LifeWiki - User contributions [en]

User:Squareroot12621

2026-07-29T22:27:04Z

Squareroot12621: Add PETS section

I'm squareroot12621, an irrational number. I've been on [https://conwaylife.com/forums/ the forums] since 2022, but I didn't get an account on LifeWiki until 2024.

Also, in case you're wondering, {{sqrt|12621}} is about 112.343.

== squareroot12621's Rules ==
; [[Rule:Supercomputer|Supercomputer]] ([https://conwaylife.com/forums/viewtopic.php?f=12&t=5647&p=186853#p186417 thread])
: A 9-state circuitry rule, with a display state. A working computer was in progress.
; [[Rule:LogicGates|LogicGates]]
: A 48-state circuitry rule with just wires, AND gates, and NOT gates.

== Conway's Story Mode ==
'''Conway's Story Mode''' (CSM) is an attempt to make Conway's Game of Life more accessible to beginners. The original thread can be found [https://conwaylife.com/forums/viewtopic.php?f=7&t=6053 here], and some drafts for CSM can be found in the subpages below.

[[User:Squareroot12621/CSM]]
:[[User:Squareroot12621/CSM/Lessons]]

== PETS ==
'''PETS''' (short for '''phpBB Enhanced Tagging System''') is a widget that lets you add and search for invisible tags in forum posts. You can get it [https://irrationalplayground.com/projects/pets here].

Gun

2026-07-26T13:40:55Z

Squareroot12621: Forgot to remove it from the text as well

{{Glossary}}
[[Image:Gosperglidergun.gif|framed|right|The first known gun, the [[Gosper glider gun]]]]
A '''gun''' is a stationary pattern that repeatedly emits [[spaceship]]s (or [[rake]]s) forever. By far the most common type of guns are '''[[glider gun]]s''', which emit [[glider]]s (the most well-known of which is the [[Gosper glider gun]]); however, guns that emit spaceships of many other speeds, including [[c/2 orthogonal]], [[2c/5 orthogonal]], and [[c/12 diagonal]], have also been created.

==History==
The first gun to be discovered, the [[Gosper glider gun]], was found by [[Bill Gosper]] in {{year|1970}}, being the first known pattern in [[Conway's Game of Life]] to exhibit [[infinite growth]]. Since then, many guns have been constructed with various periods and that fire spaceships of various speeds. Due to simple [[glider synthesis|glider syntheses]] of the [[Types_of_spaceships#Standard_spaceship|standard spaceships]] many c/2 spaceship guns are known. The first gun that did not fire gliders or c/2 spaceships was a '''Cordergun''' (a gun that fires [[Cordership]]s) constructed by [[Jason Summers]] in July, {{year|1999}}<ref name="entropymine_status" /> based on a synthesis of a variation of the [[7-engine Cordership]] by [[Stephen Silver]]. In March, {{year|2003}} [[Noam Elkies]] completed the synthesis of [[60P5H2V0]] which [[Dave Greene]] used to construct the [[P416_60P5H2V0_gun|first 2c/5 spaceship gun]] in April of the same year.

In July, {{year|2010}} Dave Greene constructed a few guns for a [[gemini|geminoid]] spaceship.<ref name="golnews201007" /> These are the first guns that shoot obliquely-traveling spaceships and at that time were the largest patterns constructed in Life, in terms of their bounding boxes.

On February 17, {{year|2013}} [[Josh Ball]] discovered a simple [[c/7 orthogonal]] spaceship, [[loafer]]. Adam P. Goucher found a synthesis for the loafer later that day, allowing the construction of c/7 orthogonal spaceship guns.<ref name="post7466" />

During March {{year|2016}} the [[copperhead]] spaceship was discovered, with a glider synthesis and several guns following suit.<ref name="post28101" />

In {{year|2019}} and {{year|2020}} guns were produced for the spaceships [[46P4H1V0]],<ref name="post84423" /> [[spider]],<ref name="post88186" /> and [[58P5H1V1]],<ref name="post97489" /> of speeds [[c/4 orthogonal]], [[c/5 orthogonal]], and [[c/5 diagonal]] respectively.

==Barrels==
{{main|Barrel}}
The barrel of a gun (or rake) is a path along which spaceships travel. For example, a double-barrelled glider gun is a gun that emits two glider streams.

==Pseudo-period guns==
A '''pseudo-[[period]] gun''' (as opposed to a [[true-period]] gun) is a gun that emits a period n stream of spaceships (or rakes) via a mechanism that oscillates with a period different from n -- this period will necessarily be a multiple of n. Pseudo period n glider guns are known to exist for all periods greater than or equal to 14, with smaller periods being impossible. The first pseudo period 14 gun was built by [[Dietrich Leithner]] in {{year|1995}}.

==True-period guns==
A '''true-period gun''' (as opposed to a [[#Pseudo-period guns|pseudo-period gun]]) is a gun that emits a period n stream of spaceships (or rakes) via a mechanism that oscillates with period equal to n. True period n guns are known to exist for all possible periods except for 17, 19, 23, 26, 29, 31, and 38. Credits for gun periods below 62 are as follows:

<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr>
{| class="wikitable sortable"
|-
! Period
! Discoverer
! Year of discovery
|-
! [[Period-14 glider gun|14]]
| [[Matthias Merzenich]] and [[James Pascua]]
| {{year|2025}}
|-
! [[Period-15 glider gun|15]]
| [[Period1GliderGun]] and [[Carson Cheng]]
| {{year|2024}}
|-
! [[Period-16 glider gun|16]]
| [[Period1GliderGun]] and [[Nora Brown]]
| {{year|2024}}
|-
! [[Period-18 glider gun|18]]
| [[400spartans]], Period1GliderGun, and [[David Raucci]]
| {{year|2025}}
|-
! [[Period-20 glider gun|20]]
| Matthias Merzenich and [[Noam Elkies]]
| {{year|2013}}
|-
! [[Period-21 glider gun|21]]
| [[Tanner Jacobi]] and David Raucci
| {{year|2021}}
|-
! [[Period-22 glider gun|22]]
| [[David Eppstein]] and [[Jason Summers]]
| {{year|2000}}
|-
! [[Period-24 glider gun|24]]
| Noam Elkies
| {{year|1997}}
|-
! [[period-25 glider gun|25]]
| [[Mitchell Riley]]
| {{year|2022}}
|-
! [[Period-27 glider gun|27]]
| David Raucci and [[goldenratio]]
| {{year|2022}}
|-
! [[Period-28 glider gun|28]]
| Matthias Merzenich and [[Paul Callahan]]
| {{year|2020}}
|-
! [[Gosper_glider_gun|30]]
| [[Bill Gosper]]
| {{year|1970}}
|-
! [[Period-32 glider gun|32]]
| Matthias Merzenich, David Raucci, [[praosylen]], [[wwei23]], and Noam Elkies
| {{year|2021}}
|-
! [[Period-33 glider gun|33]]
| [[Arie Paap]] and Matthias Merzenich
| {{year|2018}}
|-
! [[Period-34 glider gun|34]]
| [[Nora Brown]]
| {{year|2022}}
|-
! [[Period-35 glider gun|35]]
| Matthias Merzenich, [[iNoMed]], and [[hotcrystal0]]
| {{year|2024}}
|-
! [[Period-36 glider gun|36]]
| Jason Summers
| {{year|2004}}
|-
! [[Period-37 glider gun|37]]
| iNoMed, goldenratio, and [[Luke Kiernan]]
| {{year|2022}}
|-
! [[Period-39 glider gun|39]]
| [[Caleb R. Hilton]]
| {{year|2026}}
|-
! [[Period-40 glider gun|40]]
| [[Adam P. Goucher]], Jason Summers, and Matthias Merzenich
| {{year|2013}}
|-
! [[Period-41 glider gun|41]]
| iNoMed, Matthias Merzenich, [[May13]], David Raucci, and Nora Brown
| {{year|2023}}
|-
! [[Period-42 glider gun|42]]
| Tanner Jacobi and David Raucci
| {{year|2021}}
|-
! [[Period-43 glider gun|43]]
| Nora Brown
| {{year|2022}}
|-
! [[p44_pi-heptomino_hassler|44]]
| [[David Buckingham]]
| {{year|1992}}
|-
! [[period-45_glider_gun|45]]
| Matthias Merzenich
| {{year|2010}}
|-
! [[new_gun_1|46]]
| Bill Gosper
| {{year|1971}}
|-
! [[Period-47 glider gun|47]]
| [[Entity Valkyrie]] and iNoMed
| {{year|2024}}
|-
! [[Period-48 glider gun|48]]
| Noam Elkies
| {{year|1997}}
|-
! [[hotcrystal0_reaction#Generalized_form|49]]
| Tanner Jacobi, wwei23, and hotcrystal0
| {{year|2021}}
|-
! [[Period-50 glider gun|50]]
| [[Dean Hickerson]] and Noam Elkies
| {{year|1996}}
|-
! [[hotcrystal0_reaction#Generalized_form|51]]
| [[Luka Okanishi]], wwei23, and hotcrystal0
| {{year|2021}}
|-
! [[Period-52 glider gun|52]]
| [[Dave Greene]], [[Chris Cain]], Matthias Merzenich and Adam P. Goucher
| {{year|2018}}
|-
! [[Period-53 glider gun|53]]
| iNoMed and goldenratio
| {{year|2024}}
|-
! [[Quetzal#Quetzal-54|54]]
| [[Dietrich Leithner]]
| {{year|1998}}
|-
! [[Quetzal#Quetzal-55|55]]
| [[Stephen Silver]]
| {{year|1998}}
|-
! [[Quetzal#Quetzal-56|56]]
| Dietrich Leithner
| {{year|1998}}
|-
! [[Quetzal#Quetzal-57|57]]
| Matthias Merzenich
| {{year|2016}}
|-
! [[Quetzal#Quetzal-58|58]]
| [[Maia Karpovich]], Matthias Merzenich, and Chris Cain
| {{year|2016}}
|-
! [[period-59_glider_gun|59]]
| Adam P. Goucher and Jason Summers
| {{year|2009}}
|-
! [[period-60_glider_gun|60]]
| Bill Gosper
| {{year|1970}}
|-
! [[Period-61 glider gun|61]]
| Luka Okanishi
| {{year|2016}}
|}

==Smallest guns by area of bounding box==

A collection of smallest guns by bounding box area was originally created and maintained by [[Dietrich Leithner]] and [[Peter Rott]], before [[Jason Summers]] took over the maintenance. The p14-999 collection had subsequently evolved into a Git repository led by [[Chris Cain]]. Currently, the collection is maintained collaboratively at Catagolue's glider-synthesis database.

* [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/gun Current database] (Catagolue)
* [https://github.com/ceebo/glider_guns/ older repository] maintained by Chris Cain (only p14-1024)
* [https://entropymine.com/jason/life/#collections older version] maintained by Jason Summers (includes some periods in the range p1000-9999).

Note that this classification of smallest is of dubious utility: see [[Pointless optimisation game]] for more details.

==Guns in Life-like cellular automata==
Due to the existence of some small spaceships in [[Life-like cellular automata]] with birth at two live neighbours (B2), many low-period spaceship guns have been found using tools such as [[WinLifeSearch]]. In contrast, there are very few outer-totalistic rules without B2 (and B0) that are known to contain guns. The following is a list of outer-totalistic rules with neither B0 nor B2 that have known guns:
{| style="width:100%" |
|-
| valign="top" width="50%" |
* Glider guns<ref name="thread1071" />
** B3/S23 ([[Conway's Game of Life]])
** B3/S236
** B3/S2367
** B3/S23678
** B3/S2368
** B3/S237
** B3/S2378
** B3/S238 ({{rl|EightLife}})
** B36/S23 ({{rl|HighLife}})
** B36/S237
** B36/S2378
** B36/S238
** B368/S23
** B368/S238 ({{rl|LowDeath}})
** B37/S23 ({{rl|DryLife}})
** B37/S236
** B37/S237
** B37/S238
** B37/S2378
** B378/S23
** B378/S237
** B378/S2378
** B378/S238
** B38/S236
** B38/S2367
** B38/S23678
** B38/S2368
** B38/S23 ({{rl|Pedestrian Life}})
** B38/S237
** B38/S2378
** B38/S238 ({{rl|HoneyLife}})
| valign="top" |
* Other guns
** B3/S23 ([[Conway's Game of Life]])
** B3/S237
** B3/S2378
** B3/S238 ({{rl|EightLife}})
** B3/S345
** {{rl|B35/S236}}
** B357/S238 ({{rl|Pseudo Life}})
** B358/S236
** B36/S125 ({{rl|2x2}})
** B36/S23 ({{rl|HighLife}})
** B36/S237
** B36/S2378
** B36/S238
** B368/S23
** B368/S238 ({{rl|LowDeath}})
** B36/S245 ({{rl|sqrt replicator rule}})
** B368/S245 ({{rl|Move}})
** B368/S12578
** B3678/S34678 ({{rl|Day & Night}})
** B37/S23 ({{rl|DryLife}})
** B37/S238
** B378/S23
** B378/S238
** B38/S23 ({{rl|Pedestrian Life}})
** B38/S237
** B38/S2378
** B38/S238 ({{rl|HoneyLife}})
** B38/S345
|}

==See also==
* {{CategoryLink|Guns}}
* [[Dieter and Peter's glider gun collection]]
* [[LifeWiki:Game_of_Life_Status_page#Glider_gun_true-periods|Glider gun true-periods status table]]
* [[LifeWiki:Game_of_Life_Status_page#Gun_pseudo-periods|Gun pseudo-periods status table]]
* [[Quetzal]]

==References==
<references>
<ref name="entropymine_status">{{cite web|url=http://entropymine.com/jason/life/status.html |title=Game of Life Status page |accessdate=October 15, 2010}}</ref>
<ref name="golnews201007">{{LinkGoLNews|2010/07/gemini_guns_1.html|title=Gemini guns|date=July 30, 2010|author=Adam P. Goucher}}</ref>
<ref name="thread1071">{{LinkForumThread|format=ref|f=11|t=1071|title=Guns in Life-like cellular automata|author=[[Matthias Merzenich]]|date=April 11, 2013}}</ref>
<ref name="post7466">{{LinkForumThread
|format = ref
|title = Re: c/7 orthogonal spaceships
|p = 7466
|author = Shannon Omick
|date = February 18, 2013
}}</ref>
<ref name="post28101">{{LinkForumThread
|format = ref
|title = Re: is this c/10 spaceship known?
|p = 28101
|author = Alexey Nigin
|date = March 6, 2016
}}</ref>
<ref name="post84423">{{LinkForumThread
|format = ref
|title = Re: Stable signal converters
|p = 84423
|author = Goldtiger997
|date = October 22, 2019
}}</ref>
<ref name="post88186">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 88186
|author = Entity Valkyrie
|date = January 26, 2020
}}</ref>
<ref name="post97489">{{LinkForumThread
|format = ref
|title = Re: Construction practice
|p = 97489
|author = Entity Valkyrie
|date = May 22, 2020
}}</ref>
</references>

==External links==
* {{LinkWikipedia|Gun_(cellular_automaton)}}
* {{LinkLexicon|lex_g.htm#gun}}
* {{LinkLexicon|filename=lex_d.htm#doublebarrelled|patternname=Double-barrelled}}
* {{LinkForumThread|f=2|t=1657|title=Execution of Old Guns by Variable-Speed Firing Squad}}

Gun

2026-07-26T13:39:37Z

Squareroot12621: Add 39 to true-period gun chart

{{Glossary}}
[[Image:Gosperglidergun.gif|framed|right|The first known gun, the [[Gosper glider gun]]]]
A '''gun''' is a stationary pattern that repeatedly emits [[spaceship]]s (or [[rake]]s) forever. By far the most common type of guns are '''[[glider gun]]s''', which emit [[glider]]s (the most well-known of which is the [[Gosper glider gun]]); however, guns that emit spaceships of many other speeds, including [[c/2 orthogonal]], [[2c/5 orthogonal]], and [[c/12 diagonal]], have also been created.

==History==
The first gun to be discovered, the [[Gosper glider gun]], was found by [[Bill Gosper]] in {{year|1970}}, being the first known pattern in [[Conway's Game of Life]] to exhibit [[infinite growth]]. Since then, many guns have been constructed with various periods and that fire spaceships of various speeds. Due to simple [[glider synthesis|glider syntheses]] of the [[Types_of_spaceships#Standard_spaceship|standard spaceships]] many c/2 spaceship guns are known. The first gun that did not fire gliders or c/2 spaceships was a '''Cordergun''' (a gun that fires [[Cordership]]s) constructed by [[Jason Summers]] in July, {{year|1999}}<ref name="entropymine_status" /> based on a synthesis of a variation of the [[7-engine Cordership]] by [[Stephen Silver]]. In March, {{year|2003}} [[Noam Elkies]] completed the synthesis of [[60P5H2V0]] which [[Dave Greene]] used to construct the [[P416_60P5H2V0_gun|first 2c/5 spaceship gun]] in April of the same year.

In July, {{year|2010}} Dave Greene constructed a few guns for a [[gemini|geminoid]] spaceship.<ref name="golnews201007" /> These are the first guns that shoot obliquely-traveling spaceships and at that time were the largest patterns constructed in Life, in terms of their bounding boxes.

On February 17, {{year|2013}} [[Josh Ball]] discovered a simple [[c/7 orthogonal]] spaceship, [[loafer]]. Adam P. Goucher found a synthesis for the loafer later that day, allowing the construction of c/7 orthogonal spaceship guns.<ref name="post7466" />

During March {{year|2016}} the [[copperhead]] spaceship was discovered, with a glider synthesis and several guns following suit.<ref name="post28101" />

In {{year|2019}} and {{year|2020}} guns were produced for the spaceships [[46P4H1V0]],<ref name="post84423" /> [[spider]],<ref name="post88186" /> and [[58P5H1V1]],<ref name="post97489" /> of speeds [[c/4 orthogonal]], [[c/5 orthogonal]], and [[c/5 diagonal]] respectively.

==Barrels==
{{main|Barrel}}
The barrel of a gun (or rake) is a path along which spaceships travel. For example, a double-barrelled glider gun is a gun that emits two glider streams.

==Pseudo-period guns==
A '''pseudo-[[period]] gun''' (as opposed to a [[true-period]] gun) is a gun that emits a period n stream of spaceships (or rakes) via a mechanism that oscillates with a period different from n -- this period will necessarily be a multiple of n. Pseudo period n glider guns are known to exist for all periods greater than or equal to 14, with smaller periods being impossible. The first pseudo period 14 gun was built by [[Dietrich Leithner]] in {{year|1995}}.

==True-period guns==
A '''true-period gun''' (as opposed to a [[#Pseudo-period guns|pseudo-period gun]]) is a gun that emits a period n stream of spaceships (or rakes) via a mechanism that oscillates with period equal to n. True period n guns are known to exist for all possible periods except for 17, 19, 23, 26, 29, 31, 38, and 39. Credits for gun periods below 62 are as follows:

<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr>
{| class="wikitable sortable"
|-
! Period
! Discoverer
! Year of discovery
|-
! [[Period-14 glider gun|14]]
| [[Matthias Merzenich]] and [[James Pascua]]
| {{year|2025}}
|-
! [[Period-15 glider gun|15]]
| [[Period1GliderGun]] and [[Carson Cheng]]
| {{year|2024}}
|-
! [[Period-16 glider gun|16]]
| [[Period1GliderGun]] and [[Nora Brown]]
| {{year|2024}}
|-
! [[Period-18 glider gun|18]]
| [[400spartans]], Period1GliderGun, and [[David Raucci]]
| {{year|2025}}
|-
! [[Period-20 glider gun|20]]
| Matthias Merzenich and [[Noam Elkies]]
| {{year|2013}}
|-
! [[Period-21 glider gun|21]]
| [[Tanner Jacobi]] and David Raucci
| {{year|2021}}
|-
! [[Period-22 glider gun|22]]
| [[David Eppstein]] and [[Jason Summers]]
| {{year|2000}}
|-
! [[Period-24 glider gun|24]]
| Noam Elkies
| {{year|1997}}
|-
! [[period-25 glider gun|25]]
| [[Mitchell Riley]]
| {{year|2022}}
|-
! [[Period-27 glider gun|27]]
| David Raucci and [[goldenratio]]
| {{year|2022}}
|-
! [[Period-28 glider gun|28]]
| Matthias Merzenich and [[Paul Callahan]]
| {{year|2020}}
|-
! [[Gosper_glider_gun|30]]
| [[Bill Gosper]]
| {{year|1970}}
|-
! [[Period-32 glider gun|32]]
| Matthias Merzenich, David Raucci, [[praosylen]], [[wwei23]], and Noam Elkies
| {{year|2021}}
|-
! [[Period-33 glider gun|33]]
| [[Arie Paap]] and Matthias Merzenich
| {{year|2018}}
|-
! [[Period-34 glider gun|34]]
| [[Nora Brown]]
| {{year|2022}}
|-
! [[Period-35 glider gun|35]]
| Matthias Merzenich, [[iNoMed]], and [[hotcrystal0]]
| {{year|2024}}
|-
! [[Period-36 glider gun|36]]
| Jason Summers
| {{year|2004}}
|-
! [[Period-37 glider gun|37]]
| iNoMed, goldenratio, and [[Luke Kiernan]]
| {{year|2022}}
|-
! [[Period-39 glider gun|39]]
| [[Caleb R. Hilton]]
| {{year|2026}}
|-
! [[Period-40 glider gun|40]]
| [[Adam P. Goucher]], Jason Summers, and Matthias Merzenich
| {{year|2013}}
|-
! [[Period-41 glider gun|41]]
| iNoMed, Matthias Merzenich, [[May13]], David Raucci, and Nora Brown
| {{year|2023}}
|-
! [[Period-42 glider gun|42]]
| Tanner Jacobi and David Raucci
| {{year|2021}}
|-
! [[Period-43 glider gun|43]]
| Nora Brown
| {{year|2022}}
|-
! [[p44_pi-heptomino_hassler|44]]
| [[David Buckingham]]
| {{year|1992}}
|-
! [[period-45_glider_gun|45]]
| Matthias Merzenich
| {{year|2010}}
|-
! [[new_gun_1|46]]
| Bill Gosper
| {{year|1971}}
|-
! [[Period-47 glider gun|47]]
| [[Entity Valkyrie]] and iNoMed
| {{year|2024}}
|-
! [[Period-48 glider gun|48]]
| Noam Elkies
| {{year|1997}}
|-
! [[hotcrystal0_reaction#Generalized_form|49]]
| Tanner Jacobi, wwei23, and hotcrystal0
| {{year|2021}}
|-
! [[Period-50 glider gun|50]]
| [[Dean Hickerson]] and Noam Elkies
| {{year|1996}}
|-
! [[hotcrystal0_reaction#Generalized_form|51]]
| [[Luka Okanishi]], wwei23, and hotcrystal0
| {{year|2021}}
|-
! [[Period-52 glider gun|52]]
| [[Dave Greene]], [[Chris Cain]], Matthias Merzenich and Adam P. Goucher
| {{year|2018}}
|-
! [[Period-53 glider gun|53]]
| iNoMed and goldenratio
| {{year|2024}}
|-
! [[Quetzal#Quetzal-54|54]]
| [[Dietrich Leithner]]
| {{year|1998}}
|-
! [[Quetzal#Quetzal-55|55]]
| [[Stephen Silver]]
| {{year|1998}}
|-
! [[Quetzal#Quetzal-56|56]]
| Dietrich Leithner
| {{year|1998}}
|-
! [[Quetzal#Quetzal-57|57]]
| Matthias Merzenich
| {{year|2016}}
|-
! [[Quetzal#Quetzal-58|58]]
| [[Maia Karpovich]], Matthias Merzenich, and Chris Cain
| {{year|2016}}
|-
! [[period-59_glider_gun|59]]
| Adam P. Goucher and Jason Summers
| {{year|2009}}
|-
! [[period-60_glider_gun|60]]
| Bill Gosper
| {{year|1970}}
|-
! [[Period-61 glider gun|61]]
| Luka Okanishi
| {{year|2016}}
|}

==Smallest guns by area of bounding box==

A collection of smallest guns by bounding box area was originally created and maintained by [[Dietrich Leithner]] and [[Peter Rott]], before [[Jason Summers]] took over the maintenance. The p14-999 collection had subsequently evolved into a Git repository led by [[Chris Cain]]. Currently, the collection is maintained collaboratively at Catagolue's glider-synthesis database.

