transparent blocks occur; transparent blocks are twice as common as transparent blinkers, almost four times as common as transparent beehives, and more than twenty times as common as anything else.

== [[Glider synthesis]] ==
The block is the most common object produced by [[2-glider collision]]s; three head-on instances and three perpendicular ones create a clean block, and there are also other examples that produce solely blocks (in the form of bi-block, half-blockade, four skewed blocks or blockade).

== See also ==
* [[Bi-block]]
* [[Blockade]]
* [[Bricklayer]]
* [[Blockstacker]]

== References ==
<references>
<ref name="post25637">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 25637
|author = Martin Grant
|date = December 3, 2015
}}</ref>
<ref name="post96210">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 96210
|author = Goldtiger997
|date = May 6, 2020
}}</ref>
</references>

== External links ==
{{LinkLexicon|lex_b.htm#block}}
{{LinkLexicon|lex_b.htm#blockic|patternname=Blockic}}
{{LinkCatagolue|xs4_33}}
{{LinkNiemiec|p1.htm#p1-4|patternname=The 2 four-bit still-lifes}}
* [http://www.ibiblio.org/lifepatterns/october1970.html The fantastic combinations of John Conway's new solitaire game "life"] by Martin Gardner
{{LinkForumThread|f=2|t=1065|title=Blockic splitters}}
{{LinkForumThread|f=2|t=1134|title=Blockic Seeds}}

[[Category:Eaters]]
{{Symmetry|full}}

Overweight spaceship

2022-03-10T21:17:28Z

77551enpassant:

{{Pattern
|name = Overweight spaceship
|pname = 7wss
|c = 15
|bx = 8
|by = 5
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B368/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3aij/S2eik3aijnr
|isorulemax = B2n34-in5-ar67e8/S1e234-aw5-ijy6-kn7e
|plaintext = true
|rle = true
|synthesis = 13
|synthesisRLE = true
|viewerconfig = #C [[ ZOOM 24 TRACKLOOP 8 -1/2 0 THUMBSIZE 2 GPS 4 HEIGHT 500 ]]
}}
An '''overweight spaceship''' (or '''OWSS''' for short) is a would-be [[spaceship]] similar to the [[lightweight spaceship]], [[middleweight spaceship]] and [[heavyweight spaceship]], but longer. On its own an overweight spaceship is unstable. While the latter two [[xWSS]]es produce [[belly spark]]s that would die off, an overweight spaceship produces an [[egg]] that does not vanish but interferes with the body.

== Naming ==
As there are an infinite number of overweight spaceships, it becomes neccessary to distinguish between sizes. This is often done by assigning each overweight spaceship a number corresponding to the length of its "line" section in its less dense phase. As such, the smallest overweight spaceship is referred to as the "7WSS".

In this naming system, "4WSS", "5WSS" and "6WSS" would correspond to the lightweight, middleweight and heavyweight spaceships (although using such terminology is never recommended), and "3WSS" to an [[underweight spaceship]] ([[roteightor]] segment).

The length of a spaceship's belly "spark" can be seen to be this value minus four; a 7WSS's belly "spark" is three cells in length.

== As a spaceship component ==
An overweight spaceship can be escorted by true spaceships to form a [[flotilla]]. [[Standard spaceship flotilla#Two standard spaceships, one overweight spaceship|There are several possibilities]] for escorting one overweight spaceship via two standard spaceships.

For an OWSS with a top "spark" length over 4, the minimal escort size difference is 4, as shown below. It is also possible to stabilize an OWSS with more OWSSes, which then have to be stabilized by more xWSSes. Some sufficiently large extensions like this can be seen as a stabilisation of a period-4, one-dimensional [[agar]], similar to a [[greyship]] (although ultimately lacking the 50% density requirement to be truly classified as one).<ref>https://conwaylife.com/forums/viewtopic.php?f=7&t=2036&p=141393#p141393</ref>

{| style="margin:auto"
|{{EmbedViewer
|pname = lwsson7wssonlwss1
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 12 ]]
|caption = 7WSS with escorts 
|apgcode = xq4_6ruc0sur6x6ruczy1377
}}
|{{EmbedViewer
|pname = lwsson8wssonlwss1
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 12 ]]
|caption = 8WSS with escorts 
|apgcode = xq4_gcso0uvvy0gcsoz131w37d6x131
}}
||{{EmbedViewer
|pname = owssflotilla
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 12 ]]
|caption = Overweight spaceship supported by more overweight spaceships 
|apgcode = xq4_y1g0gy0o4040101uxo4040g0gzs20iy0vxvy3vxvy3vxs20iz111w2447xvgg8y0vxvgg802447x111zyd1223
}}
|}

