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|f            = 842
|f            = 842
|mcps        = 10
|mcps        = 10
|symmetry    = C1
|discoverer  = Charles Corderman
|discoverer  = Charles Corderman
|discoveryear = 1971
|discoveryear = 1971
|rulemin      = B3/S23
|rulemax      = B3/S23
|isorulemin  = B3/S23
|isorulemax  = B3/S23 <!-- rulemin and rulemax are for the full evolution -->
|synthesis    = 3
|synthesis    = 3
|synthesisRLE = true
|synthesisRLE = true
|plaintext    = true
|plaintext    = true
|rle          = true
|rle          = true
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 60 ]]
}}
}}
A '''switch engine''' (or '''Corder engine'''<ref>{{CiteLexicon|file=lex_c.htm#corderengine|name=Corder engine|accessdate=June 10, 2009}}</ref>) is a [[methuselah]] that was found by [[Charles Corderman]] in {{year|1971}}. It produces a copy of itself after 48 generation, glide-reflected 4 cells northwest (in the case of the starting configuration shown to the right), along with some active junk. If left unattended, the accumulating exhaust overtakes and destroys the engine after 24 cycles, but it can be stabilized to make [[c/12 diagonal]] [[puffer]]s and [[spaceship]]s.
A '''switch engine''' (or '''Corder engine'''<ref>{{CiteLexicon|file=lex_c.htm#corderengine|name=Corder engine|accessdate=June 10, 2009}}</ref>) is a [[methuselah]] that was found by [[Charles Corderman]] in {{year|1971}}.<ref>{{CiteLifeline|vol=4|pages=page 2}}</ref> It produces a copy of itself after 48 generations, glide-reflected 4 cells northwest (starting in the form to the right), along with some active [[junk]]. If left unattended, the accumulating exhaust overtakes and destroys the engine after 24 cycles, but it can be stabilized to make [[c/12 diagonal]] [[puffer]]s and [[spaceship]]s.


A {{gliders|3}} [[synthesis]] for a clean switch engine was discovered by [[Luka Okanishi]] on March 12, {{year|2017}}, surprisingly late for such a small synthesis.<ref name="post41557" />
== History ==
In {{year|1971}}, Charles Corderman investigated the [[fate]] of all the small [[polyomino]]es exhaustively. Records indicate that he found the switch engine while investigating the [[decomino]]es (polyominoes having 10 cells). However, record of the decomino switch engine [[predecessor]] seems to have been lost.<ref name="post21235" /> There is, however, a unique [[nonomino]] switch engine predecessor whose 2-tick descendant matches that of a switch engine:<ref name="post21249" />


==Stabilization==
{{EmbedViewer
There are two basic types of stabilized switch engine, both of which were also found by Charles Corderman: the [[period]] 288 [[block-laying switch engine]] (the more common of the two) and period 384 [[glider-producing switch engine]]. These two puffers are the most natural [[infinite growth]] patterns in [[Conway's Game of Life|Life]], being by far the most common ones to occur from non-symmetric [[soup|random starting patterns]].<ref>{{cite web|url=http://catagolue.appspot.com/census/b3s23/C1 |title=Census - Catagolue |accessdate=September 28, 2015}}</ref> Switch engine-based puffers, and combinations thereof, are also the only infinite growth patterns observed to have emerged from asymmetric soups on [[Catagolue]].
|pname        = nonominoswitchenginepredecessor
|viewerconfig = #C [[ THUMBSIZE 4 ZOOM 32 HEIGHT 480 GPS 2 THEME Book AUTOSTART T 0 PAUSE 2 T 2 PAUSE 1 LOOP 3 ]]
|position    = center
|caption      = Nonomino switch engine predecessor
|style        = width:300px;
}}
 
It is the smallest known polyomino to do so. If Corderman was examining polyominoes in order of size, then this smaller predecessor should have been found first in any case.
 
== Stabilization ==
The movement of a switch engine can be sustained in several different types of patterns.


Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the [[mosquito]]es, [[catacryst]], [[metacatacryst]], [[Gotts dots]], and [[26-cell quadratic growth]]. Patterns giving rise to block-laying switch engines can be seen under [[infinite growth]], and one giving rise to a glider-producing switch engine is shown under [[time bomb]].
=== Infinite growth ===
There are two basic types of stabilized switch engine [[orbit]]s, both of which were also found by Charles Corderman: the [[period]]-288 [[block-laying switch engine]] (the more common of the two), stabilizing in an orbit of six cycles (with additional glide symmetry) and period-384 [[glider-producing switch engine]], stabilizing in an asymmetric orbit of eight cycles. These two puffers are the most natural [[infinite growth]] patterns in [[Conway's Game of Life]], being by far the most common ones to occur from non-symmetric [[soup|random starting patterns]].<ref name="statistics">{{citeCatagolueStats}}</ref> Switch engine-based puffers and combinations thereof, such as [[pony express]] and [[birthday puffer]], are also the only infinite growth patterns observed to have emerged from asymmetric soups on [[Catagolue]].


In addition to the puffers based on a single switch engine, puffers such as [[Noah's ark]] can be created by combining two switch engines. Such puffers are generally quite [[dirty]]. However, it is also possible to create [[Cordership]]s made of switch engines that interact to remove their combined exhaust.  These move at [[c/12 diagonal]]ly and are thus the slowest known spaceships in Life other than the [[Spaceship#Adjustable_spaceships|adjustable ships]]. Such spaceships can be constructed by combining as few as [[2-engine Cordership|two]] switch engines.
Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the [[mosquito]]es, [[catacryst]], [[metacatacryst]], [[Gotts dots]], and [[20-cell quadratic growth]].  


=='Swimmer' tracks==
In addition to the puffers based on a single switch engine, puffers such as [[Noah's ark]] can be created by combining two switch engines. Such puffers are generally quite [[dirty]].
Like [[Herschel]]s, switch engines can be supported by [[conduit]]s made out of well-separated still lifes.<ref>{{cite web|url=http://pentadecathlon.com/lifenews/2005/09/bobsled_run_update.html|title=Bobsled run update|author=Dave Greene|publisher=Game of Life News|accessdate=September 21, 2014}}</ref> These 'swimmer tracks' were discovered by [[David Bell]] in 2005, and can be any length.  Stable converters have been constructed that convert Herschels to switch engines and back<ref>{{cite web|url=http://b3s23life.blogspot.com/2007/06/new-kind-of-signal-though-not-useful.html|title=A New Kind of Signal|author=Dave Greene|publisher=Work in Progress blog|accessdate=September 21, 2014}}</ref>.  Much faster, smaller and more efficient Herschel-to-swimmer converters can now be constructed with new technology, particularly [[Snark|Snark reflectors]].<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2799&p=42033#p42069|title=Re: Implications of a Three-Glider Switch Engine|author=Dave Greene|date=March 25, 2017|accessdate=February 13, 2018}}</ref>


==Stable pattern==
There are also patterns such as [[conga line switch engine extender]] which produces an extending line of switch engines. It is based on [[Ian07]]'s discovery earlier that month that a single switch engine could be stabilized by another switch engine following closely behind it.
The stable pattern that results from the switch engine has 842 [[cell]]s. It consists of 60 [[block]]s, 33 [[beehive]]s (including one [[honey farm]]), 50 [[blinker]]s (including eight [[traffic light]]s), 12 [[glider]]s, 11 [[boat]]s, 11 [[loaf|loaves]], four [[ship]]s, two [[long boat]]s, two [[pond]]s, and two [[tub]]s.
{|
|-
|[[Image:Switchengine_final.png|thumb|left|Generation 3911]]
|}


==See also==
=== Spaceship ===
*[[Ark]]
{{main|Cordership}}
*[[Cordership]]
*[[Infinite growth]]
*[[Time bomb]]


==References==
it is also possible to create spaceships made of switch engines that interact to remove their combined exhaust. They are named "Cordership" in honor of Charles Corderman. These spaceships move at [[c/12 diagonal]]ly and are thus the slowest known non-[[adjustable spaceship]]s in Life. Such spaceships can be constructed by combining as few as [[2-engine Cordership|two]] switch engines.
 