* [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/gun Current database] (Catagolue)
* [https://github.com/ceebo/glider_guns/ older repository] maintained by Chris Cain (only p14-1024)
* [https://entropymine.com/jason/life/#collections older version] maintained by Jason Summers (includes some periods in the range p1000-9999).

Note that this classification of smallest is of dubious utility: see [[Pointless optimisation game]] for more details.

==Guns in Life-like cellular automata==
Due to the existence of some small spaceships in [[Life-like cellular automata]] with birth at two live neighbours (B2), many low-period spaceship guns have been found using tools such as [[WinLifeSearch]]. In contrast, there are very few outer-totalistic rules without B2 (and B0) that are known to contain guns. The following is a list of outer-totalistic rules with neither B0 nor B2 that have known guns:
{| style="width:100%" |
|-
| valign="top" width="50%" |
* Glider guns<ref name="thread1071" />
** B3/S23 ([[Conway's Game of Life]])
** B3/S236
** B3/S2367
** B3/S23678
** B3/S2368
** B3/S237
** B3/S2378
** B3/S238 ({{rl|EightLife}})
** B36/S23 ({{rl|HighLife}})
** B36/S237
** B36/S2378
** B36/S238
** B368/S23
** B368/S238 ({{rl|LowDeath}})
** B37/S23 ({{rl|DryLife}})
** B37/S236
** B37/S237
** B37/S238
** B37/S2378
** B378/S23
** B378/S237
** B378/S2378
** B378/S238
** B38/S236
** B38/S2367
** B38/S23678
** B38/S2368
** B38/S23 ({{rl|Pedestrian Life}})
** B38/S237
** B38/S2378
** B38/S238 ({{rl|HoneyLife}})
| valign="top" |
* Other guns
** B3/S23 ([[Conway's Game of Life]])
** B3/S237
** B3/S2378
** B3/S238 ({{rl|EightLife}})
** B3/S345
** {{rl|B35/S236}}
** B357/S238 ({{rl|Pseudo Life}})
** B358/S236
** B36/S125 ({{rl|2x2}})
** B36/S23 ({{rl|HighLife}})
** B36/S237
** B36/S2378
** B36/S238
** B368/S23
** B368/S238 ({{rl|LowDeath}})
** B36/S245 ({{rl|sqrt replicator rule}})
** B368/S245 ({{rl|Move}})
** B368/S12578
** B3678/S34678 ({{rl|Day & Night}})
** B37/S23 ({{rl|DryLife}})
** B37/S238
** B378/S23
** B378/S238
** B38/S23 ({{rl|Pedestrian Life}})
** B38/S237
** B38/S2378
** B38/S238 ({{rl|HoneyLife}})
** B38/S345
|}

==See also==
* {{CategoryLink|Guns}}
* [[Dieter and Peter's glider gun collection]]
* [[LifeWiki:Game_of_Life_Status_page#Glider_gun_true-periods|Glider gun true-periods status table]]
* [[LifeWiki:Game_of_Life_Status_page#Gun_pseudo-periods|Gun pseudo-periods status table]]
* [[Quetzal]]

==References==
<references>
<ref name="entropymine_status">{{cite web|url=http://entropymine.com/jason/life/status.html |title=Game of Life Status page |accessdate=October 15, 2010}}</ref>
<ref name="golnews201007">{{LinkGoLNews|2010/07/gemini_guns_1.html|title=Gemini guns|date=July 30, 2010|author=Adam P. Goucher}}</ref>
<ref name="thread1071">{{LinkForumThread|format=ref|f=11|t=1071|title=Guns in Life-like cellular automata|author=[[Matthias Merzenich]]|date=April 11, 2013}}</ref>
<ref name="post7466">{{LinkForumThread
|format = ref
|title = Re: c/7 orthogonal spaceships
|p = 7466
|author = Shannon Omick
|date = February 18, 2013
}}</ref>
<ref name="post28101">{{LinkForumThread
|format = ref
|title = Re: is this c/10 spaceship known?
|p = 28101
|author = Alexey Nigin
|date = March 6, 2016
}}</ref>
<ref name="post84423">{{LinkForumThread
|format = ref
|title = Re: Stable signal converters
|p = 84423
|author = Goldtiger997
|date = October 22, 2019
}}</ref>
<ref name="post88186">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 88186
|author = Entity Valkyrie
|date = January 26, 2020
}}</ref>
<ref name="post97489">{{LinkForumThread
|format = ref
|title = Re: Construction practice
|p = 97489
|author = Entity Valkyrie
|date = May 22, 2020
}}</ref>
</references>

==External links==
* {{LinkWikipedia|Gun_(cellular_automaton)}}
* {{LinkLexicon|lex_g.htm#gun}}
* {{LinkLexicon|filename=lex_d.htm#doublebarrelled|patternname=Double-barrelled}}
* {{LinkForumThread|f=2|t=1657|title=Execution of Old Guns by Variable-Speed Firing Squad}}

Solifuge

2025-12-13T21:05:38Z

Squareroot12621: Normalize heading name

{{Spaceship
|name = Solifuge
|pname = solifuge
|c = 1415
|bx = 333
|by = 353
|dir = Oblique
|slope = 3
|p = 62
|m = 62
|s = (6,2)c/31
|z = (12,4)c/62
|h = 1649.7
|symmetry = n
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|discoverer = Nico Brown
|discoveryear = 2025
|rle = true
|viewerconfig = #C [[ GPS 31 HEIGHT 650 WIDTH 480 TRACKLOOP 62 12/62 -4/62 ]]
}}
'''Solifuge''' is a [[(6,2)c/31|(12,4)c/62]] spaceship constructed by [[Nico Brown]] on 30 November 2025 using a [[lumps of muck]]-based crawler he discovered the previous day.<ref name="post222000"/> Its name is another term for camel spiders (which, while arachnids like true spiders and scorpions, aren't actually true spiders), which relates to the fact that the spaceship travels [[camelwise]]. At 1,415 cells, it is over 17 times smaller than the previous smallest [[macro-spaceship]], the [[leaf bug 2]], and over 169 times smaller than the previous smallest-known [[camelship]].

==Underlying reaction==

The base reaction of the spaceship is that of a lumps of muck being displaced by (12,4) cells every 62 generations. Weirdly, the underlying LOM reaction is the exact same as that in the [[p124 lumps of muck hassler]], which has been known since 1994.<ref name="post222002"/>

All period-62 variants of the ship have the lowest period for a crawler-based spaceship, beating (34,7)c/156 technology.

== History ==
On November 30, 2025, Nico Brown completed the original {{times|2305|1560}} spaceship based on a crawler he discovered the previous day.<ref name="post222000"/> Following minor reductions by [[PK22]] and [[iNoMed]], Nico Brown made a significant reduction on December 1 to {{times|584|527}}.<ref name="post222012"/><ref name="post222061"/><ref name="post222124"/> Soon after, he made a few more small reductions resulting in a form with a minimum population of 2,764 cells and a bounding box of {{times|501|496}}.<ref name="post222124"/> The pattern was reduced further on December 3, 4 and 8, first to 2,053 cells by Nico Brown,<ref name="post222245"/> then to 2,036 cells by [[Elijah Ken]],<ref name="post222252"/> then to 1,989 cells by [[iNoMed]],<ref name="post222269"/> and six times by Nico Brown to its current 1,415-cell form.<ref name="post222287"/><ref name="post222422"/>
{{gallery item|{{EmbedViewer
|pname = originalsolifuge
|viewerconfig = #C [[ THUMBSIZE 3 WIDTH 1200 HEIGHT 1000 ]]
|position = center
|caption = The original form of the spaceship when it was first discovered
|style = width:300px;
}}}}

== Glider synthesis and gun == {{main|Glider synthesis}}
On December 8, [[hibiscus]] discovered a 236-glider synthesis of a 1,508-cell Solifuge variant. <ref name="post222433"/> This was soon reduced to 194 gliders by [[Entity Valkyrie 2]], 187 gliders by [[KtT]], 150 gliders by iNoMed and 147 gliders by [[Goldtiger997]]. <ref name="post222437"/><ref name="post222439"/>

On December 9, Entity Valkyrie 2 built a p8064 Solifuge gun for the 1,508-cell variant based on the above syntheses. <ref name="post222483"/>

==References==
<references>
<ref name="post222000">{{LinkForumThread
|format = ref
|p = 222000
|title = Re: Crawlers
|author = Nico Brown
|date = November 30, 2025
}}</ref>
<ref name="post222124">{{LinkForumThread
|format = ref
|p = 222124
|title = Re: Crawlers
|author = Nico Brown
|date = December 1, 2025
}}</ref>
<ref name="post222002">{{LinkForumThread
|format = ref
|p = 222002
|title = Re: Crawlers
|author = Entity Valkyrie 2
|date = November 30, 2025
}}</ref>
<ref name="post222012">{{LinkForumThread
|format = ref
|p = 222012
|title = Re: Crawlers
|author = PK22
|date = November 30, 2025
}}</ref>
<ref name="post222061">{{LinkForumThread
|format = ref
|p = 222061
|title = Re: Crawlers
|author = iNoMed
|date = December 1, 2025
}}</ref>
<ref name="post222245">{{LinkForumThread
|format = ref
|p = 222245
|title = Re: Crawlers
|author = Nico Brown
|date = December 3, 2025
}}</ref>
<ref name="post222252">{{LinkForumThread
|format = ref
|p = 222252
|title = Re: Crawlers
|author = Elijah Ken
|date = December 3, 2025
}}</ref>
<ref name="post222269">{{LinkForumThread
|format = ref
|p = 222269
|title = Re: Crawlers
|author = iNoMed
|date = December 4, 2025
}}</ref>
<ref name="post222287">{{LinkForumThread
|format = ref
|p = 222287
|title = Re: Crawlers
|author = Nico Brown
|date = December 4, 2025
}}</ref>
<ref name="post222422">{{LinkForumThread
|format = ref
|p = 222422
|title = Re: Crawlers
|author = Nico Brown
|date = December 8, 2025
}}</ref>
<ref name="post222433">{{LinkForumThread
|format = ref
|p = 222433
|title = Re: (12,4)c/62 technology
|author = hibiscus
|date = December 8, 2025
}}</ref>
<ref name="post222437">{{LinkForumThread
|format = ref
|p = 222437
|title = Re: (12,4)c/62 technology
|author = iNoMed
|date = December 8, 2025
}}</ref>
<ref name="post222439">{{LinkForumThread
|format = ref
|p = 222439
|title = Re: (12,4)c/62 technology
|author = KtT
|date = December 9, 2025
}}</ref>
<ref name="post222483">{{LinkForumThread
|format = ref
|p = 222483
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = December 9, 2025
}}</ref>
</references>

==External Links==
* [https://en.wikipedia.org/wiki/Solifugae Solifugae] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

Rule:LogicGates

2025-11-03T20:42:17Z

Squareroot12621: Storage cells are now set from the corner because of a crazy bug

@RULE LogicGates
@TABLE
n_states:48
neighborhood:Moore
symmetries:none

# Any
var a1={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1

# Unpowered
var n1={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45}
var n2=n1
var n3=n1
var n4=n1
# Powered
var y1={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46}
var y2=y1
var y3=y1
var y4=y1

# Splitters (vertical, horizontal)
var v1={9,10}
var h1={11,12}

# And gates (up, right, down, left)
var au1={13,14}
var ar1={15,16}
var ad1={17,18}
var al1={19,20}

# Crossovers (up right, down right, down left, up left)
var cur1={21,22,23,24}
var cdr1={25,26,27,28}
var cdl1={29,30,31,32}
var cul1={33,34,35,36}

# Not gates (up, right, down, left)
var nu1={37,38}
var nr1={39,40}
var nd1={41,42}
var nl1={43,44}

# Facing up
var u1={1,2,9,10,13,14,21,22,23,24,33,34,35,36,37,38,45,46}
# Not a powered cell facing up
var un1={0,1,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,20,21,23,25,26,27,28,29,30,31,32,33,35,37,39,40,41,42,43,44,45,47}
# Powered cells facing up
var uy1={2,10,14,22,24,34,36,38,46}
var uy2=uy1

# Facing right
var r1={3,4,11,12,15,16,21,22,23,24,25,26,27,28,39,40,45,46}
# Not a powered cell facing right
var rn1={0,1,2,3,5,6,7,8,9,10,11,13,14,15,17,18,19,20,21,22,25,26,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,47}
# Powered cells facing right
var ry1={4,12,16,23,24,27,28,40,46}
var ry2=ry1

# Facing down
var d1={5,6,9,10,17,18,25,26,27,28,29,30,31,32,41,42,45,46}
# Not a powered cell facing down
var dn1={0,1,2,3,4,5,7,8,9,11,12,13,14,15,16,17,19,20,21,22,23,24,25,27,29,31,33,34,35,36,37,38,39,40,41,43,44,45,47}
# Powered cells facing down
var dy1={6,10,18,26,28,30,32,42,46}
var dy2=dy1

# Facing left
var l1={7,8,11,12,19,20,29,30,31,32,33,34,35,36,43,44,45,46}
# Not a powered cell facing left
var ln1={0,1,2,3,4,5,6,7,9,10,11,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,33,34,37,38,39,40,41,42,43,45,47}
# Powered cells facing left
var ly1={8,12,20,31,32,35,36,44,46}
var ly2=ly1

# Comment
47, a1, a2, a3, a4, a5, a6, a7, a8, 47
# Storage
45, a1, dy1,a2, a3, a4, a5, a6, a7, 46
45, a1, ly1,a2, a3, a4, a5, a6, a7, 46
45, a1, a2, a3, uy1,a4, a5, a6, a7, 46
45, a1, a2, a3, ly1,a4, a5, a6, a7, 46
45, a1, a2, a3, a4, a5, uy1,a6, a7, 46
45, a1, a2, a3, a4, a5, ry1,a6, a7, 46
45, a1, a2, a3, a4, a5, a6, a7, dy1, 46
45, a1, a2, a3, a4, a5, a6, a7, ry1, 46
45, a1, a2, a3, a4, a5, a6, a7, a8, 45
46, a1, dy1,a2, a3, a4, a5, a6, a7, 45
46, a1, ly1,a2, a3, a4, a5, a6, a7, 45
46, a1, a2, a3, uy1,a4, a5, a6, a7, 45
46, a1, a2, a3, ly1,a4, a5, a6, a7, 45
46, a1, a2, a3, a4, a5, uy1,a6, a7, 45
46, a1, a2, a3, a4, a5, ry1,a6, a7, 45
46, a1, a2, a3, a4, a5, a6, a7, dy1, 45
46, a1, a2, a3, a4, a5, a6, a7, ry1, 45
46, a1, a2, a3, a4, a5, a6, a7, a8, 46
# Splitters
v1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 9
v1, a1, a2, a3, a4, a5, a6, a7, a8, 10
h1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 11
h1, a1, a2, a3, a4, a5, a6, a7, a8, 12
# And gates
au1, a1, a2, a3, uy1,a4, uy2,a5, a6, 14
au1, a1, a2, a3, a4, a5, a6, a7, a8, 13
ar1, a1, a2, a3, a4, a5, ry1,a6, ry2, 16
ar1, a1, a2, a3, a4, a5, a6, a7, a8, 15
ad1, a1, dy1,a2, a3, a4, a5, a6, dy2, 18
ad1, a1, a2, a3, a4, a5, a6, a7, a8, 17
al1, a1, ly1,a2, ly2,a3, a4, a5, a6, 20
al1, a1, a2, a3, a4, a5, a6, a7, a8, 19
# Crossovers
cur1, a1, a2, a3, a4, un1,a5, rn1,a6, 21
cur1, a1, a2, a3, a4, uy1,a5, rn1,a6, 22
cur1, a1, a2, a3, a4, un1,a5, ry1,a6, 23
cur1, a1, a2, a3, a4, uy1,a5, ry1,a6, 24
cdr1, dn1,a1, a2, a3, a4, a5, rn1,a6, 25
cdr1, dy1,a1, a2, a3, a4, a5, rn1,a6, 26
cdr1, dn1,a1, a2, a3, a4, a5, ry1,a6, 27
cdr1, dy1,a1, a2, a3, a4, a5, ry1,a6, 28
cdl1, dn1,a1, ln1,a2, a3, a4, a5, a6, 29
cdl1, dy1,a1, ln1,a2, a3, a4, a5, a6, 30
cdl1, dn1,a1, ly1,a2, a3, a4, a5, a6, 31
cdl1, dy1,a1, ly1,a2, a3, a4, a5, a6, 32
cul1, a1, a2, ln1,a3, un1,a4, a5, a6, 33
cul1, a1, a2, ln1,a3, uy1,a4, a5, a6, 34
cul1, a1, a2, ly1,a3, un1,a4, a5, a6, 35
cul1, a1, a2, ly1,a3, uy1,a4, a5, a6, 36
# Not gates
nu1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 38
nu1, a1, a2, a3, a4, a5, a6, a7, a8, 37
nr1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 40
nr1, a1, a2, a3, a4, a5, a6, a7, a8, 39
nd1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 42
nd1, a1, a2, a3, a4, a5, a6, a7, a8, 41
nl1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 44
nl1, a1, a2, a3, a4, a5, a6, a7, a8, 43
# Normal wire
u1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 1
u1, a1, a2, a3, a4, a5, a6, a7, a8, 2
r1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 3
r1, a1, a2, a3, a4, a5, a6, a7, a8, 4
d1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 5
d1, a1, a2, a3, a4, a5, a6, a7, a8, 6
l1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 7
l1, a1, a2, a3, a4, a5, a6, a7, a8, 8

@NAMES
0 empty
1 wire ^ off
2 wire ^ on
3 wire > off
4 wire > on
5 wire v off
6 wire v on
7 wire < off
8 wire < on
9 splitter ^v off
10 splitter ^v on
11 splitter <> off
12 splitter <> on
13 and ^ off
14 and ^ on
15 and > off
16 and > on
17 and v off
18 and v on
19 and < off
20 and < on
21 cross ^ off > off
22 cross ^ on > off
23 cross ^ off > on
24 cross ^ on > on
25 cross v off > off
26 cross v on > off
27 cross v off > on
28 cross v on > on
29 cross v off < off
30 cross v on < off
31 cross v off < on
32 cross v on < on
33 cross ^ off < off
34 cross ^ on < off
35 cross ^ off < on
36 cross ^ on < on
37 not ^ off
38 not ^ on
39 not > off
40 not > on
41 not v off
42 not v on
43 not < off
44 not < on
45 storage off
46 storage on
47 comment

@COLORS
0 0 0 0
1 128 32 32
2 255 128 128
3 128 32 32
4 255 128 128
5 128 32 32
6 255 128 128
7 128 32 32
8 255 128 128
9 96 96 24
10 255 255 64
11 96 96 24
12 255 255 64
13 32 112 64
14 64 255 128
15 32 112 64
16 64 255 128
17 32 112 64
18 64 255 128
19 32 112 64
20 64 255 128
21 128 32 32
22 192 80 80
23 192 80 80
24 255 128 128
25 128 32 32
26 192 80 80
27 192 80 80
28 255 128 128
29 128 32 32
30 192 80 80
31 192 80 80
32 255 128 128
33 128 32 32
34 192 80 80
35 192 80 80
36 255 128 128
37 32 32 128
38 128 128 255
39 32 32 128
40 128 128 255
41 32 32 128
42 128 128 255
43 32 32 128
44 128 128 255
45 96 24 96
46 255 64 255
47 128 128 128

@ICONS
XPM
"7 329 11 1"
". c #802020"
"A c #FF8080"
"B c #606018"
"C c #FFFF40"
"D c #207040"
"E c #40FF80"
"F c #202080"
"G c #8080FF"
"H c #601860"
"I c #FF40FF"
"J c #808080"
"......."
"......."
"...A..."
"..A.A.."
".A...A."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"AAA.AAA"
"AA.A.AA"
"A.AAA.A"
"AAAAAAA"
"AAAAAAA"
"......."
"..A...."
"...A..."
"....A.."
"...A..."
"..A...."
"......."
"AAAAAAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAAAAAA"
"......."
"......."
".A...A."
"..A.A.."
"...A..."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"A.AAA.A"
"AA.A.AA"
"AAA.AAA"
"AAAAAAA"
"AAAAAAA"
"......."
"....A.."
"...A..."
"..A...."
"...A..."
"....A.."
"......."
"AAAAAAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAAAAAA"
"BBBCBBB"
"BBCBCBB"
"BCBBBCB"
"BBBBBBB"
"BCBBBCB"
"BBCBCBB"
"BBBCBBB"
"CCCBCCC"
"CCBCBCC"
"CBCCCBC"
"CCCCCCC"
"CBCCCBC"
"CCBCBCC"
"CCCBCCC"
"BBBBBBB"
"BBCBCBB"
"BCBBBCB"
"CBBBBBC"
"BCBBBCB"
"BBCBCBB"
"BBBBBBB"
"CCCCCCC"
"CCBCBCC"
"CBCCCBC"
"BCCCCCB"
"CBCCCBC"
"CCBCBCC"
"CCCCCCC"
"DDDDDDD"
"DDDDDDD"
"DDDEDDD"
"DDEDEDD"
"DEDDDED"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EEEDEEE"
"EEDEDEE"
"EDEEEDE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDDDDD"
"EEEEEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDDDD"
"DEDDDED"
"DDEDEDD"
"DDDEDDD"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EDEEEDE"
"EEDEDEE"
"EEEDEEE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDDDDD"
"EEEEEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEEEEE"
"..A...."
".A.A..."
"......."
".....A."
"......A"
".....A."
"......."
"AA.AAA."
"A.A.A.."
"AAAA..."
"AAA..A."
"AA....A"
"A....A."
"......."
"..A...."
".A.A..A"
".....AA"
"....A.A"
"...AAA."
"..AAA.A"
".AAAAAA"
"AA.AAAA"
"A.A.AAA"
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"......."
".....A."
"......A"
".....A."
"......."
".A.A..."
"..A...."
"......."
"A....A."
"AA....A"
"AAA..A."
"AAAA..."
"A.A.A.."
"AA.AAA."
".AAAAAA"
"..AAA.A"
"...AAA."
"....A.A"
".....AA"
".A.A..A"
"..A...."
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"A.A.AAA"
"AA.AAAA"
"......."
".A....."
"A......"
".A....."
"......."
"...A.A."
"....A.."
"......."
".A....A"
"A....AA"
".A..AAA"
"...AAAA"
"..A.A.A"
".AAA.AA"
"AAAAAA."
"A.AAA.."
".AAA..."
"A.A...."
"AA....."
"A..A.A."
"....A.."
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"AAA.A.A"
"AAAA.AA"
"....A.."
"...A.A."
"......."
".A....."
"A......"
".A....."
"......."
".AAA.AA"
"..A.A.A"
"...AAAA"
".A..AAA"
"A....AA"
".A....A"
"......."
"....A.."
"A..A.A."
"AA....."
"A.A...."
".AAA..."
"A.AAA.."
"AAAAAA."
"AAAA.AA"
"AAA.A.A"
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"FFFFFFF"
"FFFFFFF"
"FFFGFFF"
"FFGFGFF"
"FGFFFGF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GGGFGGG"
"GGFGFGG"
"GFGGGFG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFFFFF"
"GGGGGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFFFF"
"FGFFFGF"
"FFGFGFF"
"FFFGFFF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GFGGGFG"
"GGFGFGG"
"GGGFGGG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFFFFF"
"GGGGGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGGGGG"
"HHHHHHH"
"HHIIIHH"
"HIHHHIH"
"HIHHHIH"
"HIHHHIH"
"HHIIIHH"
"HHHHHHH"
"IIIIIII"
"IIHHHII"
"IHIIIHI"
"IHIIIHI"
"IHIIIHI"
"IIHHHII"
"IIIIIII"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"

User:Squareroot12621

2025-11-03T20:27:45Z

Squareroot12621: 46-state --> 48-state

Rule:LogicGates

2025-11-03T20:26:52Z

Squareroot12621: Add storage cells (45 and 46)

@RULE LogicGates
@TABLE
n_states:48
neighborhood:Moore
symmetries:none

# Any
var a1={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1

# Unpowered
var n1={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45}
var n2=n1
var n3=n1
var n4=n1
# Powered
var y1={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46}
var y2=y1
var y3=y1
var y4=y1

# Splitters (vertical, horizontal)
var v1={9,10}
var h1={11,12}

# And gates (up, right, down, left)
var au1={13,14}
var ar1={15,16}
var ad1={17,18}
var al1={19,20}

# Crossovers (up right, down right, down left, up left)
var cur1={21,22,23,24}
var cdr1={25,26,27,28}
var cdl1={29,30,31,32}
var cul1={33,34,35,36}