== [[Glider synthesis]] ==
Many lengths of overweight spaceship can be constructed by means of [[glider synthesis]].<ref name="post77160" /> Recent syntheses are collected in the <tt>xq4</tt> synthesis listed in [[Catagolue]];<ref>{{cite web|url=https://catagolue.hatsya.com/census/b3s23/synthesis-costs/xq4|title=xq4 census|work=Catagolue|accessdate=October 28, 2019}}</ref> a number of older recipes can be found in [[Mark Niemiec]]'s synthesis database.<ref>{{cite web|url=https://conwaylife.com/ref/mniemiec/flotilla.htm#ss-owss|title=Overweight spaceship flotillae|work=Mark Niemiec's database|author=Mark Niemiec|accessdate=October 28, 2019}}</ref>

== In other rules ==
The [[non-totalistic rule]] FattyLife (B3-n4nt5qr6i/S23) is specifically tailored to support the overweight spaceship with spark length 3, making it [https://catagolue.hatsya.com/object/xq8_27deeee6/b3-n4nt5qr6is23 a p8 spaceship.]

== References ==
<references>
<ref name="post77160">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 77160
|author = Martin Grant
|date = June 5, 2019
}}</ref>
</references>

== External links ==
{{LinkLexicon|lex_o.htm#owss}}

[[Category:XWSS variants]]
__NOTOC__

Beethoven

2022-03-10T18:35:08Z

77551enpassant:

{{Oscillator
|name = Beethoven
|pname = beethoven
|type = constellation
|c = 15
|bx = 9
|by = 7
|p = 2
|m = 2
|h = 4.0
|v = 0.24
|sv = 0.24
|rulemin = B3/S2
|rulemax = B34678/S02345678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3i/S2cik
|isorulemax = B2cik345-y678/S01c2345678
|synthesis = 3
|rle = true
|plaintext = true
|apgcode = xp2_2552gggz4aa4
|viewerconfig = #C [[ GPS 2 ]]
}}
'''Beethoven'''<ref name="post63897" /> is a common [[constellation]] of two [[beehive]]s and a [[blinker]], and is the most common [[composer]].

== Etymology ==
Beethoven was named due to text-correction incorrectly changing "beehive" into Beethoven, which was in turn misinterpreted as the name of the constellation.<ref>https://conwaylife.com/forums/viewtopic.php?t=&p=63897#p63828</ref>

== Occurrence ==
One of its [[predecessor]]s is a partially consumed [[traffic light]] predecessor, which can be seen in some traffic light hasslers.<ref name="post84455" />

{{EmbedViewer
|position = center
|rle = 2o3bo$2o2b3o!
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 25 GPS 5 PAUSE 2 LOOP 30 ]]
|caption = A Beethoven forming from a [[t-tetromino]] and a block }}

== See also ==
* [[Honey farm]]
* [[Pulsar]]

== References ==
<references>
<ref name="post63897">{{LinkForumThread
|format = ref
|title = Re: Thread For Your Useless Discoveries
|p = 63897
|author = Hdjensofjfnen
|date = September 20, 2018
}}</ref>
<ref name="post84455">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discoveries Thread
|p = 84455
|author = Entity Valkyrie
|date = October 23, 2019
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xp2_2552gggz4aa4|type=pseudo-object}}

{{Symmetry|orthogonal2}}

Replicator

2022-03-04T18:16:23Z

77551enpassant: fixed type

{{Glossary}}
{{For|the cellular automaton of the same name|OCA:Replicator}}
{{move|General replicator|(there's no split template) this page would deal with the general concept of a replicator, and we'd have a "parity replicator" page for describing the common, sawtooth-like replicators}}
A '''replicator''' is any pattern that produces an arbitrary number of copies of itself. There is currently no precise definition.

== Common definitions ==
While there exist many conflicting definitions as to what a replicator is, most patterns classified as replicators tend to satisfy the following properties:
* Replicators are bound by a "parity" rule, in which the replicator will always revert to having a certain number of copies after a given integer multiple of a perfect power, usually 2, although some replicators based on higher powers exist. In effect, replicators must also be [[sawtooth]]s. Replicators which do not revert in such a fashion are usually considered to be [[wickstretcher]]s or [[spacefiller]]s, or may belong to another class entirely outside of these three.
* In addition, replicators are also generally required to leave no debris, especially if any such debris would interfere with further replication. Patterns which do leave behind objects are referred to as "dirty" replicators, and many stop replicating after an amount of time due to the chaos created. Debris also prevents replicators from acting as a sawtooth.