=== 'Swimmer' tracks ===
{{main|Switch engine channel}}
 
Like [[Herschel]]s, switch engines can be supported by [[conduit]]s made out of well-separated still lifes. These 'swimmer tracks' were first constructed by [[David Bell]] in 2005. Stable [[converter]]s have since been constructed that convert Herschels or gliders to switch engines and back.
 
== Final pattern ==
[[File:Switchengine final.png|300px|thumb|Generation 3911]]
The final pattern that results from a lone switch engine has 842 [[cell]]s. It consists of 60 [[block]]s, 33 [[beehive]]s (including one [[honey farm]]), 50 [[blinker]]s (including eight [[traffic light]]s), 12 [[glider]]s, 11 [[boat]]s, 11 [[loaf|loaves]], four [[ship]]s, two [[long boat]]s, two [[pond]]s, and two [[tub]]s.
 
== Synthesis ==
In {{year|1973}}, [[Douglas G. Petrie]] employed a {{gliders|4}} recipe of a switch engine in his [[synthesis]] for a block-laying switch engine.<ref>{{CiteLifeline|vol=10|pages=page 5}}</ref> Decades later, [[Luka Okanishi]] discovered a surprisingly small {{gliders|3}} synthesis for a clean switch engine on March 12, {{year|2017}}.<ref name="post41557" />
 
== Other rules ==
The only [[Hensel notation|two-state isotropic]] alien rule where the main mechanism of the switch engine still works is {{rl|B3/S236e}}. No single-engine orbits are known in that rule despite searches being done<ref name="post153290" /><ref name="post107613" />, but there are known Corderships that work.<ref name="post107613" />
 
== Gallery ==
{{EmbedViewer
|pname        = 8and9cellswitchenginepredecessors
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
|position    = center
|caption      = 8-cell 0, 1, 2 and 9-cell 3, 4, 5-generation switch engine predecessors<ref name="post143047" />
|style        = width:300px;
}}
 
== References ==
<references>
<references>
<ref name="post21235">{{LinkForumThread
|format = ref
|p      = 21235
|title  = Re: CMD shape switch engine
|author = Dave Greene
|date  = July 17, 2015
}}</ref>
<ref name="post21249">{{LinkForumThread
|format = ref
|p      = 21249
|title  = Re: CMD shape switch engine
|author = Dave Greene
|date  = July 18, 2015
}}</ref>
<ref name="post41557">{{LinkForumThread
<ref name="post41557">{{LinkForumThread
|format = ref
|format = ref
|p      = 41557
|title  = Re: Thread For Your Accidental Discoveries
|title  = Re: Thread For Your Accidental Discoveries
|p      = 41557
|author = Luka Okanishi
|author = Luka Okanishi
|date  = March 12, 2017
|date  = March 12, 2017
}}</ref>
<ref name="post107613">{{LinkForumThread
|format = ref
|p      = 107613
|title  = Re: Thread for basic non-CGOL questions
|author = Schiaparelliorbust
|date  = October 23, 2020
}}</ref>
<ref name="post143047">{{LinkForumThread
|format = ref
|p      = 143047
|title  = Re: Thread for your unsure discoveries
|author = dani
|date  = March 17, 2022
}}</ref>
<ref name="post153290">{{LinkForumThread
|format = ref
|p      = 153290
|title  = Re: Thread for basic questions
|author = dani
|date  = November 8, 2022
}}</ref>
}}</ref>
</references>
</references>