# Not gates (up, right, down, left)
var nu1={37,38}
var nr1={39,40}
var nd1={41,42}
var nl1={43,44}

# Facing up
var u1={1,2,9,10,13,14,21,22,23,24,33,34,35,36,37,38,45,46}
# Not a powered cell facing up
var un1={0,1,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,20,21,23,25,26,27,28,29,30,31,32,33,35,37,39,40,41,42,43,44,45,47}
# Powered cells facing up
var uy1={2,10,14,22,24,34,36,38,46}
var uy2=uy1

# Facing right
var r1={3,4,11,12,15,16,21,22,23,24,25,26,27,28,39,40,45,46}
# Not a powered cell facing right
var rn1={0,1,2,3,5,6,7,8,9,10,11,13,14,15,17,18,19,20,21,22,25,26,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,47}
# Powered cells facing right
var ry1={4,12,16,23,24,27,28,40,46}
var ry2=ry1

# Facing down
var d1={5,6,9,10,17,18,25,26,27,28,29,30,31,32,41,42,45,46}
# Not a powered cell facing down
var dn1={0,1,2,3,4,5,7,8,9,11,12,13,14,15,16,17,19,20,21,22,23,24,25,27,29,31,33,34,35,36,37,38,39,40,41,43,44,45,47}
# Powered cells facing down
var dy1={6,10,18,26,28,30,32,42,46}
var dy2=dy1

# Facing left
var l1={7,8,11,12,19,20,29,30,31,32,33,34,35,36,43,44,45,46}
# Not a powered cell facing left
var ln1={0,1,2,3,4,5,6,7,9,10,11,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,33,34,37,38,39,40,41,42,43,45,47}
# Powered cells facing left
var ly1={8,12,20,31,32,35,36,44,46}
var ly2=ly1

# Comment
47, a1, a2, a3, a4, a5, a6, a7, a8, 47
# Storage
45, dn1,a1, ln1,a2, un1,a3, rn1,a4, 45
45, a1, a2, a3, a4, a5, a6, a7, a8, 46
46, dn1,a1, ln1,a2, un1,a3, rn1,a4, 46
46, a1, a2, a3, a4, a5, a6, a7, a8, 45
# Splitters
v1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 9
v1, a1, a2, a3, a4, a5, a6, a7, a8, 10
h1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 11
h1, a1, a2, a3, a4, a5, a6, a7, a8, 12
# And gates
au1, a1, a2, a3, uy1,a4, uy2,a5, a6, 14
au1, a1, a2, a3, a4, a5, a6, a7, a8, 13
ar1, a1, a2, a3, a4, a5, ry1,a6, ry2, 16
ar1, a1, a2, a3, a4, a5, a6, a7, a8, 15
ad1, a1, dy1,a2, a3, a4, a5, a6, dy2, 18
ad1, a1, a2, a3, a4, a5, a6, a7, a8, 17
al1, a1, ly1,a2, ly2,a3, a4, a5, a6, 20
al1, a1, a2, a3, a4, a5, a6, a7, a8, 19
# Crossovers
cur1, a1, a2, a3, a4, un1,a5, rn1,a6, 21
cur1, a1, a2, a3, a4, uy1,a5, rn1,a6, 22
cur1, a1, a2, a3, a4, un1,a5, ry1,a6, 23
cur1, a1, a2, a3, a4, uy1,a5, ry1,a6, 24
cdr1, dn1,a1, a2, a3, a4, a5, rn1,a6, 25
cdr1, dy1,a1, a2, a3, a4, a5, rn1,a6, 26
cdr1, dn1,a1, a2, a3, a4, a5, ry1,a6, 27
cdr1, dy1,a1, a2, a3, a4, a5, ry1,a6, 28
cdl1, dn1,a1, ln1,a2, a3, a4, a5, a6, 29
cdl1, dy1,a1, ln1,a2, a3, a4, a5, a6, 30
cdl1, dn1,a1, ly1,a2, a3, a4, a5, a6, 31
cdl1, dy1,a1, ly1,a2, a3, a4, a5, a6, 32
cul1, a1, a2, ln1,a3, un1,a4, a5, a6, 33
cul1, a1, a2, ln1,a3, uy1,a4, a5, a6, 34
cul1, a1, a2, ly1,a3, un1,a4, a5, a6, 35
cul1, a1, a2, ly1,a3, uy1,a4, a5, a6, 36
# Not gates
nu1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 38
nu1, a1, a2, a3, a4, a5, a6, a7, a8, 37
nr1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 40
nr1, a1, a2, a3, a4, a5, a6, a7, a8, 39
nd1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 42
nd1, a1, a2, a3, a4, a5, a6, a7, a8, 41
nl1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 44
nl1, a1, a2, a3, a4, a5, a6, a7, a8, 43
# Normal wire
u1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 1
u1, a1, a2, a3, a4, a5, a6, a7, a8, 2
r1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 3
r1, a1, a2, a3, a4, a5, a6, a7, a8, 4
d1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 5
d1, a1, a2, a3, a4, a5, a6, a7, a8, 6
l1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 7
l1, a1, a2, a3, a4, a5, a6, a7, a8, 8

@NAMES
0 empty
1 wire ^ off
2 wire ^ on
3 wire > off
4 wire > on
5 wire v off
6 wire v on
7 wire < off
8 wire < on
9 splitter ^v off
10 splitter ^v on
11 splitter <> off
12 splitter <> on
13 and ^ off
14 and ^ on
15 and > off
16 and > on
17 and v off
18 and v on
19 and < off
20 and < on
21 cross ^ off > off
22 cross ^ on > off
23 cross ^ off > on
24 cross ^ on > on
25 cross v off > off
26 cross v on > off
27 cross v off > on
28 cross v on > on
29 cross v off < off
30 cross v on < off
31 cross v off < on
32 cross v on < on
33 cross ^ off < off
34 cross ^ on < off
35 cross ^ off < on
36 cross ^ on < on
37 not ^ off
38 not ^ on
39 not > off
40 not > on
41 not v off
42 not v on
43 not < off
44 not < on
45 storage off
46 storage on
47 comment

@COLORS
0 0 0 0
1 128 32 32
2 255 128 128
3 128 32 32
4 255 128 128
5 128 32 32
6 255 128 128
7 128 32 32
8 255 128 128
9 96 96 24
10 255 255 64
11 96 96 24
12 255 255 64
13 32 112 64
14 64 255 128
15 32 112 64
16 64 255 128
17 32 112 64
18 64 255 128
19 32 112 64
20 64 255 128
21 128 32 32
22 192 80 80
23 192 80 80
24 255 128 128
25 128 32 32
26 192 80 80
27 192 80 80
28 255 128 128
29 128 32 32
30 192 80 80
31 192 80 80
32 255 128 128
33 128 32 32
34 192 80 80
35 192 80 80
36 255 128 128
37 32 32 128
38 128 128 255
39 32 32 128
40 128 128 255
41 32 32 128
42 128 128 255
43 32 32 128
44 128 128 255
45 96 24 96
46 255 64 255
47 128 128 128

@ICONS
XPM
"7 329 11 1"
". c #802020"
"A c #FF8080"
"B c #606018"
"C c #FFFF40"
"D c #207040"
"E c #40FF80"
"F c #202080"
"G c #8080FF"
"H c #601860"
"I c #FF40FF"
"J c #808080"
"......."
"......."
"...A..."
"..A.A.."
".A...A."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"AAA.AAA"
"AA.A.AA"
"A.AAA.A"
"AAAAAAA"
"AAAAAAA"
"......."
"..A...."
"...A..."
"....A.."
"...A..."
"..A...."
"......."
"AAAAAAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAAAAAA"
"......."
"......."
".A...A."
"..A.A.."
"...A..."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"A.AAA.A"
"AA.A.AA"
"AAA.AAA"
"AAAAAAA"
"AAAAAAA"
"......."
"....A.."
"...A..."
"..A...."
"...A..."
"....A.."
"......."
"AAAAAAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAAAAAA"
"BBBCBBB"
"BBCBCBB"
"BCBBBCB"
"BBBBBBB"
"BCBBBCB"
"BBCBCBB"
"BBBCBBB"
"CCCBCCC"
"CCBCBCC"
"CBCCCBC"
"CCCCCCC"
"CBCCCBC"
"CCBCBCC"
"CCCBCCC"
"BBBBBBB"
"BBCBCBB"
"BCBBBCB"
"CBBBBBC"
"BCBBBCB"
"BBCBCBB"
"BBBBBBB"
"CCCCCCC"
"CCBCBCC"
"CBCCCBC"
"BCCCCCB"
"CBCCCBC"
"CCBCBCC"
"CCCCCCC"
"DDDDDDD"
"DDDDDDD"
"DDDEDDD"
"DDEDEDD"
"DEDDDED"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EEEDEEE"
"EEDEDEE"
"EDEEEDE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDDDDD"
"EEEEEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDDDD"
"DEDDDED"
"DDEDEDD"
"DDDEDDD"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EDEEEDE"
"EEDEDEE"
"EEEDEEE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDDDDD"
"EEEEEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEEEEE"
"..A...."
".A.A..."
"......."
".....A."
"......A"
".....A."
"......."
"AA.AAA."
"A.A.A.."
"AAAA..."
"AAA..A."
"AA....A"
"A....A."
"......."
"..A...."
".A.A..A"
".....AA"
"....A.A"
"...AAA."
"..AAA.A"
".AAAAAA"
"AA.AAAA"
"A.A.AAA"
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"......."
".....A."
"......A"
".....A."
"......."
".A.A..."
"..A...."
"......."
"A....A."
"AA....A"
"AAA..A."
"AAAA..."
"A.A.A.."
"AA.AAA."
".AAAAAA"
"..AAA.A"
"...AAA."
"....A.A"
".....AA"
".A.A..A"
"..A...."
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"A.A.AAA"
"AA.AAAA"
"......."
".A....."
"A......"
".A....."
"......."
"...A.A."
"....A.."
"......."
".A....A"
"A....AA"
".A..AAA"
"...AAAA"
"..A.A.A"
".AAA.AA"
"AAAAAA."
"A.AAA.."
".AAA..."
"A.A...."
"AA....."
"A..A.A."
"....A.."
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"AAA.A.A"
"AAAA.AA"
"....A.."
"...A.A."
"......."
".A....."
"A......"
".A....."
"......."
".AAA.AA"
"..A.A.A"
"...AAAA"
".A..AAA"
"A....AA"
".A....A"
"......."
"....A.."
"A..A.A."
"AA....."
"A.A...."
".AAA..."
"A.AAA.."
"AAAAAA."
"AAAA.AA"
"AAA.A.A"
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"FFFFFFF"
"FFFFFFF"
"FFFGFFF"
"FFGFGFF"
"FGFFFGF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GGGFGGG"
"GGFGFGG"
"GFGGGFG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFFFFF"
"GGGGGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFFFF"
"FGFFFGF"
"FFGFGFF"
"FFFGFFF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GFGGGFG"
"GGFGFGG"
"GGGFGGG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFFFFF"
"GGGGGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGGGGG"
"HHHHHHH"
"HHIIIHH"
"HIHHHIH"
"HIHHHIH"
"HIHHHIH"
"HHIIIHH"
"HHHHHHH"
"IIIIIII"
"IIHHHII"
"IHIIIHI"
"IHIIIHI"
"IHIIIHI"
"IIHHHII"
"IIIIIII"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"
"JJJJJJJ"

User:Squareroot12621

2025-11-03T17:22:18Z

Squareroot12621: Add LogicGates

I'm squareroot12621, an irrational number. I've been on [https://conwaylife.com/forums/ the forums] since 2022, but I didn't get an account on LifeWiki until 2024.

Also, in case you're wondering, {{sqrt|12621}} is about 112.343.

== squareroot12621's Rules ==
; [[Rule:Supercomputer|Supercomputer]] ([https://conwaylife.com/forums/viewtopic.php?f=12&t=5647&p=186853#p186417 thread])
: A 9-state circuitry rule, with a display state. A working computer was in progress.
; [[Rule:LogicGates|LogicGates]]
: A 46-state circuitry rule with just wires, AND gates, and NOT gates.

== Conway's Story Mode ==
'''Conway's Story Mode''' (CSM) is an attempt to make Conway's Game of Life more accessible to beginners. The original thread can be found [https://conwaylife.com/forums/viewtopic.php?f=7&t=6053 here], and some drafts for CSM can be found in the subpages below.

[[User:Squareroot12621/CSM]]
:[[User:Squareroot12621/CSM/Lessons]]

Rule:LogicGates

2025-11-03T16:41:11Z

Squareroot12621: Create LogicGates

@RULE LogicGates
@TABLE
n_states:46
neighborhood:Moore
symmetries:none

# Any
var a1={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1

# Unpowered
var n1={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43}
var n2=n1
var n3=n1
var n4=n1
# Powered
var y1={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44}
var y2=y1
var y3=y1
var y4=y1

# Splitters (vertical, horizontal)
var v1={9,10}
var h1={11,12}

# And gates (up, right, down, left)
var au1={13,14}
var ar1={15,16}
var ad1={17,18}
var al1={19,20}

# Crossovers (up right, down right, down left, up left)
var cur1={21,22,23,24}
var cdr1={25,26,27,28}
var cdl1={29,30,31,32}
var cul1={33,34,35,36}

# Not gates (up, right, down, left)
var nu1={37,38}
var nr1={39,40}
var nd1={41,42}
var nl1={43,44}

# Facing up
var u1={1,2,9,10,13,14,21,22,23,24,33,34,35,36,37,38}
# Not a powered cell facing up
var un1={0,1,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,20,21,23,25,26,27,28,29,30,31,32,33,35,37,39,40,41,42,43,44,45}
# Powered cells facing up
var uy1={2,10,14,22,24,34,36,38}
var uy2=uy1

# Facing right
var r1={3,4,11,12,15,16,21,22,23,24,25,26,27,28,39,40}
# Not a powered cell facing right
var rn1={0,1,2,3,5,6,7,8,9,10,11,13,14,15,17,18,19,20,21,22,25,26,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45}
# Powered cells facing right
var ry1={4,12,16,23,24,27,28,40}
var ry2=ry1

# Facing down
var d1={5,6,9,10,17,18,25,26,27,28,29,30,31,32,41,42}
# Not a powered cell facing down
var dn1={0,1,2,3,4,5,7,8,9,11,12,13,14,15,16,17,19,20,21,22,23,24,25,27,29,31,33,34,35,36,37,38,39,40,41,43,44,45}
# Powered cells facing down
var dy1={6,10,18,26,28,30,32,42}
var dy2=dy1

# Facing left
var l1={7,8,11,12,19,20,29,30,31,32,33,34,35,36,43,44}
# Not a powered cell facing left
var ln1={0,1,2,3,4,5,6,7,9,10,11,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,33,34,37,38,39,40,41,42,43,45}
# Powered cells facing left
var ly1={8,12,20,31,32,35,36,44}
var ly2=ly1

# Comment
45, a1, a2, a3, a4, a5, a6, a7, a8, 45
# Splitters
v1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 9
v1, a1, a2, a3, a4, a5, a6, a7, a8, 10
h1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 11
h1, a1, a2, a3, a4, a5, a6, a7, a8, 12
# And gates
au1, a1, a2, a3, uy1,a4, uy2,a5, a6, 14
au1, a1, a2, a3, a4, a5, a6, a7, a8, 13
ar1, a1, a2, a3, a4, a5, ry1,a6, ry2, 16
ar1, a1, a2, a3, a4, a5, a6, a7, a8, 15
ad1, a1, dy1,a2, a3, a4, a5, a6, dy2, 18
ad1, a1, a2, a3, a4, a5, a6, a7, a8, 17
al1, a1, ly1,a2, ly2,a3, a4, a5, a6, 20
al1, a1, a2, a3, a4, a5, a6, a7, a8, 19
# Crossovers
cur1, a1, a2, a3, a4, un1,a5, rn1,a6, 21
cur1, a1, a2, a3, a4, uy1,a5, rn1,a6, 22
cur1, a1, a2, a3, a4, un1,a5, ry1,a6, 23
cur1, a1, a2, a3, a4, uy1,a5, ry1,a6, 24
cdr1, dn1,a1, a2, a3, a4, a5, rn1,a6, 25
cdr1, dy1,a1, a2, a3, a4, a5, rn1,a6, 26
cdr1, dn1,a1, a2, a3, a4, a5, ry1,a6, 27
cdr1, dy1,a1, a2, a3, a4, a5, ry1,a6, 28
cdl1, dn1,a1, ln1,a2, a3, a4, a5, a6, 29
cdl1, dy1,a1, ln1,a2, a3, a4, a5, a6, 30
cdl1, dn1,a1, ly1,a2, a3, a4, a5, a6, 31
cdl1, dy1,a1, ly1,a2, a3, a4, a5, a6, 32
cul1, a1, a2, ln1,a3, un1,a4, a5, a6, 33
cul1, a1, a2, ln1,a3, uy1,a4, a5, a6, 34
cul1, a1, a2, ly1,a3, un1,a4, a5, a6, 35
cul1, a1, a2, ly1,a3, uy1,a4, a5, a6, 36
# Not gates
nu1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 38
nu1, a1, a2, a3, a4, a5, a6, a7, a8, 37
nr1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 40
nr1, a1, a2, a3, a4, a5, a6, a7, a8, 39
nd1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 42
nd1, a1, a2, a3, a4, a5, a6, a7, a8, 41
nl1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 44
nl1, a1, a2, a3, a4, a5, a6, a7, a8, 43
# Normal wire
u1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 1
u1, a1, a2, a3, a4, a5, a6, a7, a8, 2
r1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 3
r1, a1, a2, a3, a4, a5, a6, a7, a8, 4
d1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 5
d1, a1, a2, a3, a4, a5, a6, a7, a8, 6
l1, dn1,a1, ln1,a2, un1,a3, rn1,a4, 7
l1, a1, a2, a3, a4, a5, a6, a7, a8, 8

@NAMES
0 empty
1 wire ^ off
2 wire ^ on
3 wire > off
4 wire > on
5 wire v off
6 wire v on
7 wire < off
8 wire < on
9 splitter ^v off
10 splitter ^v on
11 splitter <> off
12 splitter <> on
13 and ^ off
14 and ^ on
15 and > off
16 and > on
17 and v off
18 and v on
19 and < off
20 and < on
21 cross ^ off > off
22 cross ^ on > off
23 cross ^ off > on
24 cross ^ on > on
25 cross v off > off
26 cross v on > off
27 cross v off > on
28 cross v on > on
29 cross v off < off
30 cross v on < off
31 cross v off < on
32 cross v on < on
33 cross ^ off < off
34 cross ^ on < off
35 cross ^ off < on
36 cross ^ on < on
37 not ^ off
38 not ^ on
39 not > off
40 not > on
41 not v off
42 not v on
43 not < off
44 not < on
45 comment

@COLORS
0 0 0 0
1 128 32 32
2 255 128 128
3 128 32 32
4 255 128 128
5 128 32 32
6 255 128 128
7 128 32 32
8 255 128 128
9 96 96 24
10 255 255 64
11 96 96 24
12 255 255 64
13 32 112 64
14 64 255 128
15 32 112 64
16 64 255 128
17 32 112 64
18 64 255 128
19 32 112 64
20 64 255 128
21 128 32 32
22 192 80 80
23 192 80 80
24 255 128 128
25 128 32 32
26 192 80 80
27 192 80 80
28 255 128 128
29 128 32 32
30 192 80 80
31 192 80 80
32 255 128 128
33 128 32 32
34 192 80 80
35 192 80 80
36 255 128 128
37 32 32 128
38 128 128 255
39 32 32 128
40 128 128 255
41 32 32 128
42 128 128 255
43 32 32 128
44 128 128 255
45 128 128 128

@ICONS
XPM
"7 315 9 1"
". c #802020"
"A c #FF8080"
"B c #606018"
"C c #FFFF40"
"D c #207040"
"E c #40FF80"
"F c #202080"
"G c #8080FF"
"H c #808080"
"......."
"......."
"...A..."
"..A.A.."
".A...A."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"AAA.AAA"
"AA.A.AA"
"A.AAA.A"
"AAAAAAA"
"AAAAAAA"
"......."
"..A...."
"...A..."
"....A.."
"...A..."
"..A...."
"......."
"AAAAAAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAAAAAA"
"......."
"......."
".A...A."
"..A.A.."
"...A..."
"......."
"......."
"AAAAAAA"
"AAAAAAA"
"A.AAA.A"
"AA.A.AA"
"AAA.AAA"
"AAAAAAA"
"AAAAAAA"
"......."
"....A.."
"...A..."
"..A...."
"...A..."
"....A.."
"......."
"AAAAAAA"
"AAAA.AA"
"AAA.AAA"
"AA.AAAA"
"AAA.AAA"
"AAAA.AA"
"AAAAAAA"
"BBBCBBB"
"BBCBCBB"
"BCBBBCB"
"BBBBBBB"
"BCBBBCB"
"BBCBCBB"
"BBBCBBB"
"CCCBCCC"
"CCBCBCC"
"CBCCCBC"
"CCCCCCC"
"CBCCCBC"
"CCBCBCC"
"CCCBCCC"
"BBBBBBB"
"BBCBCBB"
"BCBBBCB"
"CBBBBBC"
"BCBBBCB"
"BBCBCBB"
"BBBBBBB"
"CCCCCCC"
"CCBCBCC"
"CBCCCBC"
"BCCCCCB"
"CBCCCBC"
"CCBCBCC"
"CCCCCCC"
"DDDDDDD"
"DDDDDDD"
"DDDEDDD"
"DDEDEDD"
"DEDDDED"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EEEDEEE"
"EEDEDEE"
"EDEEEDE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDDDDD"
"EEEEEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDDDD"
"DEDDDED"
"DDEDEDD"
"DDDEDDD"
"DDDDDDD"
"DDDDDDD"
"EEEEEEE"
"EEEEEEE"
"EDEEEDE"
"EEDEDEE"
"EEEDEEE"
"EEEEEEE"
"EEEEEEE"
"DDDDDDD"
"DDDDEDD"
"DDDEDDD"
"DDEDDDD"
"DDDEDDD"
"DDDDEDD"
"DDDDDDD"
"EEEEEEE"
"EEEEDEE"
"EEEDEEE"
"EEDEEEE"
"EEEDEEE"
"EEEEDEE"
"EEEEEEE"
"..A...."
".A.A..."
"......."
".....A."
"......A"
".....A."
"......."
"AA.AAA."
"A.A.A.."
"AAAA..."
"AAA..A."
"AA....A"
"A....A."
"......."
"..A...."
".A.A..A"
".....AA"
"....A.A"
"...AAA."
"..AAA.A"
".AAAAAA"
"AA.AAAA"
"A.A.AAA"
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"......."
".....A."
"......A"
".....A."
"......."
".A.A..."
"..A...."
"......."
"A....A."
"AA....A"
"AAA..A."
"AAAA..."
"A.A.A.."
"AA.AAA."
".AAAAAA"
"..AAA.A"
"...AAA."
"....A.A"
".....AA"
".A.A..A"
"..A...."
"AAAAAAA"
"AAAAA.A"
"AAAAAA."
"AAAAA.A"
"AAAAAAA"
"A.A.AAA"
"AA.AAAA"
"......."
".A....."
"A......"
".A....."
"......."
"...A.A."
"....A.."
"......."
".A....A"
"A....AA"
".A..AAA"
"...AAAA"
"..A.A.A"
".AAA.AA"
"AAAAAA."
"A.AAA.."
".AAA..."
"A.A...."
"AA....."
"A..A.A."
"....A.."
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"AAA.A.A"
"AAAA.AA"
"....A.."
"...A.A."
"......."
".A....."
"A......"
".A....."
"......."
".AAA.AA"
"..A.A.A"
"...AAAA"
".A..AAA"
"A....AA"
".A....A"
"......."
"....A.."
"A..A.A."
"AA....."
"A.A...."
".AAA..."
"A.AAA.."
"AAAAAA."
"AAAA.AA"
"AAA.A.A"
"AAAAAAA"
"A.AAAAA"
".AAAAAA"
"A.AAAAA"
"AAAAAAA"
"FFFFFFF"
"FFFFFFF"
"FFFGFFF"
"FFGFGFF"
"FGFFFGF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GGGFGGG"
"GGFGFGG"
"GFGGGFG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFFFFF"
"GGGGGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFFFF"
"FGFFFGF"
"FFGFGFF"
"FFFGFFF"
"FFFFFFF"
"FFFFFFF"
"GGGGGGG"
"GGGGGGG"
"GFGGGFG"
"GGFGFGG"
"GGGFGGG"
"GGGGGGG"
"GGGGGGG"
"FFFFFFF"
"FFFFGFF"
"FFFGFFF"
"FFGFFFF"
"FFFGFFF"
"FFFFGFF"
"FFFFFFF"
"GGGGGGG"
"GGGGFGG"
"GGGFGGG"
"GGFGGGG"
"GGGFGGG"
"GGGGFGG"
"GGGGGGG"
"HHHHHHH"
"HHHHHHH"
"HHHHHHH"
"HHHHHHH"
"HHHHHHH"
"HHHHHHH"
"HHHHHHH"

Talk:Pseudo-random number generator

2025-02-27T12:46:27Z

Squareroot12621: Forgot to add signature

== Python code in the footnote ==

This code:
<pre>__import__('sys').setrecursionlimit(1<<m);print((λ m,l: (λ g,s: ('\n'*(2-l)).join(map(λ n: str((λ f: f(f))(λ f: λ c,i,o,p: (λ o: 'A('+s(m,n)+')='+str(o)+': '+', '.join(map(λ g: (str(len(tuple(g[1]))) if l else s(m,g[0])+': ('+','.join(map(λ g: '('+str(g[0])+','+str(g[1][1])+')',g[1]))+')'),__import__('itertools').groupby(sorted(enumerate(zip(c,map(λ i: g(n,i),range(1<<n)))),key=λ x: x[1][0]),key=λ x: x[1][0]))) if all(c) else f(f)(c,c.index(0),o,p+1))(o+(c[i]==p)) if c[i] else f(f)(c[:i]+(p,)+c[i+1:],g(n,i),o,p))((0,)*(1<<n),0,0,1)),range(1,m))))(λ n,i: i<<1&(1<<n)-1|i&1^i>>n-1,λ n,k: ' '*(len(str(n))-len(str(k)))+str(k)))(10,False))</pre>
probably should not be in a footnote, because it takes up too much room. Besides, it doesn't even work as Python code, since <code>λ</code> isn't treated the same way as <code>lambda</code>. &horbar;[[User:Squareroot12621|squareroot12621]] ([[User talk:Squareroot12621|talk]]) 12:46, 27 February 2025 (UTC)

Talk:Pseudo-random number generator

2025-02-27T02:06:54Z

Squareroot12621: Added section Python code in the footnote

Why not

2025-02-23T15:34:32Z

Squareroot12621: Add period after July 1977

{{Oscillator
|name = Why not
|pname = whynot
|c = 14
|bx = 7
|by = 7
|fc = 39.9
|p = 2
|m = 2
|h = 15
|v = 0.68
|symmetry = -c
|discoverer = David Buckingham
|discoveryear = 1977
|rulemin = B3/S23
|rulemax = B3678/S2345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B3enqr/S2ci3cy
|isorulemax = B2ikn34-ejkt5-e678/S2345678
|synthesis = 7
|synthesisRLE = true
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ LOOP 2 GPS 2 THUMBSIZE 2 ]]
|apgcode = xp2_4k1u1k4zw121
|pentadecathlonid = 14P2.20
}}
'''Why not''' is a {{period|2}} [[oscillator]] found by [[David Buckingham]] in July {{year|1977}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref>

This oscillator resembles [[by flops]] very strongly; indeed, by flops can be transformed into why not simply by placing an extra cell at one of the two Y-shaped appendages at a given side. Performing this on both sides gives [[why bother]].