There are further ways in which a replicator can be defined, such as strength, which measures its power to be a [[unit cell]].

== Common classifications ==
One common way to classify different types of replicators is "dimensionality". This gives two main classes of replicator:
* one-dimensional replicators, which replicate along a line and behave as linear sawtooths,
* two-dimensional replicators, which replicate across the plane and behave as quadratic sawtooths.

These two cases are the most-commonly seen on the standard 2D [[square tiling]]; different tilings can allow for different replicator dimensionality classifications, as can different [[neighbourhood]]s. Even the square tiling harbors replicators which diverge from this classification, such as a three-way replicator which traces out a Sierpinski triangle shape rather than a line or square;<ref name="post54221" /> these could be considered log2(3)-dimensional. Such replicators have also been sighted on the [[hexagonal tiling]].<ref name="post73811" />

== Examples in Life ==

=== Elementary replicators ===
As of February 2022, no finite elementary replicators are known in Life, however there are patterns which can be considered "failed" replicators which are incapable of expanding infinitely:

* The [[pre-pulsar]] produces an exact copy of itself after 15 generations. However, these duplicated copies then react with each other to form the [[pulsar]], instead of replicating again. The pre-pulsar is therefore generally not considered a true replicator. The skewed variant of the pre-pulsar, and other pre-pulsar-like patterns of consistent spacing, also copy themselves after 15 generations, and also cannot replicate infinitely.
* The [[pi-heptomino]] sequence eventually produces two pi-heptominos to each side, however these are rapidly attacked by the rest of the explosion and are therefore denied further evolution.

=== Construction-based replicators ===
In 1982, Berlekamp, Conway, and Guy proved that Life supports universal computation and universal construction, and thus that there exist self-replicating machines in Life.<ref>{{Citation|last1=Berlekamp|first1=Elwyn R.|last2=Conway|first2=John H.|last3=Guy|first3=Richard K.|year=2004|volume=4|edition=2nd|title=Winning Ways for Your Mathematical Plays|pages=927-961}}</ref>

Prior to 2013, no explicit examples of construction-based replicators in Life were known. However, on November 23, 2013, [[Dave Greene]] constructed [[linear propagator|an explicit example]] by feeding a universal [[salvo|slow-salvo]] constructor (without any underlying universal computer) a tape of gliders that functions as a recipe for the constructor's own construction.<ref>{{Cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1006&p=9901#p9901|title=Re: Geminoid Challenge|author=Dave Greene|date=November 23, 2013|accessdate=November 24, 2013}}</ref> In 2018, the emergence of the [[0E0P metacell]] enabled the construction of [[B3/S23]] replicators of every class in Okanishi's classification (explained below).

== Examples in other rules ==
Replicators occur naturally in some [[cellular automata]].<ref>{{cite web|url=https://www.ics.uci.edu/~eppstein/ca/replicators/|title=Cellular Automata: Replicators |author=David Eppstein|accessdate=February 17, 2016}}</ref> Possibly the most well-known example in a Life-like cellular automaton is the simple replicator in {{rl|HighLife}} (B36/S23), which repeatedly copies itself along a diagonal line every 12 generations according to a one-dimensional parity rule (commonly cited as Wolfram [[Rule 90]], however a closer analysis puts Rule 6, range 1/2 as a more appropiate classification).

{| style="margin-left:auto;margin-right:auto;"
| [[File:Replicator.png|frame|left|Replicator in HighLife {{JavaRLE|replicator|brief}}]]
| [[File:Replicator animation.gif|framed|left|Replication sequence]]
|}

Other rules with replicators include [[tHighLife]].

Parity-rule replicators are common in B1 rules. For example, the pattern consisting of a single alive [[cell]] is a replicator in many B1 rules such as {{rl|Gnarl}} (B1/S1). In the parity-rule Life-like cellular automata {{rl|Replicator}} rule (B1357/S1357) and {{rl|Fredkin}} rule (B1357/S02468), every pattern is a replicator.

Replicators can alternatively be used to create [[spaceship]]s by using objects to delete one replicated part, such as HighLife's [[bomber]] and the [[pre-pulsar spaceship]] in normal Life. [[Shuttle]]s can also be created by subduing replicators, as seen in [[Pre-pulsar shuttle 28]] and [[Pre-pulsar shuttle 29]].