== [[List of common oscillators|Commonness]] ==
It first appeared [[natural]]ly on April 15, {{year|2015}}, in a [[soup]] submitted to [[Catagolue]] by [[Brett Berger]].<ref name="post18762" />
{{Needs Catagolue specifics}}

== [[Glider synthesis]] ==
[[Goldtiger997]] found an 8-glider synthesis for the oscillator on August 23, {{year|2016}},<ref name="post34664" /> and reduced the cost to {{gliders|7|brief}} gliders on January 21, {{year|2019}} with [[Tutorials/Glider_syntheses#synthesise-patt.py_-_synthesising_active_objects|a new script for 3-glider collisions]].<ref name="post68316" />

== References ==
<references>
<ref name="post18762">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 18762
|author = Brett Berger
|date = April 16, 2015
}}</ref>
<ref name="post34664">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 34664
|author = Goldtiger997
|date = August 23, 2016
}}</ref>
<ref name="post68316>{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 68316
|author = Goltiger997
|date = January 21, 2019
}}</ref>
</references>

== External links ==
{{LinkLexicon|filename=lex_w.htm#whynot}}
{{LinkCatagolue|xp2_4k1u1k4zw121}}
{{LinkPentadecathlonObject|14P2.20}}

__NOTOC__

Tutorials/General technology

2025-02-22T22:56:42Z

Squareroot12621: Fix consideraion --> consideration

So now, after [[Tutorials/Finding rules|coming across a good cellular automata]], you have decided to do something less abstract with it — something more significant than random [[soup search]]ing and more engaging than automatic [[Tutorials/Software|software]] searching. Then you should begin to consider [[signal]] [[circuitry]], the very connection between microscopic evolution and macroscopic construction. (Actually, that is approximately what [[cellular automata]] were originally created for: the basis of modelling self-replicating systems. But this tutorial does not quite deal with very artificial constructor-computer rules like [http://en.wikipedia.org/wiki/Von_Neumann_cellular_automata JvN29].)

==What is a signal and what do they do?==

A '''signal''' is a moving configuration different from its background, and thus carrying some information from binary presence(1)/absence(0) to [[phase]] [https://conwaylife.com/forums/viewtopic.php?f=2&t=2356 difference]. In terms of cellular automata, the following [[pattern]]s can serve as signals:
*[[Spaceship]]s in an [[Vacuum_(empty_space)|empty medium]],
*[[Fuse]]s, [[drifter]]s and [[negative spaceship]]s in some nonempty media, and
*Active [[reaction]]s, especially [[methuselah]]s, in [[conduit]]s.

A signal travels through the space at a certain [[speed]], which is an important measure since timing (especially synchronization) decides whether signal circuitry works or not.

Signals transform and interact in various ways. A lone signal can be created, reflected and/or flipped, delayed/advanced, multiplicated, transformed into other signal(s), or destroyed. Two or more signals, when [[synchronized]], can be subject to reactions that annihilate or perform logic operations. These rely on some devices, namely [[gun]]s/[[factory]]s, [[reflector]]s, advancer, [[pulse divider]]s, [[fanout]]s, [[converter]]s, [[eater]]s, Boolean [[logic gate]]s, etc.

Note that signal circuitry in cellular automata is very different from that with other physical implementations. For instance, there is no [https://en.wikipedia.org/wiki/Conservation_of_mass law of mass conservation] (i.e. [[population]] count is not fixed for many CAs) nor notion of [https://en.wikipedia.org/wiki/Potential_energy potential] difference in a force field (i.e. translational invariance is held for almost every CA rules).

==How to find these building blocks==

Constructing signal circuitry involves both human idea and computer power. Here are some simple demonstration may provide hints on how to do that.

===Example 1: [[Conway's Game of Life]], with the Gosper glider gun===

====The signal: glider====

Imagine travelling back to the early Life days in the 1970s. When tracking the evolution of small [[polyomino]] patterns, Life enthusiasts observed a moving configuration as follows:

<center>{{LV:Viewer|x = 3, y = 3, rule = B3/S23
bo$2bo$3o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 4 LOOP 4 TRACK 0.25 0.25 ]]
}}</center>

Soon the spaceship became known as the [[glider]], and found its part in the signal circuitry. Let's analyze its movement.

The shown glider travels one cell down and one cell right in four [[tick]]s, during which it shows two alternating shapes in a glide-symmetric manner. To reflect these facts we have some terminologies:
[[Image:Color_of_a_glider.png|x150px|thumb|right|Time-lapse visualization of glider-related concepts]]
* '''[[Phase]]''': the arrangement of cells in one tick. A glider has 4 phases.
* '''[[Period]]''': the minimum number of ticks passed to appear in the same phase. A glider is period 4.
* '''[[Speed]]''': the displacement in a period divided by period. A glider has speed (1,1)[[c]]/4.
* '''[[Mod]]''': because the 1st&3rd phase are identical considering reflection and translation, and so does the 2nd&4th, a glider is said to have a mod of 4/2 = 2.
* '''[[Lane]]''': the diagonal linear region where a travelling glider has covered or will cover. Since it is diagonal, a new metric for the distance parallel and perpendicular to the direction is invented. Define one '''[[half-diagonal]]''' (1hd) as the length of one half diagonal line of the square cell, that is, the distance between the blue line and the red line on the right. Two half-diagonals is a [[full-diagonal]] (1fd), and one half of a half-diagonal is a [[quarter-diagonal]] (1qd).

Additionally, we will need to define '''[[parity]]''' and '''[[color]]''' so as to describe the relationship between two gliders. Gliders in the 1st and 3rd phase (or 2nd and 4th, with pairwise identical shapes) are said to have the same parity. Gliders in the same phase <i>up to rotation but no reflection</i> are considered to have the same color if their corresponding cell coordinates have even sum (or odd sum).

====The signal sink: eater 1====

An important question following the discovery of glider is, what can we use when we want to suppress a glider? A number of collisions between a glider and some simple patterns have been tested. Fortunately, the following 7-cell [[fishhook]]-shaped [[still life]] can kill a glider and then recover in four ticks.

<center>{{LV:Viewer|x = 9, y = 9, rule = B3/S23
bo$2bo$3o3$5b2o$5bobo$7bo$7b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 4 LOOP 12 ]]
}}</center>

This is called an [[eater]], a subgroup of [[catalyst]]s. It is reusable, and it allows for gliders to be eaten at any time without adjusting phases.

====The signal source: Gosper glider gun====

Since the discovery of glider, people have been seeking for patterns that generates gliders. Later, a sustainable collision between two [[queen bee]]s was discovered that could yield gliders again and again. This is known as the period-30 [[Gosper glider gun]]:

<center>{{LV:Viewer|x = 41, y = 27, rule = B3/S23
24bo$22bobo$12b2o6b2o$11bo3bo4b2o12b2o$10bo5bo3b2o12b2o$2o8bo3bob2o4bo
bo$2o8bo5bo7bo$11bo3bo$12b2o$23bo$24b2o$23b2o6$30bobo$31b2o$31bo5$38bo
$39b2o$38b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 AUTOSTART GPS 8 LOOP 30 ZOOM 8 ]]
}}</center>

Generally, a signal device may take a number of inputs and yield some outputs. When there are more outputs than inputs, it is said to be an [[over-unity reaction]]. With assistance, this kind of reactions are useful for constructing signal emitters. Taking no inputs and giving outputs periodically, the Gosper glider gun can be considered a degenerate example of over-unity reaction.

The glider gun has a period of 30, making a stream of gliders with apparent gaps. Indeed, gliders can be packed more densely; the minimum separation is 14 ticks, as can be seen in the [[period-14 glider gun]]. However, attempts to put a glider somewhere so that it goes across the stream perpendicularly unaffected will fail. Actually, the period needs to be at least 38 for two glider streams in order to be permeable:

<center>{{LV:Viewer|x = 49, y = 27, rule = B3/S23
2bo$obo$b2o3$46bobo$46b2o$47bo2$11bo$12bo$10b3o3$38bo$36b2o$37b2o3$21b
o$19bobo$20b2o3$27bobo$27b2o$28bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 ]]
}}</center>

This fact motivates us to find higher-period glider guns. We can simply arrange two period-30 glider guns and see how the gliders interact.

====Signal interactions: glider collisions====

Next, we want to know how gliders can react with each other. Beginning with the simplest case of two gliders, we enumerated [[two-glider collision]]s. Of particular interest are the cases where two gliders destroy each other completely:

<center>{{LV:Viewer|x = 325, y = 35, rule = B3/S23
100bo36bo18bo$4bo18bo19bo16bo19bo18bo19bo16bo18bo36bo$3bo18bo19bo16bo
19bo19b3o16bo17b3o16b3o15bo17bo$3b3o16b3o17b3o14b3o17b3o36b3o51bo18b3o
$172b3o4$136bo$4b3o17b3o89bo18b2o55bo$4bo19bo20bo17bo20bo13b2o15b2o18b
obo14b2o20bo16b2o$5bo19bo18b2o16b2o19b2o13bobo14bobo34bobo18b2o16bobo$
44bobo15bobo18bobo12bo53bo20bobo7$261bo$215bo22bo21bo62bo$176bo15bo21b
o22bo22b3o18bo22bo17bo$175bo15bo22b3o20b3o40bo22bo18b3o$32bo16bo17bo
16bo16bo15bo17bo16bo22b3o13b3o86b3o20b3o$12bo18bo16bo17bo16bo16bo15bo
17bo16bo$11bo19b3o14b3o15b3o14b3o14b3o13b3o15b3o14b3o$11b3o4$170b3o15b
3o59b2o$22b3o16b3o16b3o15b3o15b3o14b3o16b3o15b3o19bo17bo11b2o23b2o20bo
bo20b2o40b2o$3o21bo18bo18bo17bo17bo16bo18bo17bo18bo17bo13b2o23b2o21bo
21b2o12b2o26b2o$2bo20bo18bo18bo17bo17bo16bo18bo17bo50bo24bo44bo15b2o
24bo$bo285bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 WIDTH 1400 HEIGHT 400 ZOOM 4 ]]
}}</center>

These annihilation reactions will be the basis of signal devices below.

Also we observe the cases with clean output glider:

<center>{{LV:Viewer|x = 29, y = 14, rule = B3/S23
7bo$6bo20bo$6b3o17bo$26b3o7$23bo$b2o19b2o$obo19bobo$2bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 ]]
}}</center>

Looking closer, they are actually [[kickback]] reactions in which one of the gliders is reflected 180 degrees, which is somewhat limited. It would be better if there were two-glider collisions in Game of Life that

* give the output on a lane perpendicular to both of the inputs,
* kill one of the inputs while keeping the other unaffected, as in a [[Heisenburp]]-type fly-by deletion, or
* are clean unity or over-unity reactions themselves.

Yet, the 90-degree kickback reaction can be sometimes useful. In the following pattern, two gliders bounce back and forth between two period-30 streams of gliders, deleting every other glider and resulting the following glider gun:

<center>{{LV:Viewer|x = 74, y = 71, rule = B3/S23
67b2o$67b2o6$44bo$42b3o$41bo$41b2o24b3o$66bo3bo$65bo5bo$65bo5bo$68bo$
66bo3bo$67b3o$68bo3$69b3o$69b3o$68bo3bo$62bobo$62b2o3b2o3b2o$25bo37bo$
25b2o20bo$24bobo18bobo$46b2o2$3b2o51bo$3b2o49b2o$55b2o$17b2o$18b2o49b
2o$17bo51b2o3$47bobo$47b2o$10bo37bo$2o3b2o3b2o20bo$9bobo18bobo$bo3bo
25b2o$2b3o$2b3o36bo$39b2o$40b2o$5bo$4b3o$3bo3bo$5bo$2bo5bo$2bo5bo23bob
o$3bo3bo24b2o$4b3o26bo9$5b2o$5b2o3$17bobo$17b2o$18bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 WIDTH 600 HEIGHT 600 ZOOM 8 AUTOSTART GPS 8 LOOP 120 ]]
}}</center>

(Note: the mechanism has an overall period of 120, but the output glider stream is period-60. We consider this as a [[pseudo-period]] 60 glider gun. )

The other 2-glider collisions are not [[clean]], as they leave some debris after interaction. These may also increase the period of a glider stream; as an example, the following [[true-period]] p60 glider gun uses a block-making reaction.

<center>{{LV:Viewer|x = 53, y = 39, rule = B3/S23
23bo$23bobo$26b2o6b2o$12b2o12b2o4bo3bo$12b2o12b2o3bo5bo$23bobo4b2obo3b
o8b2o$23bo7bo5bo8b2o$32bo3bo$34b2o$24bo$22b2o$23b2o6$15bobo$15b2o$16bo
4bo$20b2o$20bobo6$28b2o$27b2o$29bo$39b2o$37bo3bo$obo25bo7bo5bo8b2o$2o
26bobo4b2obo3bo8b2o$bo15b2o12b2o3bo5bo$17b2o12b2o4bo3bo$31b2o6b2o$28bo
bo$28bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 HEIGHT 400 WIDTH 600 ZOOM 8 AUTOSTART GPS 8 LOOP 60 ]]
}}</center>

====Signal reflectors====

Signals don't turn around themselves, so reflectors are needed to adjust their orientation. Generally, a signal reflector takes one input signal and gives one output in a different direction.

With two Gosper glider guns, a period-30 [[glider reflector]] can be constructed. The plan is

* When there is no glider input, the two guns should not emit any glider at all.
* When a third glider comes in, it suppresses one of the two gliders above, leaving another one escape.

Take the first 90-degree annihilation reaction above, and we can construct the following period-30 oscillator with guns in-phase:

<center>{{LV:Viewer|x = 37, y = 43, rule = B3/S23
11bo$11bobo$14b2o6b2o$2o12b2o4bo3bo$2o12b2o3bo5bo$11bobo4b2obo3bo8b2o$
11bo7bo5bo8b2o$20bo3bo$22b2o$12bo$10b2o$11b2o6$3bobo$3b2o$4bo4$5bo$4b
2o$4bobo6$12b2o$11b2o$13bo$23b2o$21bo3bo$12bo7bo5bo8b2o$12bobo4b2obo3b
o8b2o$b2o12b2o3bo5bo$b2o12b2o4bo3bo$15b2o6b2o$12bobo$12bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 600 GPS 8 LOOP 30 ]]
}}</center>

Drop in a third glider so that it destroys one of the gun outputs:

<center>{{LV:Viewer|x = 45, y = 43, rule = B3/S23
19bo$19bobo$22b2o6b2o$8b2o12b2o4bo3bo$8b2o12b2o3bo5bo$19bobo4b2obo3bo
8b2o$19bo7bo5bo8b2o$28bo3bo$30b2o$20bo$o17b2o$b2o16b2o$2o5$11bobo$11b
2o$12bo4$13bo$12b2o$12bobo6$20b2o$19b2o$21bo$31b2o$29bo3bo$20bo7bo5bo
8b2o$20bobo4b2obo3bo8b2o$9b2o12b2o3bo5bo$9b2o12b2o4bo3bo$23b2o6b2o$20b
obo$20bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 600 ]]
}}</center>

That's it, a working 180-degree glider reflector! But with 180-degree reflectors only we cannot get a glider to wherever it needs to be. We will then look for a 90-degree reflector. Relocate the glider so that it destroys a gun output <i>head-on</i> rather than <i>at right angles</i>, which leads to the following two:

<center>{{LV:Viewer|x = 104, y = 43, rule = B3/S23
18bo59bo$18bobo57bobo$21b2o6b2o50b2o6b2o$7b2o12b2o4bo3bo35b2o12b2o4bo
3bo$7b2o12b2o3bo5bo34b2o12b2o3bo5bo$18bobo4b2obo3bo8b2o35bobo4b2obo3bo
8b2o$18bo7bo5bo8b2o35bo7bo5bo8b2o$27bo3bo55bo3bo$29b2o58b2o$19bo59bo$
17b2o58b2o$18b2o58b2o6$o9bobo48bo8bobo$b2o7b2o50b2o6b2o$2o9bo49b2o8bo
4$12bo59bo$11b2o58b2o$11bobo57bobo6$19b2o58b2o$18b2o58b2o$20bo59bo$30b
2o58b2o$28bo3bo55bo3bo$19bo7bo5bo8b2o35bo7bo5bo8b2o$19bobo4b2obo3bo8b
2o35bobo4b2obo3bo8b2o$8b2o12b2o3bo5bo34b2o12b2o3bo5bo$8b2o12b2o4bo3bo
35b2o12b2o4bo3bo$22b2o6b2o50b2o6b2o$19bobo57bobo$19bo59bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 1000 ]]
}}</center>

Why are both included here? Because we start to take color and parity into consideration. As stated above, the relationship between two gliders is described with the concepts of color and parity. As they are independent considerations, there is a total of 2 × 2 = 4 combinations of preserving and changing cases.

However, the color-changing/preserving and parity-changing/preserving considerations are actually insufficient for arbitrary glider timing adjustments. Suppose two 90-degree reflectors are combined into a flexible 180-degree reflector. By moving in or out the composite device by one full diagonal, the path length will be changed both on the outward lane and the inward lane, thereby advancing or delaying the glider by 4 × 2 = 8 ticks. A partial solution is to swap the two 90-degree reflectors when one is color-changing and the other is color-preserving; this changes the timing by 4 ticks. Yet, we still need to develop mechanisms at different mod-8 timings for a complete [[toolkit]].

Another consideration is called [[repeat time]], or [[recovery time]]; it measures the temporal difference between two succesive signals that can be reflected successfully. As demonstrated below, one of the reflectors above has a repeat time of 60 generations.

<center>{{LV:Viewer|x = 59, y = 43, rule = B3/S23
33bo$33bobo$o35b2o6b2o$b2o19b2o12b2o4bo3bo$2o20b2o12b2o3bo5bo$33bobo4b
2obo3bo8b2o$33bo7bo5bo8b2o$42bo3bo$44b2o$34bo$32b2o$33b2o6$15bo9bobo$
16b2o7b2o$15b2o9bo4$27bo$26b2o$26bobo6$34b2o$33b2o$35bo$45b2o$43bo3bo$
34bo7bo5bo8b2o$34bobo4b2obo3bo8b2o$23b2o12b2o3bo5bo$23b2o12b2o4bo3bo$
37b2o6b2o$34bobo$34bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 600 ]]
}}</center>

====Signal inverter/NOT gate/AND (NOT) gate====

A Boolean logic NOT gate, or signal inverter, takes an input and gives an inverted output. When fed with a glider at certain timing, the device should not emit any glider; if no glider enters, it should emit gliders periodically. Such mechanism processes binary digital data, not analogue ones; it won't work if the glider's timing is incorrect.

It is easy to see that two-glider annihilation reactions is the key to inversion:

<center>{{LV:Viewer|x = 49, y = 36, rule = B3/S23
42b2o$42b2o6$obo$b2o$bo$42b3o$41bo3bo$40bo5bo$40bo5bo$8bo34bo$9b2o30bo
3bo$8b2o32b3o$43bo3$44b3o$44b3o$43bo3bo$37bobo$37b2o3b2o3b2o$38bo4$23b
o$24b2o5bo$23b2o4b2o$30b2o2$44b2o$44b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 600 ]]
}}</center>

From this, it seems that a hole (vacancy site) among an [[intermittent stream]] of spaceships is similar to a single spaceship traversing the vacuum in terms of the signal carried. NOT is the most basic operation done to such a stream, and it does not destroy nor create information.

A related operation is AND (NOT), that is, a two-input AND gate with one of its inputs inversed first. We don't actually need a AND gate to do this, though; the following will work. There is an output glider if there is the northeast glider and not the northwest glider:

<center>{{LV:Viewer|x = 71, y = 12, rule = B3/S23
o19bo19bo19bo$2bo5bo12b2o5bo13bo5bo12b2o5bo$2o4bo13b2o4bo13b2o4b2o12b
2o4b2o$7b2o18b2o18b2o18b2o5$7b2o18b2o18b2o18b2o$7bo19bo19bo19bo$8b3o
17b3o17b3o17b3o$10bo19bo19bo19bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 400 WIDTH 600 STOP 40 ]]
}}</center>

An eater absorbes the extra northwest glider in case it doesn't get annihilated.

====OR gate====

A Boolean logic OR gate takes two inputs and gives an output. When fed with at least a glider at certain timing, the device should emit a glider at the same timing. It is the inverse operation of NOR.

The simple fact that <i>A</i> NOR <i>B</i> = 1 AND ( NOT <i>A</i> ) AND ( NOT <i>B</i> ) allows for the construction:

<center>{{LV:Viewer|x = 79, y = 46, rule = B3/S23
24bo$22bobo$12b2o6b2o$11bo3bo4b2o12b2o$10bo5bo3b2o12b2o$2o8bo3bob2o4bo
bo$2o8bo5bo7bo$11bo3bo$12b2o$23bo$24b2o46b2o$23b2o47b2o4$39b2o$39bo12b
obo$30bobo4bobo12b2o$31b2o4b2o14bo$31bo$72b3o$71bo3bo$70bo5bo$30bo39bo
5bo$30b2o6bo34bo$29bobo7b2o30bo3bo$38b2o32b3o$73bo3$74b3o$38b2o34b3o$
39bo5bobo25bo3bo$36b3o7b2o19bobo$36bo9bo20b2o3b2o3b2o$68bo4$53bo$54b2o
5bo$53b2o4b2o$60b2o2$74b2o$74b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 600 WIDTH 800 STOP 120 ]]
}}</center>

Alternatively, a suitable three-glider annihilation can also work in place of two AND (NOT) gates.

<center>{{LV:Viewer|x = 79, y = 46, rule = B3/S23
24bo$22bobo$12b2o6b2o$11bo3bo4b2o12b2o$10bo5bo3b2o12b2o$2o8bo3bob2o4bo
bo$2o8bo5bo7bo$11bo3bo$12b2o$23bo$24b2o46b2o$23b2o47b2o6$30bobo$31b2o$
31bo$72b3o$71bo3bo$70bo5bo$46bo23bo5bo$38bo5b2o27bo$39b2o4b2o24bo3bo$
38b2o32b3o$73bo3$37b2o35b3o$38b2o34b3o$37bo7bobo25bo3bo$46b2o19bobo$
46bo20b2o3b2o3b2o$68bo4$53bo$54b2o5bo$53b2o4b2o$60b2o2$74b2o$74b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 600 WIDTH 800 STOP 120 ]]
}}</center>

Try disabling the northeast glider or the southwest one to see the effect.

Now that an OR gate (and of course a NOR gate) is ready, we may draw the conclusion that this signal circuitry is [[universal computer|universal]] to the same extent as some other implementations of the well-known universal [https://en.wikipedia.org/wiki/NOR_logic NOR logic] — but wait a moment! There are some other issues.

====Signal duplicator/fanout and memory storage====

A signal duplicator takes an input and gives two outputs. It is the simplest case of a fanout (or a splitter), i.e. devices that increase the number of signals.

The period-60 glider gun above shows that a block-synthesizing reaction can consume two gliders in a row, performing NOT operation twice. Then apply NOT again and positive signals are emitted well:

<center>{{LV:Viewer|x = 130, y = 73, rule = B3/S23
30bo$28bobo$18b2o6b2o$17bo3bo4b2o12b2o$16bo5bo3b2o12b2o$6b2o8bo3bob2o
4bobo$6b2o8bo5bo7bo$17bo3bo$18b2o$29bo$30b2o$29b2o3$47bo$45b2o$46b2o$
36bobo$37b2o$37bo$96b2o$96b2o3$44bo$45b2o76b2o$44b2o77b2o4$95b3o$94bo
3bo$51bobo39bo5bo$52b2o39bo5bo$24bo27bo43bo$22bobo69bo3bo24b3o$12b2o6b
2o73b3o24bo3bo$11bo3bo4b2o12b2o60bo24bo5bo$10bo5bo3b2o12b2o15bo69bo5bo
$2o8bo3bob2o4bobo26b2o6bo64bo$2o8bo5bo7bo25bobo7b2o31b3o26bo3bo$11bo3b
o43b2o32b3o27b3o$12b2o78bo3bo27bo$23bo76bobo$24b2o65b2o3b2o3b2o$23b2o
76bo23b3o$125b3o$124bo3bo$118bobo$118b2o3b2o3b2o$108bo10bo$30bobo76b2o
$31b2o75b2o$31bo4bo$36b2o36bo19b2o$35bobo37b2o17b2o16bo$74b2o34b2o$
111b2o2$125b2o$125b2o$28b2o$29b2o$28bo$17b2o$16bo3bo$5b2o8bo5bo7bo$5b
2o8bo3bob2o4bobo$15bo5bo3b2o12b2o$16bo3bo4b2o12b2o48bo$17b2o6b2o63b2o
5bo$27bobo59b2o4b2o$29bo66b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 800 WIDTH 1200 STOP 300 ]]
}}</center>

This is essentially a way to retrieve information. One of the outputs can be circulated back to input:

<center>{{LV:Viewer|x = 136, y = 128, rule = B3/S23
106bo$106bobo$109b2o6b2o$95b2o12b2o4bo3bo$95b2o12b2o3bo5bo$106bobo4b2o
bo3bo8b2o$106bo7bo5bo8b2o$115bo3bo$117b2o$107bo$105b2o$106b2o5$99b2o$
99b2o2$104bo$103b2o$103bobo3$92bo$90b2o$91b2o$111b2o$110b2o$112bo$73b
2o47b2o$74bo45bo3bo$74bobo34bo7bo5bo8b2o$75b2o34bobo4b2obo3bo8b2o$100b
2o12b2o3bo5bo$100b2o12b2o4bo3bo$114b2o6b2o$111bobo$83bo27bo$82b2o$82bo
bo6$90b2o$89b2o$91bo5$98bo$97b2o$30bo66bobo$28bobo$18b2o6b2o$17bo3bo4b
2o12b2o$16bo5bo3b2o12b2o$6b2o8bo3bob2o4bobo$6b2o8bo5bo7bo74b2o$17bo3bo
82b2o$18b2o86bo$29bo86b2o$30b2o82bo3bo$29b2o74bo7bo5bo8b2o$105bobo4b2o
bo3bo8b2o$94b2o12b2o3bo5bo$47bo46b2o12b2o4bo3bo$45b2o61b2o6b2o$46b2o
57bobo$36bobo66bo$37b2o$37bo$96b2o$96b2o3$44bo$45b2o76b2o$44b2o77b2o4$
95b3o$94bo3bo$51bobo39bo5bo$52b2o39bo5bo$24bo27bo43bo$22bobo69bo3bo24b
3o$12b2o6b2o73b3o24bo3bo$11bo3bo4b2o12b2o60bo24bo5bo$10bo5bo3b2o12b2o
15bo69bo5bo$2o8bo3bob2o4bobo26b2o6bo64bo$2o8bo5bo7bo25bobo7b2o31b3o26b
o3bo$11bo3bo43b2o32b3o27b3o$12b2o78bo3bo27bo$23bo76bobo$24b2o65b2o3b2o
3b2o$23b2o76bo23b3o$125b3o$124bo3bo$118bobo$118b2o3b2o3b2o$108bo10bo$
30bobo76b2o$31b2o75b2o$31bo4bo$36b2o36bo19b2o$35bobo37b2o17b2o16bo$74b
2o34b2o$111b2o2$125b2o$125b2o$28b2o$29b2o$28bo$17b2o$16bo3bo$5b2o8bo5b
o7bo$5b2o8bo3bob2o4bobo$15bo5bo3b2o12b2o$16bo3bo4b2o12b2o48bo$17b2o6b
2o63b2o5bo$27bobo59b2o4b2o$29bo66b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 1200 WIDTH 1200 ]]
}}</center>

What's special about this loop? It stores information and sends them repeatedly. By adjusting its memory we can make a stream of gliders distributed in, say, a ...1101000... sequence:

<center>{{LV:Viewer|x = 136, y = 128, rule = B3/S23
106bo$106bobo$109b2o6b2o$95b2o12b2o4bo3bo$95b2o12b2o3bo5bo$106bobo4b2o
bo3bo8b2o$106bo7bo5bo8b2o$115bo3bo$117b2o$107bo$105b2o$106b2o5$99b2o$
99b2o2$104bo$103b2o$103bobo3$92bo$90b2o$91b2o$111b2o$110b2o$112bo$73b
2o47b2o$74bo45bo3bo$74bobo34bo7bo5bo8b2o$75b2o34bobo4b2obo3bo8b2o$100b
2o12b2o3bo5bo$100b2o12b2o4bo3bo$114b2o6b2o$111bobo$83bo27bo$82b2o$82bo
bo6$90b2o$89b2o$91bo5$98bo$97b2o$30bo66bobo$28bobo$18b2o6b2o$17bo3bo4b
2o12b2o$16bo5bo3b2o12b2o$6b2o8bo3bob2o4bobo$6b2o8bo5bo7bo74b2o$17bo3bo
82b2o$18b2o61bo24bo$29bo51b2o33b2o$30b2o48bobo31bo3bo$29b2o74bo7bo5bo
8b2o$105bobo4b2obo3bo8b2o$94b2o12b2o3bo5bo$47bo46b2o12b2o4bo3bo$45b2o
61b2o6b2o$46b2o57bobo$36bobo66bo$37b2o$37bo$96b2o$96b2o2$66bo$44bo21b
2o$45b2o18bobo55b2o$44b2o77b2o4$95b3o$94bo3bo$51bobo39bo5bo$52b2o39bo
5bo$24bo27bo43bo$22bobo69bo3bo24b3o$12b2o6b2o73b3o24bo3bo$11bo3bo4b2o
12b2o60bo24bo5bo$10bo5bo3b2o12b2o15bo69bo5bo$2o8bo3bob2o4bobo26b2o71bo
$2o8bo5bo7bo25bobo40b3o26bo3bo$11bo3bo77b3o27b3o$12b2o78bo3bo27bo$23bo
76bobo$24b2o65b2o3b2o3b2o$23b2o76bo23b3o$125b3o$124bo3bo$118bobo$118b
2o3b2o3b2o$108bo10bo$30bobo76b2o$31b2o75b2o$31bo4bo$36b2o56b2o$35bobo
56b2o16bo$110b2o$111b2o2$125b2o$125b2o$28b2o$29b2o$28bo$17b2o$16bo3bo$
5b2o8bo5bo7bo$5b2o8bo3bob2o4bobo$15bo5bo3b2o12b2o$16bo3bo4b2o12b2o48bo
$17b2o6b2o63b2o5bo$27bobo59b2o4b2o$29bo66b2o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 1200 WIDTH 1200 ]]
}}</center>

====Exercise: XOR gate and AND gate====

OR, XOR and AND are three symmetric two-input Boolean logic gates whose outputs are not trivially all 0's. When an XOR gate is fed with only one of the two gliders at certain timing, the device should emit a glider at the same timing; otherwise the output has no glider. An AND gate emits a glider {{iff}} both glider inputs are fed.

Building these gates is within NOR logic's capability, but can they be simpler? Sure! Now their construction is left to the reader as an exercise.

Hint: there is already an AND (NOT) gate. Another hint: a key XOR reaction is

<center>{{LV:Viewer|x = 10, y = 13, rule = B3/S23
8bo$7bo$7b3o2$2bo$obo$b2o4$4b2o$4bobo$4bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 4 ZOOM 1 ]]
}}</center>

====Scope====

We have demonstrated the signal circuitry technology with gliders, eaters and period-30 Gosper glider guns. Its diverse possibility with simple components has attracted Life enthusiasts [https://conwaylife.com/wiki/File:Lifeline_vol_11_p10.jpg since inception], applications of which goes from [http://pentadecathlon.com/lifeNews/2005/12/rule_110_unit_cell.html an early] [[Rule 110]] [[unit cell]] and [[deep cell]] to [[Pulsar Pixel Display|pulsar pixel raster line display]], [[8-bit programmable computer]] and [[Remini]] self-constructing puffer. Further discussion on the forums can be found [https://conwaylife.com/forums/viewtopic.php?f=2&t=81 here] and [https://conwaylife.com/forums/viewtopic.php?f=2&t=243 here].

There is lots of room for future advancement.

* About the signal: we have used gliders only, going at a fixed direction and speed. However, there are also other signal carriers such as the period-4 c/2 orthogonal spaceships [[LWSS]], [[MWSS]] and [[HWSS]], the perturbation in a diagonal [[2c/3 wire]], and even methuselahs [[Herschel]], [[B-heptomino]], etc. In some cases information transmission and interaction may be better with some of them. But developing other signal circuitry needs pretty different methods, as can particularly be seen in the history of [https://conwaylife.com/ref/lifepage/patterns/bhept/bhept.html Herschel circuitry].
* About the signal devices:
** Their [[bounding box]] cannot be ignored. Sometimes it may be too bulky, in particular the [[clearance]] may be poor in some direction, so that it needs compactifying.
** Their timing should be treated carefully. When shifting a period-30 device so that input glider path lengthens by, say, <i>N</i> full-diagonals, the phase of the device should be delayed by 4<i>N</i> ticks at the same time, which is inconvenient. [[Stable]] circuitry has only one phase, so they do not need to be adjusted. On the other hand, there are many patterns at different periods other than 30 that are equally capable of building signal circuitry with.
** Their mechanism can be more diverse.
*** The inner workings of a Gosper glider gun has not been discussed above, instead it is used as a whole. As a result we missed things like an [[inline inverter]] and the following duplicator.

<center>{{LV:Viewer|x = 49, y = 27, rule = B3/S23
25bo$25bobo$8b2o18b2o4b2o$6bo3bo17b2o4b2o$2o3bo5bo16b2o$2o2b2obo3bo8bo
4bobo$5bo5bo9bo3bo$6bo3bo5bo2b3o$8b2o5$28bo8bo$26bobo6bobo$27b2o4b2o
12b2o$20bobo10b2o12b2o$18bo3bo10b2o$11b2o5bo8b2o6bobo$11b2o4bo4bo3bo2b
o7bo$18bo8b2o$18bo3bo$20bobo2$35b2o$35bobo$35bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 ]]
}}</center>

*** Other patterns with period being a factor of 30 (i.e. p15 [[pentadecathlon]], [[p3 bumper]] and [[p5 bumper]]) or a multiple of 30 (i.e. p120 [[Simkin glider gun]]) exist, and they no doubt can be incorporated in period-30 technology. Even period-1 [[still life]]s can be employed; we missed another small duplicator using a block mentioned in the [[fanout]] article.
*** Can transient (unstable, short-lived) patterns play a part? Yes! As a glider can be reflected by dying [[spark]]s, as shown below with [[duoplet]] and [[banana spark]], there could be a larger class of reflectors (e.g. a [[buckaroo]]) that are not based on 2-glider annihilations, hopefully completing the mod-8 timing toolkit requirement above.

<center>{{LV:Viewer|x = 18, y = 5, rule = B3/S23
2bo10bo$obo8bobo$b2o9b2o$4bo10b2o$3bo13bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
}}</center>

* The constructions so far, or rather, drawing and copy&pasting, have been done manually. For a self-replicating system (like the aforementioned Remini), everything has to be built and destructed by the pattern itself. This is far beyond the scope of this way too basic tutorial, though; more knowledge about [[Tutorials/Seed building|building a seed]] and [[Tutorials/slsparse|using a professional program]] is required.

In the following sections, we will briefly see how signal circuitry can be developed in other cellular automata without the familiar glider. Prerequisities including signal and its source & sink are in fact easy to satisfy for many [[alien]] rules. For those who concentrates on Game of Life, these can be skipped.

===Example 2: Banks-I, with the wire===
{{alsosee|OCA:Banks-I|Introduction to Banks-I}}
Banks-I is an [[isotropic non-totalistic cellular automaton]] for which investigation began in the infant of Game of Life. It was proposed as a CA modelling a general-purpose computer. In this rule, a "wire" consists of a three-cell-thick block of live cells, and a "signal" is carried by a duoplet-shaped perturbation travelling at [[lightspeed]] along the edge of a wire. A five-cell bump extension and an additional cell on the edge can kill a signal.

<center>{{LV:Viewer|x = 52, y = 56, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
o18bo$5ob14o$4ob15o$20o6b5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b
3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b
3o4b2o$16ob3o7b3o4b3o4b3o4b3o$20o7b3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b
3o$27b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o7b3o4b
3o4b3o4b3o$4ob15o7b3o4b3o4b3o4b3o$5ob14o7b3o4b3o4b3o4b3o$o18bo7b3o4b3o
4b2o5b3o$28b2o4b3o4bobo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$
20o6b5o2b5o2b5o2b5o$17ob2o$16ob3o$o18bo5$o13bo4bo$5ob14o$4ob15o$20o6b
5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b
3o$o6bo11bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b4o3b2o$16ob3o7b3o4b3o4b
3o4b3o$20o6b4o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$27b
3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o7b3o4b3o4b3o4b3o$4ob15o7b3o3b
4o4b3o4b4o$5ob14o7b3o4b3o4b3o4b3o$o12bo5bo7b3o4b3o4b2o5b3o$28b2o4b3o4b
obo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o6b5o2b5o2b5o2b5o$
17ob2o$16ob3o$o5bo12bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 WIDTH 600 HEIGHT 600 ]]
}}</center>

Signals can be emitted at regular intervals with a period-2<sup><i>N</i></sup> "clock", or in essence, signal factories. In addition there is a fanout wire junction and a 90-degree reflector.

<center>{{LV:Viewer|x = 30, y = 16, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
5bo11bo$5b13o$bo3b13o$b17o$3obo12bo$4bo5$9bo19bo$9b21o$bo7b21o$b29o$7o
bo20bo$8bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 ]]
}}</center>
<center>{{LV:Viewer|x = 75, y = 28, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
14b5o30b5o$15b3o32b3o$15b3o32bobo$15b3o32b2o$15b3o32b3o$15b3o32b3o$15b
3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$o14b3o32b3o$3ob14o15bo16b3o$
2ob31o16b3o$15o3b16o15b4o$o12b2o3b16o16b3o$13b2o3b3o12bo16b3o$12b4o2b
3o28b4o4bo$18b3o30b7o16bo$18b3o30b24o$18b3o30bo6b17o$18b3o37b17o$18b3o
37bo15bo$18b3o$18b3o$18b3o$18b3o$18b3o$17b5o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 500 ]]
}}</center>

===Example 3: B2a/S, with the replicator===

B2a/S is also an [[isotropic non-totalistic cellular automaton]], but with only one birth transition. It is characterized by the only moving and growing configuration, the [[domino]] [[replicator]], that messes up every random pattern:

<center>{{LV:Viewer|x = 1, y = 2, rule = B2a/S
o$o!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 AUTOSTART GPS 2 PAUSE 2 LOOP 33 T 32 PAUSE 2 ]]
}}</center>

However, the replicator can be tamed by itself. Thus, four such replicators form a stable period-4 oscillator:

<center>{{LV:Viewer|x = 7, y = 7, rule = B2a/S
2bo$2bo$2o2$5b2o$4bo$4bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
}}</center>

Two copies of this loop bounds another replicator, making a period-64 shuttle:

<center>{{LV:Viewer|x = 111, y = 7, rule = B2a/S
2bo105bo$2bo105bo$2o107b2o$39bo$5b2o32bo64b2o$4bo101bo$4bo101bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 WIDTH 1000 ]]
}}</center>

A column of these shuttles at adequate spatial and time offsets serves as the railway for another replicator to run in a single direction:

<center>{{LV:Viewer|x = 111, y = 87, rule = B2a/S
2bo105bo$2bo105bo$2o107b2o$55bo31bo$5b2o48bo31bo16b2o$4bo101bo$4bo101b
o10$2bo105bo$2bo105bo$2o107b2o$39bo$5b2o32bo64b2o$4bo101bo$4bo101bo10$
2bo105bo$2bo105bo$2o107b2o$23bo31bo$5b2o16bo31bo48b2o$4bo101bo$4bo101b
o10$2bo105bo$2bo105bo$2o107b2o$71bo$5b2o64bo32b2o$4bo101bo$4bo101bo10$
2bo105bo$2bo105bo$2o21b2o84b2o$55bo31bo$5b2o48bo31bo16b2o$4bo101bo$4bo
101bo10$2bo105bo$2bo105bo$2o107b2o$39bo$5b2o32bo64b2o$4bo101bo$4bo101bo!
#C [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ZOOM 8 HEIGHT 1000 WIDTH 1000 ]]
}}</center>

That's it, a signal! Elaboration on the scheme is up to the reader.

===Example 4: Live Free or Die, with the puffers and rakes===

Live Free or Die (B2/S0) is an explosive rule. There are small spaceships and [[puffer]]s and [[rake]]s; with several reactions such as [[catch and throw]], [[fly-by deletion]] and [[reanimation]], a [https://conwaylife.com/forums/viewtopic.php?p=107139#p107139 Rule 110 simulator] has come to life. In-depth analysis is also up to the reader.

==Summary==

Be innovative! There are lots of wonders on the journey of alien signal circuitry. To summarize the idea:

Before setting off, search for interesting patterns. The components of signal circuitry — still lifes, oscillators, spaceships, guns, methuselahs and many thing else — can arise in random [[soup]] searching, for example. Advanced patterns like [[Tutorials/Finding conduits|conduits]] and [[Tutorials/Catalyses|catalysts]] require sophisticated search utilities and ideas.

Make sure what will be the signal, and list its properties. Compare with the glider above in case you are not sure what to do. Good signals are small and [[common]]/[[natural]] ones.

Construct signal source and sink (if these cannot be found, then probably you need to turn to other signals), and then, construct devices based on signal interactions.

Build complex patterns ([[infinite growth]] at different rates, [[unit cell]] for different CAs, even [[engineered spaceship]]s if equipped with knowledge on construction, etc), post them to the [https://conwaylife.com/forums/viewforum.php?f=11 Other Cellular Automata] subforum in the Conwaylife.com forums, have fun and profit (e.g. getting an entry in [[OCADOTY]])!

As for the classical Game of Life, well, good luck with crazy, brand new applications!

{{Tutorial}}

Lx65 duplicator

2024-09-20T10:47:16Z

Squareroot12621: Remove extra "can".

{{Conduit
|name = Lx65 duplicator
|pname = lx65r64
|type = elementary
|conduitfor = Herschel
|c = 50
|bx = 28
|by = 14
|m = R
|dx = 11
|dy = 9
|step = 64
|recovery = 46
|dependent = no
|spartan = yes
|discoverer = Mitchell Riley
|discoveryear = 2024
|rulemin = B3/S23
|rulemax = B38/S238
|isorulemin = B3/S23
|isorulemax = B34ce8/S234ce8
|rle = true
|viewerconfig = #C [[ ZOOM 12 GPS 20 WIDTH 560 HEIGHT 560 THUMBSIZE 2 PAUSE 2 T 64 PAUSE 2 T 65 PAUSE 2 LOOP 66 ]]
}}

'''Lx65 Duplicator''' (full technical name: '''Lx65_R64''') is an [[elementary]] [[Herschel]] [[fanout]] conduit. It was discovered by [[Mitchell Riley]] on September 13, {{year|2024}}.<ref name="message1284172080513941617" /> It is a duplicator which acts as an [[R64]] conduit and an [[Lx65]] conduit. Both [[ghost Herschel]]s mark the output locations.

Its [[recovery time]] is 46 ticks if both of the [[FNG]]'s are suppressed -- e.g., if both output Herschels are connected to [[dependent conduit]]s. Both FNGs can hit and destroy each other if both are left unperturbed. If the FNGs are [[eat]]en, through the use of [[7x9 eater]]s with one [[weld]]ed to a [[eater 5]], the recovery time is 61 ticks.

The Lx65 duplicator is a completely [[stable]] [[Lx65]] conduit, which means that conduits with unusual periods can use this duplicator to rotate and flip a Herschel left. It is also both compact and spartan, consisting of two [[block]]s, one [[eater 1]], and one [[loaf]] which acts as a [[transparent object]].