While the vast majority of one-dimensional replicators follow Rule 90, ones bound by other rules are known, such as [[Rule 150]]<ref name="post51593" /><ref name="post61459" /> and [http://www.wolframalpha.com/input/?i=rule+1208925819614629174771760,+range+3 Rule 1208925819614629174771760].<ref name="post61463" /> However, the last is not a sawtooth.

Two-dimensional replicators will either be a square (if the fastest travelling corner of the mass of replicators is moving either orthogonally or diagonally), a rectangle (if some of the replicators are moving in an oblique direction), or a rhombus (if some of the replicators are moving faster than the others in a certain direction).

== Construction-based replicators ==
John von Neumann proved the existence of a pattern of about 200,000 cells that self-replicates in a 29-state von Neumann neighbourhood cellular automaton.<ref>{{Citation|last=Gardner|first=Martin|year=1983|publisher=W.H. Freeman|title=Wheels, Life, and Other Mathematical Amusements|pages=226-227}}</ref> In particular, the cellular automaton supports both [[universal computer|universal computation]] (by simulating a [[Turing machine]]) and [[universal constructor|universal construction]] and so a [[universal computer]], connected to a universal constructor, would self-replicate when given a blueprint of itself.

A universal computer and constructor is likely to exist also for {{rl|B35/S236}} but no specific examples have been constructed.<ref>{{Cite web|url=http://www.ics.uci.edu/~eppstein/ca/b35s236/|title=B35/S236|author=David Eppstein|accessdate=February 9, 2016}}</ref> Therefore, replicators presumably exist in that rule, as in many other rules that appear to meet the requirements for construction universality.

== Classifying replicators ==
=== Okanishi's classifications ===
A classification scheme for two-dimensional replicators was proposed by [[Luka Okanishi]] in December 2016:<ref name="thread2648" />
* Successful replicators:
** Class S (strict); the replicated patterns appears 1, 2, 4, 4, 4, 8, 16, 8, 4, 8, ... times ({{OEIS|A173531}}).
** Class R (rectangular); same as above, although all copies of the replicator must be present.
** Class Q (quadruple); the replicated pattern appears 1, 4, 4, 16, 4, 16, 16, 64, 4, 16, ... times ({{OEIS|A102376}}).
** Class X (fourfold XOR): 1, 4, 8, 16, 16, 32, 32, 64, 32, 64, ... times ({{OEIS|A189007}}).
** Class U (unusual): all others.
* Failed replicators:
** Class A (almost)
** Class D (dirty)
** Class F (spacefilling)

=== XOR-based classifications ===
An alternative classification for replicators was proposed in November 2018, based on underlying XOR rules.<ref name="post65242" /> This classification was soon abandoned with the widening support of [[outer-totalistic]] rules of higher ranges, which revealed many more replication habits which did not fit into this system.

== See also ==
* [[Gemini]]
* [[Linear propagator]]

== References ==
<references>
<ref name="post51593">{{LinkForumThread
|format = ref
|title = Re: Thread for basic non-CGOL questions
|p = 51593
|author = Connor Steppie
|date = October 4, 2017
}}</ref>
<ref name="post61459">{{LinkForumThread
|format = ref
|title = Replicators and other patterns that simulate even 1D rules
|p = 61459
|author = Connor Steppie
|date = June 29, 2018
}}</ref>
<ref name="post61463">{{LinkForumThread
|format = ref
|title = Re: Replicators that simulate even 1D rules
|p = 61463
|author = AforAmpere
|date = June 29, 2018
}}</ref>
<ref name="post54221">{{LinkForumThread
|format = ref
|title = Re: 2D Replicator Classes
|p = 54221
|author = LaundryPizza03
|date = December 25, 2017
}}</ref>
<ref name="post73811">{{LinkForumThread
|format = ref
|title = Re: 2D Replicator Classes
|p = 73811
|author = AlephAlpha
|date = March 24, 2019
}}</ref>
<ref name="thread2648">{{LinkForumThread
|f = 11
|t = 2648
|title = 2D Replicator Classes
|author = [[Luka Okanishi]] (AbhpzTa)
|format = ref
|date = December 23, 2016
}}</ref>
<ref name="post65242">{{LinkForumThread
|format = ref
|title = New method of classifying two-dimensional replicators
|p = 65242
|author = Connor Steppie
|date = November 1, 2018
}}</ref>
</references>

== External links ==
{{LinkWikipedia|Replicator_(cellular_automaton)}}
{{LinkLexicon|lex_r.htm#replicator}}