==Gallery==
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = lx65r64improve
|viewerconfig = #C [[ AUTOSTART ZOOM 6 GPS 20 WIDTH 700 HEIGHT 500 PAUSE 2 T 150 PAUSE 2 T 215 PAUSE 2 T 216 PAUSE 2 LOOP 317 ]]
|position = center
|caption = [[Composite]] conduit with an Lx65_R64 conduit improved with repeat time 61<ref name="message194030" />
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = lx65chain
|viewerconfig = #C [[ AUTOSTART ZOOM 5 GPS 60 WIDTH 700 HEIGHT 500 PAUSE 2 LOOP 320 ]]
|position = center
|caption = Chain of Lx65 conduits<ref name="message194032" />
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = p256hfactory
|viewerconfig = #C [[ AUTOSTART ZOOM 6 GPS 60 WIDTH 700 HEIGHT 500 LOOP 256 ]]
|position = center
|caption = {{period|256}} Herschel [[factory]]<ref name="message194038" />
|style = width:300px;
|apgcode = xp256_yg2552zyhs2mzyi2078ykggzyc32acyec871y4h98gwoge2zyaoowcik8yk33w121yf696zygcczyboggzyd23wggc173ypo8zyi123ys113zyzya66zcicyfg8gwooyk2596w33zyb8e13w12ihy4gs26ye6a8ozyj11zzyzy88kk8
}}}}
{{gallery item|{{EmbedViewer
|position = center
|caption = Periodic p4, p5 and p6 Herschel duplicators based on Lx65.
|viewerconfig = #C [[ HEIGHT 320 WIDTH 1100 ZOOM 6 GPS 10 AUTOSTART T 0 PAUSE 2 T 64 PAUSE 2 T 65 PAUSE 2 LOOP 66 ]]
|rle = x = 164, y = 28, rule = B3/S23
14b2o63b2o63b2o$15bo13b2o49bo64bo$15b3o11bobo48b3o62b3o$31bo2b2o$26bo
2bob2o2b2o$2o23bobobo5bobob2o24b2o63b2o$bo22b2o5b2o2bob2obo25bo23bo3b
2o35bo23b2o$bobo20b2o3b2o2bobo30bobo20bobobobo35bobo20bo2bo$2b2o19bo3b
obob2o2bo31b2o20bobobo38b2o20bobobo$22bo2b2o2bobo3b2o51b2obob2o58b2obo
bo$22bo4b3obo55bo3bo3bo59bobob2o$22bo8b2o54bo4bobobo53b2o2b2obo2bo$22b
o4b3obo55bo3b2o3bo59bobobob2o$22bo2b2o2bobo3b2o50bo4bob2o57b2obob3o2bo
$23bo3bobob2o2bo51bo3bo62bo2bo3b2o$2bo21b2o3b2o2bobo31bo20b2obob5o34bo
21bob5o$2bobo19b2o5b2o2bob2obo26bobo19bobo2bo2bo34bobo20bo4bo$2b3o20bo
bobo5bobob2o26b3o19bo2bo39b3o21b4o$4bo21bo2bob2o2b2o32bo20b2o42bo23bo$
31bo2b2o124bo$29bobo127b2o$29b2o4$14b3o62b3o62b3o$14bo64bo64bo$13b2o
63b2o63b2o!
|style = width:300px
}}}}
{{gallery bottom}}

==References==
<references>
<ref name="message1284172080513941617">{{CiteDiscord
|author = Mitchell Riley
|date = September 13, 2024
|channel = cgol
|id = 1284172080513941617
}}</ref>
<ref name="message194030">{{LinkForumThread
|format = ref
|title = Re: The Hunting of the Elementary Conduits
|author = Entity Valkyrie 2
|date = September 13, 2024
|p = 194030
}}</ref>
<ref name="message194032">{{LinkForumThread
|format = ref
|title = Re: The Hunting of the Elementary Conduits
|author = Confocaloid
|date = September 13, 2024
|p = 194032
}}</ref>
<ref name="message194038">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|author = Period1GliderGun
|date = September 13, 2024
|p = 194038
}}</ref>
</references>

==See also==
* [[Lx65]]
* [[R64]]
* [[Bx106]]
* [[Fanout]]

Eater head siamese eater tail

2024-09-08T17:39:09Z

Squareroot12621: Shrink the pattern in the infobox slightly.

{{Stilllife
|name = Eater head siamese eater tail
|pname = eaterheadsiameseeatertail
|c = 12
|bx = 7
|by = 4
|fc = 19.9
|symmetry = n
|discoverer = Robert Wainwright
|discoverer2 = Everett Boyer
|discoveryear = 1973
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], {{rl|HighLife}}
|isorulemin = B/S2aek3jnr
|isorulemax = B2-ae34-an5-q678/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs12_178c453
|niemiecid = 12.85
|pentadecathlonid = 12.23
|viewerconfig = [[ ZOOM 44 ]]
}}
'''Eater head siamese eater tail''' (or '''eater [[siamese]] eater''', or '''eater with [[nine]]''') is a {{slcells|12|text=12-cell}} [[still life]].

== Occurrence ==
{{related|List of common still lifes}}
Eater head siamese eater tail is the fifty-eighth [[List of common still lifes|most common still life]] in [[Achim Flammenkamp's census]], being less common than [[cis-boat on dock]] but more common than [[cis-block on long bookend]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>

It is the 57th most common still life on [[Adam P. Goucher]]'s [[Catagolue]], being less common than [[trans-bookend and bun]] but more common than [[block on cover]]. It is the 5th most common still life with 12 cells, being less common than [[trans-block on long bookend]] but more common than [[block on cover]].<ref>{{citeCatagolueStats|May 5, 2023}}</ref>

The [[octo3obj database]] contains 19 matches for collisions with the still life present in the ash.

== Construction ==
{{gliders|4|text=Four gliders}} suffice to construct this still life.<ref name="xs12_178c453" /> Different known [[Glider synthesis|syntheses]] can be found in [[Mark Niemiec's database]].<ref name="niemiec" />

{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 23, y = 22, rule = B3/S23
o$b2o$2o3$15b2o$15bobo$15bo3$8b3o$10bo$9bo7$20b2o$20bobo$20bo!
|viewerconfig = #C [[ THEME Book ZOOM 10 X 0 Y -2 AUTOSTART GPS 12 T 0 PAUSE 3 T 88 PAUSE 2 LOOP 89 ]]
|position = center
|caption = A 4G synthesis<ref name="xs12_178c453" />
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 90, y = 29, rule = B3/S23
43b2o$43b2o$2o$obo56b3o17b3o$2bo$2b2o38bo45b2o$3bo38bo21b2o18b2o2b2o$
3o20bo18bo21b2o18b2o$o22bobo9b3o$15bo7b2o$15bo49bo19bo$15bo49bo19bo$
20bo44bo19bo$19bobo$19bobo$20bo$13b3o4$58bo$57b2o$57bobo4$49b2o18b2o$
50b2o18b2o$49bo19bo!
|viewerconfig = #C [[ THEME Book ZOOM 6 AUTOSTART GPS 12 T 0 PAUSE 3 T 96 PAUSE 2 LOOP 97 ]]
|position = center
|caption = Four [[1G seed]]s from the [[octo3obj database]]
|style = width:300px;
}}}}
{{gallery bottom}}

== See also ==
* [[Eater 1]]
* [[Eater head siamese eater head]]
* [[Eater tail siamese eater tail]]
* [[Shuriken]]

== References ==
<references>

<ref name="xs12_178c453">[https://catagolue.hatsya.com/object/xs12_178c453/b3s23 xs12_178c453] on [[Catagolue]]</ref>
<ref name="niemiec">{{LinkNiemiec|p1-12.htm|The 121 twelve-bit still-lifes|rle=12/12-85.rle|nobullet=nobullet}}</ref>

</references>

== External links ==
* {{LinkCatagolue|xs12_178c453|patternname=Eater with nine}}
* {{LinkPentadecathlonObject|id=12.23|archivedate=20221029054939}}

__NOTOC__

Isotropic non-totalistic rule

2024-09-01T13:06:35Z

Squareroot12621: Slightly clearer wording in Dualities.

An '''isotropic non-totalistic rule''' (abbreviated '''INT''') is a generalization of the concept of a [[Life-like rule]], where the state of a cell after one [[tick]] depends on how the alive neighbours are arranged, not just their counts.

Patterns in isotropic non-totalistic rules preserve their behaviour when mirrored or rotated, as is the case in totalistic and outer-totalistic rulespaces. This is not necessarily the case for [[non-isotropic rule]]s.

== Square grid ==
For generalisations of usual outer-totalistic rules,<ref group="note">rules that operate on the [[square grid]], with a [[Moore neighbourhood]] of range 1, and two [[cellstate]]s</ref> the following notation system is used. This notation is often referred to as ''Hensel notation'', a system originally devised and named after [[Alan Hensel]].

[[Rulestring]]s use the standard B[counts]/S[counts] system, the same as with outer-totalistic rules. Letters can be appended to each number to specify if birth or survival should happen depending on how surrounding cells are arranged; a minus sign can be placed between the number and letters to instead exclude listed arrangements. If a number is not followed by any letters, all arrangements will be accepted, as is the case for outer-totalistic rules.

For example, the rule {{rl|tlife}} differs from [[Life]] in two ways:
* a living cell ''will not survive'' if it has two diametrically-opposite orthogonal neighbours, like the central cell of a [[blinker]],
* a living cell ''will survive'' if it has four neighbours, like the two middle cells in the [[beacon]]'s dense phase.

tlife otherwise functions identically to Life. We can express tlife using Hensel notation, which gives the rulestring ''B3/S2-i34q'' - survival on 2i is negated using a preceding minus sign, and survival on 4q is permitted. Birth and survival on 3 neighbours do not have any extra letters, indicating that arrangement is ignored for these. Note the similarity to Life's rulestring, ''B3/S23'', since there are only two cases where behaviour is different.

A full list of letters and what arrangements they correspond to is as follows:
{{Isotropic non-totalistic transitions (square grid)}}

== Hexagonal grid ==
Much like the Moore neighbourhood of the square grid, it is possible to define isotropic non-totalistic rules on the [[hexagonal grid]]. The standard notation used for the hexagonal grid, ''Callahan notation'', was devised by [[Paul Callahan]] and generalises outer-totalistic hexagonal rulestrings in much the same way as for square-grid Moore rulestrings. The higher symmetry of hexagons combined with the smaller number of neighbours results in a comparatively smaller transition table, requiring only three letters compared to the thirteen needed for the square grid; these were chosen in analogy to arene substitution patterns<ref>{{LinkWikipedia|Arene_substitution_pattern|name=Arene substitution pattern|nobullet=nobullet}}</ref> in aromatic chemistry.<ref>{{LinkCallahan|hexrule.txt|patternname=Experiments with a somewhat "Life-like" hexagonal CA (long)}}</ref><ref>{{cite web|url=https://conwaylife.com/forums/download/file.php?id=261|title=ExtendedCallahanHexagonal.gif|work=ConwayLife.com forums|accessdate=December 8, 2018}}</ref>

A full list of transitions is as follows:
{{Isotropic non-totalistic transitions (hexagonal grid)}}

== Generalizations ==
{{main|Higher-range isotropic non-totalistic rule}}
Isotropic non-totalistic rules can be generalized to higher ranges, higher cell state counts and other grid types.

== Properties ==

=== Hensel's notation ===
This notation has the following symmetry: For any letter ''x'' and number {{nowrap|''n'' ≠ 4}}, ''nx'' is defined if and only {{nowrap|(8 - ''n'')''x''}} is defined and moreover {{nowrap|(8 - ''n'')''x''}} is the complement (change live cells to dead and dead cells to live; ignore the center cell) of ''nx''.

==== Ability for a pattern to escape its bounding shape ====
To allow patterns to exceed their initial bounding box, a rule must have at least one of B1(c,e), B2(c,a) and B3i enabled, and to escape their bounding diamond, at least one of B1(c,e), B2(e,a), B3a.

Irrespective of other transitions, for patterns in a rule to be able to exit their bounding octagon, of the 2<sup>7</sup> combinations across these 7 transitions, those where any of B1c, B1e and B2a are enabled provide 2<sup>6</sup>+2<sup>5</sup>+2<sup>4</sup>, leaving only 2<sup>4</sup> cases in which both B2e and B2c, or both B3i and B3a, must be on, of which there are 7 such cases, providing an upper bound of 119/128ths of the 2<sup>102</sup> such INT rules. These are necessary for spaceships, as well as for a finite pattern to be [[Turing-complete]] (because otherwise, it may only enter fixedly many states depending on its initial size).

What restrictions apply for rules with B0 remain to be described.

==== von Neumann emulation ====
The <tt>2<sup>6</sup>=64</tt> isotropic 2-state rules in the [[von Neumann neighbourhood]] can be simulated via isotropic non-totalistic rules on the Moore neighbourhood; for example, B1/SV becomes B1e2ak3inqy4ny5e/S.

To be a von Neumann rule, birth and survival transitions in the following equivalence classes must be the same:
:<tt>0 : 0=1c=2n=2c=3c=4c</tt>

:<tt>1 : 1e=2a=2k=3i=3n=3y=3q=4n=4y=5e</tt>

:<tt>2e: 2e=3k=3a=3j=4k=4a=4q=4w=5a=5j=5k=6e</tt>
:<tt>2i: 2i=3r=4i=4t=4z=5r=6i</tt>

:<tt>3 : 3e=4j=4r=5i=5n=5y=5q=6a=6k=7e</tt>

:<tt>4 : 4e=5c=6c=6n=7c=8</tt>

For it to be outer-totalistic, the <tt>2e</tt> and <tt>2i</tt> transitions must be equivalent.

A similar set of constraints is given in the static symmetry article, that are sufficient for the preservation of [[Minor static symmetries#D8_2 symmetry|D8_2 symmetry]].

==== Dualities ====
<div class="mw-collapsible mw-collapsed">Note that though the black/white reversal exists for all rules, in general the [[strobing dual]] of a rule is a pair of INT rules that alternate over time (even and odd iterations), and the [[checkerboard dual]] a pair that alternate over space (even and odd squares in a chequerboard tiling). The members of each pair coincide in duals of [[self-complementary]] rules (that are their own [[black/white reversal]]), such as [[OCA:Day & Night|Day & Night]]. Each self-complementary rule is a member of an equivalence class, not of a pair, but of a quartet.<div class="mw-collapsible-content">

They are generated as follows,
* For the black/white reversal, take the bitwise NOT of the input and output.
* For the strobing dual,
:: in even generations, take the bitwise NOT of the output, and
:: in odd generations, take the bitwise NOT of the input.
* For the checkerboard dual,
:: for even-parity cells, XOR the input with an "X" in the four corners and centre, and
:: for odd-parity cells, XOR the input with an "O" in the four edges.
<tt>
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! Outer<br>total
! Identity
! colspan="2" | [[Black/white reversal|Black/white<br>reversal]]
! colspan="4" | [[Strobing dual|Strobing{{br}}dual]]
! colspan="4" | [[Checkerboard dual|Checkerboard{{br}}dual]]
|-
|rowspan="2"| ||rowspan="2"| ||rowspan="2"|b||rowspan="2"|s||colspan="2"|even||colspan="2"|odd|| colspan="2" |even
| colspan="2" |odd
|-
| b || s || b || s || b || s || b || s
|-
| 0|| ||~s8 ||~b8 ||~b0 ||~s0 || s8 || b8 ||~s4c||~b4c|| b4e|| s4e
|-
|rowspan=" 2"|1||c||~s7c||~b7c||~b1c||~s1c|| s7c|| b7c||~s3c||~b3c|| b5c|| s5c
|-
|e||~s7e||~b7e||~b1e||~s1e|| s7e|| b7e||~s5e||~b5e|| b3e|| s3e
|-
|rowspan=" 6"|2||c||~s6c||~b6c||~b2c||~s2c|| s6c|| b6c||~s2c||~b2c|| b6c|| s6c
|-
|e||~s6e||~b6e||~b2e||~s2e|| s6e|| b6e||~s6e||~b6e|| b2e|| s2e
|-
|k||~s6k||~b6k||~b2k||~s2k|| s6k|| b6k||~s4n||~b4n|| b4r|| s4r
|-
|a||~s6a||~b6a||~b2a||~s2a|| s6a|| b6a||~s4y||~b4y|| b4j|| s4j
|-
|i||~s6i||~b6i||~b2i||~s2i|| s6i|| b6i||~s6i||~b6i|| b2i|| s2i
|-
|n||~s6n||~b6n||~b2n||~s2n|| s6n|| b6n||~s2n||~b2n|| b6n|| s6n
|-
|rowspan="10"|3||c||~s5c||~b5c||~b3c||~s3c|| s5c|| b5c||~s1c||~b1c|| b7c|| s7c
|-
|e||~s5e||~b5e||~b3e||~s3e|| s5e|| b5e||~s7e||~b7e|| b1e|| s1e
|-
|k||~s5k||~b5k||~b3k||~s3k|| s5k|| b5k||~s5a||~b5a|| b3a|| s3a
|-
|a||~s5a||~b5a||~b3a||~s3a|| s5a|| b5a||~s5k||~b5k|| b3k|| s3k
|-
|i||~s5i||~b5i||~b3i||~s3i|| s5i|| b5i||~s3y||~b3y|| b5y|| s5y
|-
|n||~s5n||~b5n||~b3n||~s3n|| s5n|| b5n||~s3n||~b3n|| b5n|| s5n
|-
|y||~s5y||~b5y||~b3y||~s3y|| s5y|| b5y||~s3i||~b3i|| b5i|| s5i
|-
|q||~s5q||~b5q||~b3q||~s3q|| s5q|| b5q||~s3q||~b3q|| b5q|| s5q
|-
|j||~s5j||~b5j||~b3j||~s3j|| s5j|| b5j||~s5j||~b5j|| b3j|| s5j
|-
|r||~s5r||~b5r||~b3r||~s3r|| s5r|| b5r||~s5r||~b5r|| b3r|| s3r
|-
|rowspan="13"|4||c||~s4e||~b4e||~b4c||~s4c|| s4e|| b4e||~s0 ||~b0 || b8 || s8
|-
|e||~s4c||~b4c||~b4e||~s4e|| s4c|| b4c||~s8 ||~b8 || b0 || s0
|-
|k||~s4k||~b4k||~b4k||~s4k|| s4k|| b4k||~s4a||~b4a|| b4a|| s4a
|-
|a||~s4a||~b4a||~b4a||~s4a|| s4a|| b4a||~s4k||~b4k|| b4k|| s4k
|-
|i||~s4t||~b4t||~b4t||~s4t|| s4t|| b4t||~s4i||~b4i|| b4t|| s4t
|-
|n||~s4r||~b4r||~b4r||~s4r|| s4r|| b4r||~s2k||~b2k|| b6k|| s6k
|-
|y||~s4j||~b4j||~b4j||~s4j|| s4j|| b4j||~s2a||~b2a|| b6a|| s6a
|-
|q||~s4w||~b4w||~b4w||~s4w|| s4w|| b4w||~s4w||~b4w|| b4q|| s4q
|-
|j||~s4y||~b4y||~b4y||~s4y|| s4y|| b4y||~s6a||~b6a|| b2a|| s2a
|-
|r||~s4n||~b4n||~b4n||~s4n|| s4n|| b4n||~s6k||~b6k|| b2k|| s2k
|-
|t||~s4i||~b4i||~b4i||~s4i|| s4i|| b4i||~s4t||~b4t|| b4i|| s4i
|-
|w||~s4q||~b4q||~b4q||~s4q|| s4q|| b4q||~s4q||~b4q|| b4w|| s4w
|-
|z||~s4z||~b4z||~b4z||~s4z|| s4z|| b4z||~s4z||~b4z|| b4z|| s4z
|-
|rowspan="10"|5||c||~s3c||~b3c||~b5c||~s5c|| s3c|| b3c||~s7c||~b7c|| s1c|| b1c
|-
|e||~s3e||~b3e||~b5e||~s5e|| s3e|| b3e||~s1e||~b1e|| b7e|| s7e
|-
|k||~s3k||~b3k||~b5k||~s5k|| s3k|| b3k||~s3a||~b3a|| b5a|| s5a
|-
|a||~s3a||~b3a||~b5a||~s5a|| s3a|| b3a||~s3k||~b3k|| b5k|| s5k
|-
|i||~s3i||~b3i||~b5i||~s5i|| s3i|| b3i||~s5y||~b5y|| b3y|| s3y
|-
|n||~s3n||~b3n||~b5n||~s5n|| s3n|| b3n||~s5n||~b5n|| b3n|| s3n
|-
|y||~s3y||~b3y||~b5y||~s5y|| s3y|| b3y||~s5i||~b5i|| b3i|| s3i
|-
|q||~s3q||~b3q||~b5q||~s5q|| s3q|| b3q||~s5q||~b5q|| b3q|| s3q
|-
|j||~s3j||~b3j||~b5j||~s5j|| s3j|| b3j||~s3j||~b3j|| b5j|| s5j
|-
|r||~s3r||~b3r||~b5r||~s5r|| s3r|| b3r||~s3r||~b3r|| b5r|| s5r
|-
|rowspan=" 6"|6||c||~s2c||~b2c||~b6c||~s6c|| s2c|| b2c||~s6c||~b6c|| b2c|| s2c
|-
|e||~s2e||~b2e||~b6e||~s6e|| s2e|| b2e||~s2e||~b2e|| b6e|| s5e
|-
|k||~s2k||~b2k||~b6k||~s6k|| s2k|| b2k||~s4r||~b4r|| b4n|| s4n
|-
|a||~s2a||~b2a||~b6a||~s6a|| s2a|| b2a||~s4j||~b4j|| b4y|| s4y
|-
|i||~s2i||~b2i||~b6i||~s6i|| s2i|| b2i||~s2i||~b2i|| b6i|| s6i
|-
|n||~s2n||~b2n||~b6n||~s6n|| s2n|| b2n||~s6n||~b6n|| b2n|| s2n
|-
|rowspan=" 2"|7||c||~s1c||~b1c||~b7c||~s7c|| s1c|| b1c||~s5c||~b5c|| b3c|| s3c
|-
|e||~s1e||~b1e||~b7e||~s7e|| s1e|| b1e||~s3e||~b3e|| b5e|| s5e
|-
|8|| ||~s0 ||~b0 ||~b8 ||~s8 || s0 || b0 ||~s4e||~b4e|| b4c|| s4c
|}</tt>
</div></div>

== Software support ==
Support for isotropic non-totalistic rules on the square grid was implemented into [[Golly]] in August 2016 with the release of version 2.8. Prior to this, they could be ran as custom table rules under the [[RuleLoader]] algorithm, for which this was widely used. As of August 2024, Golly does not support Callahan notation for hexagonal rules.

[[LifeViewer]] supports Hensel notation for the square grid as of build 177 (officially build 182),<ref>https://conwaylife.com/forums/viewtopic.php?f=3&t=1622&p=29766#p29766</ref> and Callahan notation as of build 313.<ref>https://conwaylife.com/forums/viewtopic.php?f=3&t=1622&p=73364#p73364</ref>

[[Adam P. Goucher]]'s [[apgsearch]] was modified to support isotropic non-totalistic rules by [[praosylen]] on December 17, 2015.<ref name="post25942" /> This hacked version was later modified in late January 2016 to be able to upload the search results to [[Catagolue]].<ref name="post26878" /> However, apgsearch did not gain native support for these rules until v4.2, released on September 10, 2017, which can search isotropic non-totalistic rules without [[B0]].<ref name="post50771" /> v4.66 and above also support the searching of isotropic hexagonal neighbourhood rules.<ref name="post66090" />

== See also ==
* [[Life-like cellular automaton]]
* [[Non-isotropic cellular automaton]]
* [[Generations]]
* [[Larger than Life]]
* [[:Category:Dualities|Dualities]]
:* [[Checkerboard dual]]
* [[List of isotropic non-totalistic cellular automata]]

== Notes ==
<references group="note"/>

== References ==
<references>
<ref name="post25942">{{LinkForumThread
|format = ref
|f = 9
|t = 1480
|p = 25942
|author = praosylen
|title = Re: Hacking apgsearch
|date = December 17, 2015
}}</ref>
<ref name="post26878">{{LinkForumThread
|format = ref
|f = 7
|t = 1784
|p = 26878
|author = Adam P. Goucher
|title = Re: apgsearch v2.2
|date = January 21, 2016
}}</ref>
<ref name="post50771">{{LinkForumThread
|format = ref
|title = Re: apgsearch v4.2
|p = 50771
|author = Adam P. Goucher
|date = September 10, 2017
}}</ref>
<ref name="post66090">{{LinkForumThread
|format = ref
|p = 66090
|title = Re: Non-totalistic hex rules
|author = Adam P. Goucher
|date = December 1, 2018
}}</ref>
</references>

== External links ==
* {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors2.html|title=Table of non-totalistic neighborhoods|accessdate=2016-06-12}}
* {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors.html|title=Rule notation|accessdate=2016-06-12}} (note that the linked page describes an earlier version of Hensel notation that has fallen into disuse)
* {{LinkForumThread|f=11|t=936|title=Non-totalistic Rules - notations, projects, & discussion}}

[[Category:Cellular automata| Isotropic non-totalistic cellular automaton]]
[[Category:Isotropic non-totalistic rules| Isotropic non-totalistic cellular automaton]]

User:Squareroot12621/CSM/Lessons

2024-07-11T17:11:27Z

Squareroot12621: Finished 2 and part of 3.

''Main page: [[User:Squareroot12621]]''<br>
''CSM subpage: [[User:Squareroot12621/CSM]]''

This page contains drafts for lessons in Conway's Story Mode.

== Lesson 1: What ''Is'' CGoL? ==
=== Text ===
*Conway's Game of Life is a "zero-player game," devised by mathematician John Conway in 1969.
*CGoL, as we'll call it, operated on an infinite square grid. Each square in this grid is called a ''cell''.
*Each cell can have two states: alive and dead. We'll mark alive cells in light colors, and dead cells in dark colors.
*In CGoL, you set up some configuration of alive and dead cells (called a ''pattern''), at the start.
*After that, each cell changes according to its own state, as well as the states of its ''neighbors''.
*A cell has 8 neighbors, arranged in a ring. Here, the orange cells are neighbors of the white cell:
:{{EmbedViewer
|rle = x = 3, y = 3, rule = csmcolors
3C$CAC$3C!
|position = left
|viewerconfig = #C [[ WIDTH 480 HEIGHT 570 THUMBSIZE 4 ZOOM 64 GRID GRIDMAJOR 0 COLOR GRID 64 64 64 ]]
}}
<div style="margin-bottom:148pt"></div>
*You'll learn more about the rules that the cells follow to change state in the next lesson, Lesson 2.
*For now, though, you'll just be given a question to answer. Don't worry, it's not that hard.

=== Question ===
'''Question:''' Which sample configuration has more alive cells?
{{EmbedViewer
|rle = $2b5bo$3bo3bobo$3bo3bo$3bo3bo2bo$2bo5b2o$8bobo!
|position = left
|viewerconfig = #C [[ WIDTH 900 HEIGHT 700 THUMBSIZE 4 ZOOM 64 GRID OFF THEME Mono X 1 Y 0.5 LABELZOOMRANGE 1 999 LABEL 2.5 -1.2 16 "A" POLYLINE -0.5 -0.5 5.5 -0.5 5.5 7.5 -0.5 7.5 -0.5 -0.5 32 LABEL 8.5 -1.2 16 "B" POLYLINE 5.5 -0.5 11.5 -0.5 11.5 7.5 5.5 7.5 5.5 -0.5 32 ]]
}}
<div style="margin-bottom:176pt"></div>
'''A:''' Oops! This only has 4 alive cells, which is smaller than the 10 alive cells that B has. ''(gives 1 star)''<br>
'''B:''' Great job! B does have more cells than A, with 10 alive cells compared to 4. ''(gives 3 stars)''

== Lesson 2: What Do Cells Do? ==
=== Text ===
*Last lesson, you learned that CGoL is made of cells that, collectively, make up a square grid.
*However, when you place the cells down, they don't just sit around doing nothing all day.
*Instead, the entire grid goes through ''generations'', or iterations, which happen to every cell at once.
*During a generation, each cell changes state according a few simple rules:
*'''1.''' If an alive cell is surrounded by two or three other alive cells, it stays alive.
*'''2.''' If a dead cell is surrounded by exactly three alive cells, it becomes alive.
*'''3.''' All other cells become dead. (So tragic.)
*Fortunately, in this program, you won't have to simulate any patterns yourself—the computer will.
*This lesson has an exercise, and in it, you'll just get to know the CGoL Simulator.
*To finish the exercise, all you'll have to do is run a certain pattern to a certain point.

=== Exercise ===
'''Objective:''' This is the CGoL Simulator. All you have to do here is run this sample pattern for 100 generations. You can see the generation number at the top.<br>
'''Library:''' ''None.''<br>
'''Pattern:'''
{{EmbedViewer
|rle = bo2bo$2o$o3bo$2o2bo$bob2o$2bo!
|position = left
|viewerconfig = #C [[ WIDTH 480 HEIGHT 640 THUMBSIZE 4 ZOOM 64 GRID GRIDMAJOR 0 COLOR GRID 64 64 64 THEME Mono ]]
}}
<div style="margin-bottom:164pt"></div>

'''Hint:''' You can run the pattern by pressing the ⏵ button at the top of the screen.<br>
'''Win Condition:''' The pattern is run for 100 generations.<br>
'''1 Star:''' ''None.''<br>
'''2 Stars:''' ''None.''<br>
'''3 Stars:''' The pattern is run for 100 generations.<br>
'''Win Text:''' Great job! You'll learn more about what the pattern created in the next lesson.

== Lesson 3: Basic Objects ==
=== Text ===
*When you ran that last pattern, the end result was that two different objects appeared:
:{{EmbedViewer
|rle = 2o3bo$2o3bo$5bo!
|position = left
|viewerconfig = #C [[ WIDTH 480 HEIGHT 320 THUMBSIZE 4 ZOOM 64 GRID GRIDMAJOR 0 COLOR GRID 64 64 64 THEME Mono X 0.5 ]]
}}
<div style="margin-bottom:101pt"></div>
*In this lesson, we'll look at both of these objects, and we'll even make another one in the Exercise.
*First, let's look at the 2×2 square on the left. This object is called a ''block''.
:[viewer]
*As you saw in the pattern (hopefully), the block doesn't really look like it's changing.
*Similar objects are called ''still lifes'', or ''still lives'' if your device has autocorrect.
*Now, the object on the right is a bit different. This object has been named the ''blinker''.
:[viewer]
*However, it is actually not a still life, because it has two different states that it switches between.
*These different ''phases'' are what put things like blinkers in a different category, called ''oscillators''.
*Oscillators also have a ''period'', which is the number of phases it cycles through. A blinker has a period of 2.
*And, yes, still lifes are technically just period-1 oscillators, but it's easier to think of them as being…well, still lifes.
*In this lesson's exercise, you'll make another still life—the beehive.

User:Squareroot12621/CSM/Lessons

2024-07-11T01:15:10Z

Squareroot12621: Created page. Will do Lessons 2+ later.

User:Squareroot12621/CSM

2024-07-10T23:46:38Z

Squareroot12621: Created page.

''Main page: [[User:Squareroot12621]]''

'''Conway's Story Mode''' (CSM) is an attempt to make Conway's Game of Life more accessible to beginners. The main thread is located [https://conwaylife.com/forums/viewtopic.php?f=7&t=6053 here], and this subpage contains drafts for CSM.

== Sections ==

[[User:Squareroot12621/CSM/Lessons]]

User:Squareroot12621

2024-07-10T23:38:42Z

Squareroot12621: Added CSM section.

I'm squareroot12621, an irrational number. I've been on [https://conwaylife.com/forums/ the forums] since 2022, but I didn't get an account on LifeWiki until 2024.

Also, in case you're wondering, {{sqrt|12621}} is about 112.343.

== squareroot12621's Rules ==
; [[Rule:Supercomputer|Supercomputer]] ([https://conwaylife.com/forums/viewtopic.php?f=12&t=5647&p=186853#p186417 thread])
: A 9-state circuitry rule, with a display state. A working computer is in progress.

== Conway's Story Mode ==
'''Conway's Story Mode''' (CSM) is an attempt to make Conway's Game of Life more accessible to beginners. The original thread can be found [https://conwaylife.com/forums/viewtopic.php?f=7&t=6053 here], and some drafts for CSM can be found in the subpages below.

[[User:Squareroot12621/CSM]]
:[[User:Squareroot12621/CSM/Lessons]]

Pulsar

2024-06-06T00:50:02Z

Squareroot12621: "A 8-cell" --> "An 8-cell"

{{Oscillator
|name = Pulsar
|pname = pulsar
|c = 48
|bx = 15
|by = 15
|fc = 12.1
|p = 3
|m = 3
|h = 42.7
|v = 0.73
|rotor = Pulsar
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B3578/S023678
|isorulemin = B3ainq/S2-cn3ejnr
|isorulemax = B2i34-aeiwz56-in78/S01c234-jny5-e678
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xp3_co9nas0san9oczgoldlo0oldlogz1047210127401
|pentadecathlonid = 48P3.1
|animated = true
|viewerconfig = #C [[ HEIGHT 600 THUMBSIZE 3 ZOOM 30 GPS 2 ]]
}}
'''Pulsar''' (rarely referred to as '''Cambridge pulsar CP 48-56-72'''{{refn|group=note|The numbers refer to [[Population signature|the populations of the three phases]]. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.}}) is a large but surprisingly common {{period|3}} [[oscillator]]. It was found by [[John Conway]] in March {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref>

== Extensions and interactions ==
The [[rotor]] of a pulsar consists of four mutually stabilizing quadrants; alternate arrangements exist for any odd multiple of 4 (for the version with 12 copies, see [[quasar]]). A closely related oscillator — the [[pulsar quadrant]] — includes just the external "horns" of the rotor and can be stabilized on its own.

Two other oscillators, the [[bracket pulsar]] and [[cross]], can be extended in much the same way.

{{EmbedViewer
|pname = pulsarlikeoscillators
|viewerconfig = #C [[ GPS 4 LOOP 3 ZOOM 12 ]]
|position = center
|caption = The pulsar (left), cross (center) and bracket pulsar (right)
|style = width:300px;
}}

===Arms===
There exists a heptomino, that acts as a p3 oscillator partial but can mutually stabilise with a quadrant of the pulsar's nucleus, replacing a standard horn in its blinker phase to comprise an "arm" and causing it to undergo a different period-3 evolutionary sequence. Due to its interference with the quadrant's nucleus, only a single arm may exist per quadrant. Despite an arm requiring the flipping of only six cells' states in this phase, no arm variant has occurred naturally, assumedly due to the pulsar's fragility. However, the two variants with two arms in D2_+1 symmetry,<ref group=note name="var1_d2plus1" /> and the variants with four arms in D4_+1 and C4_1 symmetry,<ref group=note name="var2_d4plus1_c41" /> have occurred seminaturally.

The same heptomino can also mutually support a quadrant from a different orientation, replacing another quadrant as one of its two supports, allowing two distinct two-quadrant half-pulsars with arms.
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 99, y = 78, rule = B3/S23
9b2o$10b2o$4b3o3b2o$11bo$2bo4bobo4bo$2bo4bobo4bo$2bo4bobo4bo$4b3o3b3o
2$4b3o3b3o$2bo4bobo4bo$2bo4bobo4bo$2bo4bobo4bo2$4b3o3b3o6$6b2ob2o15b2o
60b2o$5b2o3b2o13b2o60b2o$5b2o3b2o13b2o3b3o11b3o3b3o13b3o3b3o12b2o3b3o$
5bo5bo13bo61bo$2bo4bobo4bo7bo4bobo17bobo14bo4bobo12bo4bobo4bo$2bo4bobo
4bo7bo4bobo3b3o5b3o3bobo3b3o8bo4bobo3b3o6bo4bobo4bo$2bo4bobo4bo7bo4bob
o4b3o3b3o4bobo4b3o7bo4bobo4b3o5bo4bobo4bo$4b3o3b3o11b3o3b3o3bo3bo3b3o
3b3o3bo9b3o3b3o3bo7b3o3b3o2$4b3o3b3o11b3o3b3o11b3o3b3o9bo3b3o3b3o11b3o
3b3o3bo$2bo4bobo4bo7bo4bobo4bo7bo4bobo4bo7b3o4bobo4bo7bo4bobo4b3o$2bo
4bobo4bo7bo4bobo4bo7bo4bobo4bo8b3o3bobo4bo7bo4bobo3b3o$2bo4bobo4bo7bo
4bobo4bo7bo4bobo4bo14bobo4bo7bo4bobo2$4b3o3b3o11b3o3b3o11b3o3b3o13b3o
3b3o11b3o3b3o6$6b2ob2o15b2ob2o18b2o17b2o$5b2o3b2o13b2o3b2o18b2o15b2o$
5b2o3b2o13b2o3b2o12b3o3b2o15b2o3b3o$5bo5bo13bo5bo19bo15bo$2bo4bobo4bo
7bo4bobo4bo12bobo4bo9bo4bobo$2bo4bobo4bo7bo4bobo4bo6b3o3bobo4bo9bo4bob
o3b3o$2bo4bobo4bo7bo4bobo4bo5b3o4bobo4bo9bo4bobo4b3o$4b3o3b3o11b3o3b3o
7bo3b3o3b3o13b3o3b3o3bo2$o3b3o3b3o11b3o3b3o11b3o3b3o13b3o3b3o$3o4bobo
4bo7bo4bobo4bo7bo4bobo4bo9bo4bobo4bo$b3o3bobo4bo7bo4bobo4bo7bo4bobo4bo
9bo4bobo4bo$7bobo4bo7bo4bobo4bo7bo4bobo4bo9bo4bobo4bo$25bo19bo21bo$4b
3o3b3o12b2o3b3o12b2o3b3o14b2o3b3o$25b2o18b2o20b2o$26b2o18b2o20b2o4$6b
2ob2o15b2o$5b2o3b2o13b2o41b2o$5b2o3b2o13b2o3b3o11b3o3b3o14b2o$5bo5bo
13bo41b2o3b3o$2bo4bobo4bo7bo4bobo17bobo17bo$2bo4bobo4bo7bo4bobo3b3o5b
3o3bobo3b3o8bo4bobo$2bo4bobo4bo7bo4bobo4b3o3b3o4bobo4b3o7bo4bobo3b3o$
4b3o3b3o11b3o3b3o3bo3bo3b3o3b3o3bo7bo4bobo4b3o$66b3o3b3o3bo$4b3o3b3o
11b3o3b3o11b3o3b3o$2bo4bobo4bo7bo4bobo4bo7bo4bobo4bo7bo3b3o3b3o$2bo4bo
bo4bo7bo4bobo4bo7bo4bobo4bo7b3o4bobo4bo$2bo4bobo4bo7bo4bobo4bo7bo4bobo
4bo8b3o3bobo4bo$5bo5bo13bo5bo13bo5bo17bobo4bo$5b2o3b2o13b2o3b2o13b2o3b
2o21bo$5b2o3b2o13b2o3b2o13b2o3b2o14b3o3b2o$6b2ob2o15b2ob2o15b2ob2o21b
2o$71b2o!
|viewerconfig = #C [[ GPS 4 LOOP 3 ZOOM 6 HEIGHT 600 ]]
|position = center
|caption = All pulsar arm variants
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 31, y = 13, rule = B3/S23
26b2o$25b2o$4bo5bo9bo4b2o$4bo5bo9bo4bo$4b2o3b2o9b2o2b3o$24bobobo$3o2b
2ob2o2b3ob3o2b2ob2o2b3o$2bobobobobobo5bobobo$4b3ob3o9b3o2b2o$5bo3bo11b
o4bo$4b2o3b2o9b2o4bo$4b2o3b2o9b2o$3b2o5b2o7b2o!
|viewerconfig = #C [[ GPS 4 LOOP 3 ZOOM 12 ]]
|position = center
|caption = The cis- and trans- forms<ref group=note name="var3_cis_trans" /> of the half-pulsar with arms
|style = width:300px;
}}}}
{{gallery bottom}}

===Dependent oscillators===

{{EmbedViewer
|rle = x = 28, y = 28, rule = B3/S23
2b3o3b3o2$o4bobo4bo$o4bobo4bo$o4bobo4bo$2b3o3b3o2$2b3o3b3o$o4bobo4bo$o
4bobo4bo$o4bobo4bo2$2b3o3b3o3$9b2o6b3o3b3o$10bo$6b4ob2o2bo4bobo4bo$10b
obo2bo4bobo4bo$10bo4bo4bobo4bo$10bo6b3o3b3o$10bo$17b3o3b3o$15bo4bobo4b
o$15bo4bobo4bo$15bo4bobo4bo2$17b3o3b3o!
|viewerconfig = #C [[ GPS 4 LOOP 3 ZOOM 12 HEIGHT 600 ]]
|position = center
|caption = Two can support a [[Highest volatility period-3 oscillators|highly volatile small period-3 oscillator]] that contains a tub in one phase (as [[seminatural]]ly occurred in [[tetramer]] form<ref group=note name="var4_tetramer" />)
|style = width:300px;
|apgcode = xp3_s0111s0s1110szo0555o0o5550oz1044410144401zy24445r4cws0111s0s1110szy63y0o0555o0o5550ozyb1044410144401
}}

== Occurrence ==
{{related|List of common oscillators}}
Despite its size, pulsar is the fourth most common oscillator (and the most common of [[period]] greater than 2) in [[Achim Flammenkamp's census]]; the only oscillators more common are [[blinker]], [[toad]], and [[beacon]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is by far the most common period-3 oscillator, being about 45,000 times more common than [[jam]].<ref>{{citeCatagolue|page=census/b3s23/C1|title=Census|accessdate=October 27, 2018}}</ref> Overall, the pulsar is the twenty-first most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref name="statistics">{{citeCatagolueStats|March 1, 2023}}</ref>

Compared to Catagolue's typical {{times|16|16}} soups, the pulsar is 30% more common in {{times|8|8}} soups and 14% more common in {{times|10|10}} soups; this is probably because a pulsar is more likely to survive if there is nothing around it.

The pulsar-on-[[pentadecathlon]] I is the largest object to have occurred in the B3/S23/C1 census as of July 2023, with 100 cells in its maximum phase, and with first known natural occurrence on Catagolue in April {{year|2015}}.<ref name="post18884" /><ref name="statistics" />

The smallest pattern by population that evolves into a pulsar has seven cells; there are several of these.{{refn|group=note|An example is {{headerlessRLE|3bo$o5bo$b2ob2o!}}, which evolves into another 7-cell predecessor after one tick.}}

== Construction ==

Pulsar can be [[Glider synthesis|constructed]] with {{gliders|3|text=3 gliders}}; there are multiple known syntheses.<ref name="niemiec" /><ref group=note name="octo" />

A direct [[Herschel]]-to-pulsar [[factory]] was found by yoleo in October 2023.<ref name="post169256" />
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 41, y = 33, rule = B3/S23
30bo5bo$30bo5bo$30b2o3b2o2$26b3o2b2ob2o2b3o$bo7b2o17bobobobobobo$b2o6b
obo18b2o3b2o$obo6bo$30b2o3b2o$28bobobobobobo$26b3o2b2ob2o2b3o2$30b2o3b
2o$30bo5bo$30bo5bo16$24b3o$24bo$25bo!
|viewerconfig = #C [[ HEIGHT 450 THEME Book ZOOM 10 X -2 Y -4 AUTOSTART GPS 12 T 0 PAUSE 3 T 8 PAUSE 1 T 87 PAUSE 1 T 152 PAUSE 1 T 209 PAUSE 1 T 230 PAUSE 1 LOOP 231 ]]
|position = center
|caption = A [[Three-glider collision|three-glider synthesis]]<ref name="niemiec" />
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 30, y = 14, rule = B3/S23
19b3o3b3o2$17bo4bobo4bo$bo15bo4bobo4bo$2bo14bo4bobo4bo$3o16b3o3b3o2$
19b3o3b3o$17bo4bobo4bo$17bo4bobo4bo$17bo4bobo4bo2$2o2b2o13b3o3b3o$2o2b2o!
|viewerconfig = #C [[ HEIGHT 450 THEME Book ZOOM 10 X -4 Y 0 AUTOSTART GPS 12 T 0 PAUSE 3 T 16 PAUSE 1 T 50 PAUSE 1 T 54 PAUSE 1 T 78 PAUSE 1 T 90 PAUSE 1 LOOP 91 ]]
|position = center
|caption = A [[Blockic]] [[one-glider seed]] for the pulsar<ref name="niemiec" /><ref name="post8334" />
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 41, y = 46, rule = B3/S23
8b2o$8b2o6b2o$16bo$14bobo$14b2o2$11b2o$10bo2bo$2b2o7b2o$bobo$bo$2o5$5b
o$5bobo$5b3o$7bo2$39b2o$39b2o10$23b2o$22bobo$22bo$21b2o7$27b2o$26bobo$
26bo$25b2o!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 10 X 4 Y 0 THEME Book AUTOSTART T 0 PAUSE 3 T 299 PAUSE 1 LOOP 300 ]]
|position = center
|caption = H-to-pulsar [[factory]]<ref name="post169256" />
|style = width:300px;
}}}}
{{gallery bottom}}

== In other rules ==

In {{rl|Pedestrian Life}} (B38/S23), the pulsar is about 400 times less common than in [[Life]] because the [[pre-pulsar]] does not evolve into it. However, there are new predecessors, making it still the most common period-3 oscillator.<ref>{{citeCatagolue|page=census/b38s23/C1|title=census/b38s23/C1|accessdate=March 19, 2023}}</ref>
{{EmbedViewer
|rle = x = 12, y = 5, rule = B38/S23
2bo$bobo5b3o$o3bo4bo$bobo5b3o$2bo!
|viewerconfig = #C [[ HEIGHT 450 THEME Book ZOOM 20 X 2 Y 0 AUTOSTART GPS 8 T 0 PAUSE 3 T 44 PAUSE 1 LOOP 45 ]]
|position = center
|caption = A pulsar evolving from a pre-traffic light and a [[pi heptomino]] in {{rl|Pedestrian Life}}
|style = width:300px;
}}

As a more extreme example, the pulsar is about 1500 times less common in {{rl|Grounded Life}} (B35/S23) than in [[Life]] because the [[pre-pulsar]] does not evolve into it, instead evolving to a common alien oscillator. Furthermore, there are no new predecessors, accounting for the extreme increase in rarity. Despite all of these, it still the most common period-3 oscillator.
{{EmbedViewer
|rle = x = 5, y = 3, rule = B35/S23
o3bo$2ob2o$o3bo!
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 3 ZOOM 36 GPS 2 AUTOSTART ]]
|position = center
|caption = An 8-cell [[pre-pulsar]] predecessor from Life is a p4 oscillator in Grounded Life
}}

On the other hand, in {{rl|EightLife}} (B3/S238), the pulsar is 170 times more common than in [[Life]] because the [[pi-heptomino]] evolves into it.<ref>{{citeCatagolue|page=census/b38s23/C1|title=census/b3s238/C1|accessdate=March 26, 2023}}</ref>
{{EmbedViewer
|rle = x = 3, y = 3, rule = B3/S238
3o$obo$obo!
|viewerconfig = #C [[ HEIGHT 450 THEME Book ZOOM 15 AUTOSTART GPS 15 T 0 PAUSE 3 LOOP 135 ]]
|position = center
|caption = A pulsar evolving from a [[pi heptomino]] in {{rl|EightLife}}
|style = width:300px;
}}

== See also ==
* [[Pre-pulsar]]
* [[Quasar]]
* [[Pulsar Pixel Display]]

== Notes ==
<references group="note">
<ref name="octo">There are 77 matches for the pulsar in the [[octo3g database]] (out of 464746 lines). There are also 404 matches in the [[octo3obj database]] (out of 3421907 lines), and 99 matches in the [[octohash database]] (out of 455380 lines). If all collisions with at least one occurrence of pulsar in the ash are included, then there are 632 results in the octo3g database (including three collisions with two pulsars in the ash), 4833 results in the octo3obj database (including 53 results with two pulsars in the ash) and 551 results in the octohash database (including two collisions with two pulsars in the ash).</ref>
<ref name="var1_d2plus1">{{LinkCatagolue|xp3_gwe7h0h7ewgz30kkk303kkk03z70ggg707ggg07|patternname=variant 1|style=raw}}, {{LinkCatagolue|xp3_w8ogx7kz36ada7079fa63zc65rle0e9v56czw11y0e2|patternname=variant 2|style=raw}}</ref>
<ref name="var2_d4plus1_c41">{{LinkCatagolue|xp3_xk7x7kz36af97079fa63zc65v9e0e9v56czx2exe2|patternname=D4_+1 variant|style=raw}}, {{LinkCatagolue|xp3_wgwe7h0g444zg030kkk303kkk1336z1332ggg707gow7zy5231|patternname=C4_1 variant|style=raw}}</ref>
<ref name="var3_cis_trans">{{LinkCatagolue|xp3_co9nac0can9oczwhhg505ghh|patternname=cis- form|style=raw}}, {{LinkCatagolue|xp3_w8ogwk1hhz36ad2b06ati36zw4441|patternname=trans- form|style=raw}}</ref>
<ref name="var4_tetramer">{{LinkCatagolue|xp3_ybs0111s0s1110szy6u0gwo0555o0o5550owg0uzy21115611w1044410144401w1165111zs0111s0s1110syds0111s0s1110szo0555o0o5550oydo0555o0o5550oz1044410144401yd1044410144401zy24445r4cws0111s0s1110swc4r5444zy63y0o0555o0o5550oy03zyb1044410144401|patternname=tetramer form|style=raw}}</ref>
</references>

== References ==
<references>
<ref name="niemiec">{{LinkNiemiec|p3.htm#g3-p3|title=The 1 period 3 oscillator buildable from 3 gliders|rle=lg/48pu.rle|nobullet=nobullet}}</ref>
<ref name="post8334">{{LinkForumThread
|format = ref
|p = 8334
|title = Blockic Seeds
|author = knightlife
|date = June 23, 2013
}}</ref>
<ref name="post18884">{{LinkForumThread
|format = ref
|p = 18884
|title = Re: Soup search results
|author = gameoflifeboy
|date = April 20, 2015
}}</ref>
<ref name="post169256">{{LinkForumThread
|format = ref
|p = 169256
|title = Re: Thread For Your Useless Discoveries
|author = yoleo
|date = October 17, 2023
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_p.htm#pulsar}}
* {{LinkCatagolue|xp3_co9nas0san9oczgoldlo0oldlogz1047210127401}}
* {{LinkPentadecathlonObject|id=48P3.1|archivedate=20221104142127|patternname=Pulsar}}

{{Symmetry|full}}
{{Sparker|p=3|strength=weak}}

[[Category:Extendable oscillators]]

Spark

2024-06-06T00:45:13Z

Squareroot12621: "a 8-cell" --> "an 8-cell"

{{Glossary}}
A '''spark''' is a [[pattern]] that dies. The term is typically used to describe a collection of [[cell]]s periodically thrown off by an [[oscillator]] or [[spaceship]], but other dying patterns, particularly those consisting of only one or two cells (such as those produced by certain [[glider]] collisions, for example), are also described as sparks. For examples of small sparks see [[unix]] and [[heavyweight spaceship]].

{{EmbedViewer
|pname = unix
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 3 ]]
|position = center
|caption = The two sparks of [[unix]]
|style = width:300px;
}}

== Long-lived sparks ==
Seven sparks that are longer-lived are shown below:
* Top left: Very common, although not that long-lived (7 generations). Note that the longest-lived spark in this list goes through this phase near the end.
* Top middle left: The [[table]], which becomes the [[line-of-six spark]] in three generations and dies twelve later, for a total lifespan of 15.
* Top middle right: An 8-tick predecessor of the [[phi spark]], which is very common. The phi spark lasts 9 generations, giving a total of 17 generations. This is not the only way a phi spark can form.
* Top far right: A fairly common unnamed sequence that dies out in 16-20 generations depending on the phase it enters the sequence. It does not get large enough to qualify as an object in the [[list of common evolutionary sequences]].
* Bottom left: A common way for a c/2 frontend to die, resulting in an edgeshot spark. The block isn't the only thing that can perturb the B-heptomino. In the form shown, it lasts 21 generations.
* Bottom middle left: The [[Z-hexomino]], which lasts 45 generations before dying completely. It is only common in rotationally symmetric soups.
* Bottom middle right: A [[two-glider collision]] that lasts 94 generations before dying completely.
* Bottom right: The original [[diehard]]. The version shown below lasts 137 generations, but patterns often enter later in the sequence. It is moderately common.

{{EmbedViewer
|pname = longlivedsparks
|viewerconfig = #C [[ GPS 12 ZOOM 8 ]]
|position = center
|caption = The seven sparks described above
|style = width:300px;
}}

There is also a large symmetric spark that arises from an 8-cell pattern<ref>Headerless RLE: {{headerlessRLE|bo3bo$3ob3o!}}</ref> consisting of two [[T]]s placed one cell apart. This spark can be harnessed to create a glider rake, one of which is included with [[Golly]]'s basic rake examples.

==Sparker==
A '''sparker''' is an oscillator or spaceship that produces sparks.<ref>{{CiteLexicon|file=lex_s.htm#sparker|name=Sparker|accessdate=May 24, 2009}}</ref>

Sparkers can produce a variety of different sparks:<ref>{{LinkNiemiec|lifeterm.htm#spark|title=Sparkers|nobullet=nobullet}}</ref> A reference collection of oscillating sparkers up to period 16 can be found on [https://conwaylife.com/forums/viewtopic.php?p=173952#p173952 this forum thread].

* [[Dot]]: A single detached bit at an edge.
** Edge bit: A detached dot spark caused by the birth of three cells in a line, e.g. [[middleweight volcano]].
** [[Corner dot|Corner bit]]/diagonal bit: A detached dot spark caused by the birth of three cells that form a [[pre-block]]-like shape, e.g. [[blocker]].
** Fountain bit: A dot spark with no other bits in the row behind it, e.g. [[fountain]], or [[superfountain]] if there are no live cells in the next two rows.
* [[Domino]]: Two orthogonally connected bits at an edge, detached from the rest of an oscillator.
** Horizontal domino: A domino spark parallel to the edge it appears on, e.g. [[heavyweight volcano]].
** Vertical domino: A domino spark perpendicular to the edge it appears on. Oscillators that make these are called "pipsquirters", e.g. [[pipsquirter 1]].
** Delayed domino: A domino spark where one bit appears first, and the other is added later, e.g. [[figure eight]].
** Fountain domino: A domino spark with no other bits in the two rows behind it, e.g. [[258P3]].
* [[Duoplet]]: Two diagonally connected detached bits at a corner, e.g. [[Merzenich's p31]]. Historically sometimes also called a "diagonal domino", but it is not a [[polyomino]].
** Non-reflecting duoplet: A duoplet spark that is incapable of reflecting gliders, e.g. [[41P7.2]].
** Reflecting duoplet: A duoplet spark that is capable of reflecting gliders, e.g. [[34P14 shuttle]].
* [[Banana spark]]: A three-bit spark capable of reflecting gliders, e.g. [[buckaroo]].
* [[Finger]]: Like a vertical domino, but the domino is attached orthogonally to something, e.g. [[T-nosed p4]].
* [[Thumb]]: Like a corner bit, but the dot is diagonally attached to something, e.g. [[Thumb 1]].
* [[Obo spark]]: two dot sparks separated by one empty cell. This often has a 1-generation predecessor of a {{times|3|3}} square with two corners missing, such as in [[Beluchenko's p40]] and [[p76 pi-heptomino hassler]].

Sparkers are often referred to by their type of spark. For example, '''dot sparker''' and '''domino sparker'''. [[David Raucci]] has coined the term '''functional dot sparker''' for sparkers that are not dot sparkers but can act like one, e.g. vertical dominoes, duoplets and thumb sparkers.<ref name="post148136" />

==Strength of sparkers==
A sparker oscillator can be considered "strong", "moderate" or "weak" depending on its relation to the rest of the oscillator. This does not necessarily correlate to how accessible the spark is, because examples like [[101]] which have very inaccessible sparks are still considered "strong" under the following classification scheme:

* "Strong": the oscillator creates a spark that is a separate [[island]], and the oscillator is not affected if the spark is removed, e.g. [[unix]], [[blocker]] and [[middleweight volcano]].
* "Moderate": the oscillator creates a spark that is a separate island, but the spark is still required for the oscillator to survive, e.g. [[mold]], [[fumarole]] and [[figure eight]].
* "Weak": the oscillator includes one or more cells at its edge that remain connected to the oscillator, but can still be used to [[catalyst|catalyze]] other nearby patterns, e.g. [[caterer]], [[T-nosed p4]] and [[thumb 1]].

==Smoke==
'''Smoke''' is debris that is fairly long-lived but eventually dies out completely. Thus, it is basically a large spark, but the term is used especially when talking about the output from a [[spaceship]] (as in a [[Types of spaceships#Smoking ship|smoking ship]]).<ref>{{CiteLexicon|lex_s.htm#smoke|name=Smoke|accessdate=June 10, 2009}}</ref>

==Tail spark==
A '''tail spark''' is a spark that appears at the back of a spaceship.<ref>{{CiteLexicon|lex_t.htm#tailspark|name=Tail spark|accessdate=May 21, 2009}}</ref> For example, there is a one-[[bit]] tail spark at the back of a [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]] in their less dense [[phase]]s.

==Belly spark==
The '''belly spark''' is the part of a [[middleweight spaceship]]'s or [[heavyweight spaceship]]'s spark that is not its tail spark.<ref>{{CiteLexicon|file=lex_b.htm#bellyspark|title=Belly spark|accessdate=May 14, 2016}}</ref>

==See also==
* {{CategoryLink|Sparkers}}
* [[Fallback]]

==References==
<references>
<ref name="post148136">{{LinkForumThread
|format = ref
|title = Re: Thread for basic questions
|author = David Raucci
|p = 148136
|date = July 10, 2022
}}</ref>
</references>

==External links==
* {{LinkWikipedia|Spark_(cellular_automaton)}}
* {{LinkLexicon|lex_s.htm#spark}}
* {{LinkForumThread|f=2|t=5821|title=The Hunting of the Spark Conduits}}

[[Category:Sparks| ]]

Queen bee shuttle

2024-06-06T00:27:24Z

Squareroot12621: "a 18-cell-wide" --> "an 18-cell-wide"

{{Oscillator
|name = Queen bee shuttle
|pname = transqueenbeeshuttle
|family = Queen bee shuttle
|f1 = Shuttle
|c = 20
|bx = 22
|by = 7
|fc = 28.4
|p = 30
|m = 15
|h = 17.9
|v = 0.96
|sv = 0.96
|discoverer = Bill Gosper
|discoverer2 = Robert W. April
|discoverer3 = Richard P. Howell
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-k/S23-kr
|isorulemax = B2n34ceqyz5jkq6-in7c8/S234cekz5ekr6-ac7c8
|synthesis = 5
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xp30_w33z8kqrqk8zzzx33
|pentadecathlonid = 20P30.2
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 21 GPS 10 ]]
}}
The '''queen bee shuttle''' (or '''basic shuttle'''<ref>{{CiteLexicon|file=lex_b.htm#basicshuttle|name=Basic shuttle|accessdate=June 11, 2009}}</ref>) can refer to one of two very closely related {{period|30}} [[shuttle]] [[oscillator]]s in which a [[queen bee]] travels back and forth between two [[block]]s (see [[#Isomers|Isomers]]). It was found by [[Bill Gosper]] in {{year|1970}}<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> and was the first period-30 oscillator to be found. In terms of its minimum population of {{cells|20}} [[cell]]s, it is the smallest known oscillator with period greater than 15.<ref>{{cite web|url=https://web.archive.org/web/20220520073223/http://www.pentadecathlon.com/objects/class2/class2.php?part=1 |title=Class 2 Objects Catalog - Oscillators |accessdate=April 8, 2009}}</ref>

The queen bee shuttle is the basis of [[Gosper glider gun]], the first known and most compact gun in Game of Life.

== Isomers ==
There are two possible [[isomer]]s for the queen bee shuttle; the version shown in the infobox to the right being the "[[trans]]"-version.

=== Cis-queen bee shuttle ===
{{EmbedViewer
|pname = cisqueenbeeshuttle
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 10 AUTOSTART ]]
|position = center
|caption = Cis-queen bee shuttle; blocks are "on the same side" ([[kinetic symmetry]] n-e)
|style = width:300px;
|apgcode = xp30_w33z8kqrqk8zzzw33
}}

=== Trans-queen bee shuttle ===
{{EmbedViewer
|pname = transqueenbeeshuttle
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 10 AUTOSTART ]]
|position = center
|caption = Trans-queen bee shuttle; blocks are "on different sides" ([[kinetic symmetry]] n.e)
|style = width:300px;
|apgcode = xp30_w33z8kqrqk8zzzx33
}}

=== Comparison ===
{| class="wikitable" style="margin-left:auto; margin-right:auto; text-align:center"
! Image
! Name
! Info
! [[Kinetic symmetry]]
! [[apgcode]]
! [[Glider synthesis|Cost in gliders]]
|-
! [[File:Cisqueenbeeshuttle.png|128px]]
! Cis-queen bee shuttle
| Blocks are "on the same side"
| n-e
| {{LinkCatagolue|xp30_w33z8kqrqk8zzzw33|style=raw}}
| 5
|-
! [[File:Transqueenbeeshuttle.png|128px]]
! Trans-queen bee shuttle
| Blocks are "on different sides"
| n.e
| {{LinkCatagolue|xp30_w33z8kqrqk8zzzx33|style=raw}}
| 5
|}

== Glider synthesis ==
There are a few 4-glider components that turn any one-sided stabilization of the queen bee, such as a block, into a queen bee shuttle variant, yielding 6-glider [[Glider synthesis|syntheses]] for both common variants. The synthesis of the cis-queen bee shuttle was later reduced to 5 gliders in July 2020,<ref name="post100652" /> and an alternate 6-glider synthesis of the trans-queen bee shuttle has also been found.<ref name="post147138" />
An alternate 5-glider synthesis of the cis-queen bee shuttle was found in March 2023.<ref name="post159582" /><ref name="j4000837544" /> The trans-queen bee shuttle was reduced to 5 gliders by Carson Cheng on May 28, {{year|2024}}.<ref name="post186105" />

{{EmbedViewer
|pname = block2queenbeeshuttle
|viewerconfig = #C [[ ZOOM 4 WIDTH 600 HEIGHT 600 ]]
|position = center
|caption = A collection of nine such 4-glider components mentioned above, turning a block into a queen bee shuttle
|style = width:300px;
}}

== Variations ==
The shuttles were originally stabilized against one another in a square of eight shuttles, but many other stabilisations of the queen bee are now known, such as [[buckaroo]] (which utilises an [[eater 1]]), [[hectic]] (which relies on [[glider]]s) and {{LinkCatagolue|code=xp30_wmm0e93z643xgk333kgzc4ozwdd0eio|style=raw|patternname=a thin one}} (allowing a 20-cell wide footprint with an unnamed still life) and {{LinkCatagolue|code=xp30_wssx3us8zwgogw31z2566652zy725brb52zxooy4oo|style=raw|patternname=the thinnest known one}} (allowing an 18-cell-wide (albeit 25-cell-tall) one using other queen bees), the latter two of which are useful in bounding box reductions.

The '''queen bee loop''' (or '''ouroboros bees'''), another form of the queen bee shuttle that was found in 1970 (also by Bill Gosper), is a closed loop made of four queen bees that clean up each other's [[beehive]]s. It was forgotten about in many sources and independently rediscovered in {{year|2008}} by [[Nicolay Beluchenko]].<ref>{{LinkGoLNews|2008/11/new_small_period_oscillators_2.html|title=New Small Period Oscillators|date=November 23, 2008|author=Heinrich Koenig}}</ref> It is also possible to create a partial loop oscillator consisting of two or three queen bees by removing one or two of the queen bees in the loop and placing two stabilizing blocks appropriately.

{| style="margin-left:auto;margin-right:auto;" |
|-
|{{EmbedViewer
|pname = queenbeeloop
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 ]]
|caption = A queen bee loop
|style = width:360px;
}}
|{{EmbedViewer
|pname = partialqueenbeeloop
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 ]]
|caption = A partial queen bee loop with only three queen bees
|style = width:360px;
}}
|}

== Occurrence ==
{{related|List of common oscillators}}
The cis-queen bee shuttle and the trans-queen bee shuttle are the 18th and 19th most [[common]] naturally-occurring oscillators in [[Achim Flammenkamp's census]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> On [[Catagolue]], it is the most common period 30 oscillator, with all other natural oscillators of that period featuring it in some form.<ref>{{citeCatagolueStats|October 27, 2018}}</ref>

The trans version is about 2% more common than the cis version on Catagolue.

[[Catagolue#Contributor engagement|Catagolue]] has a dedicated badge which will be given out to anyone who discovers a new variant of this oscillator.

== Gallery ==
{|style="margin:auto;width:300px;"
|{{EmbedViewer
|pname = queenbeeshuttlepredecessor
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = Queen bee shuttle [[dimer]] predecessor made up of a [[pi-heptomino]], two [[blinker]]s and two blocks. Found by Gosper in April {{year|1992}}.
}}
|-
|{{EmbedViewer
|pname = p26queenbeeshuttle
|position = center
|viewerconfig = #C [[ GPS 13 THUMBSIZE 2 ]]
|caption = A period-26 version of the queen bee shuttle, found by [[James Pascua]] based on a partial by [[Entity Valkyrie]]<ref name="post122080" />
}}
|-
|{{EmbedViewer
|pname = queenbeeshuttlesrephasingblinker
|position = center
|caption = The shuttle produces a spark at the blocks that can be used to [[Phase_shift|rephase]] a [[blinker]]; two must be used to make a functioning oscillator from this reaction to prevent formation of a deadly traffic light.
}}
|}

== References ==
<references>
<ref name="j4000837544">{{CiteCatagolueJob|job=4000837544|date=March 25, 2023}}</ref>
<ref name="post100652">{{LinkForumThread
|format = ref
|title = Re: Randomly enumerating glider syntheses
|p = 100652
|author = Ian07
|date = July 18, 2020
}}</ref>
<ref name="post122080">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 122080
|author = James Pascua
|date = February 8, 2021
}}</ref>
<ref name="post147138">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 147138
|author = Carson Cheng
|date = June 15, 2022
}}</ref>
<ref name="post159582">{{LinkForumThread
|format = ref
|p = 159582
|title = Re: Synthesising Oscillators
|author = Carson Cheng
|date = March 25, 2023
}}</ref>
<ref name="post186105">{{LinkForumThread
|format = ref
|p = 186105
|title = Re: Synthesising Oscillators
|author = Carson Cheng
|date = May 28, 2024
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_q.htm#queenbeeshuttle}}
* {{LinkCatagolue|xp30_y68sul3zggxggy1123z127e721y6oke7ekozy5ckogzy5ca731|patternname=Queen bee loop}}
* {{LinkPentadecathlonObject|20P30.1}}
* {{LinkPentadecathlonObject|20P30.2}}

{{Symmetry|osc=turn180}}
{{Sparker|p=30|type=dot|strength=strong}}

Meta-dove and house

2024-06-05T17:23:43Z

Squareroot12621: "a 18-cell" --> "an 18-cell"

{{Stilllife
|name = Meta-dove and house
|pname = metadoveandhouse
|c = 18
|bx = 8
|by = 6
|fc = 27.9
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S23nr
|isorulemax = B2kn34-ijk5-enq6-i78/S012345678
|synthesis = 5
|plaintext = true
|rle = true
|apgcode = xs18_m2s0si96z11
|pentadecathlonid = 18.637
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 ]]
}}
'''Meta-dove and house''' is an {{slcells|18}}-[[cell]] strict [[still life]] consisting of a [[dove]] and a [[house]] stabilising each other. It is one of four ways in which a dove and a house can be arranged to create a still life, and one of the three which have two separate [[island]]s.

This specific [[isomer]] is [[Pattern naming|named]] ''meta'' due to the two inducting faces not being skewed from each other.

== [[List of common still lifes|Commonness]] ==
Meta-dove and house is the 34th most common 18-cell still life.

== [[Glider synthesis]] ==
A {{gliders|5}} [[synthesis]] for this still life was found in July {{year|2020}}.<ref name="post100652" />

== See also ==
* [[Dove bridge house]]

== References ==
<references>
<ref name="post100652">{{LinkForumThread
|format = ref
|title = Re: Randomly enumerating glider syntheses
|p = 100652
|author = Ian07
|date = July 18, 2020
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xs18_m2s0si96z11}}

__NOTOC__

Hat with cape

2024-06-05T13:58:56Z

Squareroot12621: 22th --> 22nd.

{{Stilllife
|name = Hat with cape
|pname = hatwithcape
|c = 13
|bx = 7
|by = 4
|fc = 24.7
|rulemin = B/S23
|rulemax = B378/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B/S2-i3nr
|isorulemax = B2in34-airy5-ny6-i78/S012345678
|synthesis = 5
|plaintext = true
|rle = true
|apgcode = xs13_17871ac
|niemiecid = 13.175
|pentadecathlonid = 13.13
}}
'''Hat with cape''' is a {{slcells|13|text=13-bit}} [[still life]].

== Construction ==
Hat with cape is known to be [[Glider synthesis|constructible]] with 5 gliders.<ref name="catagolue_object" /> A {{gliders|5}} synthesis was found in {{year|2014}}.<ref name="post15258" />

{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 41, y = 37, rule = B3/S23
30bo$29bo$29b3o$7bo$8bo$6b3o7$36b2ob2o$35bobobo$34bo2bobo$34b2o2bo5$
11bo$11b2o$10bobo2$25b2o$25bobo$25bo8$b2o$obo$2bo!
|viewerconfig = #C [[ HEIGHT 440 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 67 PAUSE 1 T 68 PAUSE 2 LOOP 69 ]]
|position = center
|caption = A 5G synthesis<ref name="post15258" />
}}
|-
|{{EmbedViewer
|rle = x = 48, y = 38, rule = B3/S23
32bo$31bo$31b3o3$10bo$8bobo$9b2o$2bo$obo$b2o3$13bo$14bo$12b3o4$23b2ob
2o15b2ob2o$24bobo15bobobo$24bobo14bo2bobo$25bo15b2o2bo5$5b2o$4bobo3b2o
$6bo2bobo$11bo13b3o$25bo$26bo3$7b2o$8b2o$7bo!
|viewerconfig = #C [[ HEIGHT 420 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 30 PAUSE 1 T 53 PAUSE 1 T 54 PAUSE 2 LOOP 55 ]]
|position = center
|caption = A 8G conversion from [[hat]]<ref name="niemiec" />
}}
|}

== Occurrence ==
{{related|List of common still lifes|List of still lifes with 13 cells}}
Hat with cape is the 22nd most common 13-cell still life out of 240.

Two [[three-glider collision]]s have an occurrence of hat with cape in the ash.{{refn|Collisions converge to a sequence with 6 escaping gliders and final population 308. Headerless RLEs are {{headerlessRLE|65bo$63b2o$64b2o$60bo$61bo$59b3o132$2o$b2o$o!}} and {{headerlessRLE|6bo$4b2o$5b2o$bo$2bo$3o132$93b2o$92b2o$94bo!}}}}

== References ==
<references>
<ref name="catagolue_object">{{LinkCatagolue|xs13_17871ac|style=nobullet}}</ref>
<ref name="niemiec">{{LinkNiemiec|p1-13.htm|Life Thirteen-Bit Still-Lifes|rle=13/13-175.rle|nobullet=nobullet}}</ref>
<ref name="post15258">{{LinkForumThread
|format = ref
|p = 15258
|title = Re: 4 glider syntheses
|author = BobShemyakin
|date = December 27, 2014
}}</ref>
</references>

== External links ==
* {{LinkCatagolue|xs13_17871ac}}
* {{LinkPentadecathlonObject|id=13.13|archivedate=20221113231913}}
* {{LinkNiemiec|p1-13.htm|Life Thirteen-Bit Still-Lifes|rle=13/13-175.rle}}

__NOTOC__

User:Squareroot12621

2024-06-04T23:49:05Z

Squareroot12621: Changed the formatting of the Rules section to allow for descriptions of the rules.

Rule:Supercomputer

2024-06-04T15:26:27Z

Squareroot12621: Created page.

@RULE Supercomputer
@TABLE
n_states:9
neighborhood:Moore
symmetries:rotate4reflect
var a1={0,1,2,3,4,5,6,7,8}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var h1={2,5}
var h2=h1
1, 0,0,0,a1,h1,0,1,1, 2
1, 0,0,0,0,h1,a1,1,1, 2
1, 1,0,0,1,h1,3,1,0, 1
1, 0,0,0,a1,h1,a2,1,1, 1
1, 1,3,h1,0,0,0,1,0, 1
1, h1,3,0,0,0,3,h2,1, 1
1, 1,0,1,1,h1,3,1,0, 1
1, 0,0,0,1,h1,3,1,h2, 1
1, 0,0,0,h1,3,1,h2,3, 1
1, h1,1,a1,0,0,0,h2,1, 1
1, h2,a1,a2,a3,a4,a5,a6,a7, 2
2, a1,a2,a3,a4,a5,a6,a7,a8, 3
3, a1,a2,a3,a4,a5,a6,a7,a8, 1
4, a1,0,a2,0,a3,0,a4,h1, 5
5, a1,a2,a3,a4,a5,a6,a7,a8, 4
6, 2,a1,a2,a3,a4,a5,a6,a7, 7
6, 3,a1,a2,a3,a4,a5,a6,a7, 7
6, 5,a1,a2,a3,a4,a5,a6,a7, 7
6, 1,a1,a2,a3,a4,a5,a6,a7, 6
6, 4,a1,a2,a3,a4,a5,a6,a7, 6
6, 7,a1,a2,a3,a4,a5,a6,a7, 7
7, a1,a2,a3,a4,a5,a6,a7,a8, 8
8, a1,a2,a3,a4,a5,a6,a7,a8, 6
@NAMES
0 empty
1 wire
2 head
3 tail
4 diode off
5 diode on
6 display off
7 display on
8 display fading
@COLORS
0 0 0 0
1 0 128 128
2 255 128 0
3 128 128 64
4 0 255 0
5 255 255 64
6 255 255 255
7 255 0 255
8 255 128 255

User:Squareroot12621

2024-06-04T15:20:32Z

Squareroot12621: Created page.