==External links==
== External links ==
{{LinkWeisstein|SwitchEngine.html}}
* {{LinkLexicon|lex_s.htm#switchengine}}
{{LinkLexicon|lex_s.htm#switchengine}}
<!-- *[http://www.calcyman.co.uk/life/corder.htm Corderships and Switch Engines] at [http://www.calcyman.co.uk/ www.calcyman.co.uk] -->
<!-- *[http://www.calcyman.co.uk/life/corder.htm Corderships and Switch Engines] at [http://www.calcyman.co.uk/ www.calcyman.co.uk] -->
* {{LinkLexicon|filename=lex_n.htm#nonominoswitchenginepredecessor|patternname=Nonomino switch engine predecessor}}
* {{cite web
|url  = https://web.archive.org/web/20200728034553/http://www.pentadecathlon.com/objects/class4/typeB/SwitchEngine1/switchEngine1.php
|title = Single Switch Engine
|work  = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}
* {{cite web
|url  = https://web.archive.org/web/20200509142738/http://www.pentadecathlon.com/objects/class4/typeB/switchEngine2/switchEngine2.php
|title = Double Switch Engine
|work  = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}
* {{cite web
|url  = https://web.archive.org/web/20200508230804/http://www.pentadecathlon.com/objects/class4/typeB/switchEngineN/switchEngineN.php
|title = Multiple Switch Engines
|work  = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}


[[Category:Puffer engines]]
[[Category:Puffer engines]]
__NOTOC__
[[Category:Patterns involving switch engines| ]]

Latest revision as of 20:44, 21 August 2024

Switch engine
x = 6, y = 4, rule = B3/S23 bobo$o$bo2bo$3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 60 ]]
View static image
Pattern type Methuselah
Number of cells 8
Bounding box 6 × 4
MCPS 10
Lifespan 3911 generations
Final population 842
L/I 488.9
F/I 105.3
F/L 0.215
L/MCPS 391.1
Static symmetry C1
Discovered by Charles Corderman
Year of discovery 1971

A switch engine (or Corder engine[1]) is a methuselah that was found by Charles Corderman in 1971.[2] It produces a copy of itself after 48 generations, glide-reflected 4 cells northwest (starting in the form to the right), along with some active junk. If left unattended, the accumulating exhaust overtakes and destroys the engine after 24 cycles, but it can be stabilized to make c/12 diagonal puffers and spaceships.

History

In 1971, Charles Corderman investigated the fate of all the small polyominoes exhaustively. Records indicate that he found the switch engine while investigating the decominoes (polyominoes having 10 cells). However, record of the decomino switch engine predecessor seems to have been lost.[3] There is, however, a unique nonomino switch engine predecessor whose 2-tick descendant matches that of a switch engine:[4]

x = 6, y = 3, rule = B3/S23 3o$2bobo$2b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ZOOM 32 HEIGHT 480 GPS 2 THEME Book AUTOSTART T 0 PAUSE 2 T 2 PAUSE 1 LOOP 3 ]]
Nonomino switch engine predecessor
(click above to open LifeViewer)
RLE: here Plaintext: here

It is the smallest known polyomino to do so. If Corderman was examining polyominoes in order of size, then this smaller predecessor should have been found first in any case.

Stabilization

The movement of a switch engine can be sustained in several different types of patterns.

Infinite growth

There are two basic types of stabilized switch engine orbits, both of which were also found by Charles Corderman: the period-288 block-laying switch engine (the more common of the two), stabilizing in an orbit of six cycles (with additional glide symmetry) and period-384 glider-producing switch engine, stabilizing in an asymmetric orbit of eight cycles. These two puffers are the most natural infinite growth patterns in Conway's Game of Life, being by far the most common ones to occur from non-symmetric random starting patterns.[5] Switch engine-based puffers and combinations thereof, such as pony express and birthday puffer, are also the only infinite growth patterns observed to have emerged from asymmetric soups on Catagolue.

Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the mosquitoes, catacryst, metacatacryst, Gotts dots, and 20-cell quadratic growth.

In addition to the puffers based on a single switch engine, puffers such as Noah's ark can be created by combining two switch engines. Such puffers are generally quite dirty.

There are also patterns such as conga line switch engine extender which produces an extending line of switch engines. It is based on Ian07's discovery earlier that month that a single switch engine could be stabilized by another switch engine following closely behind it.

Spaceship

Main article: Cordership

it is also possible to create spaceships made of switch engines that interact to remove their combined exhaust. They are named "Cordership" in honor of Charles Corderman. These spaceships move at c/12 diagonally and are thus the slowest known non-adjustable spaceships in Life. Such spaceships can be constructed by combining as few as two switch engines.

'Swimmer' tracks

Main article: Switch engine channel

Like Herschels, switch engines can be supported by conduits made out of well-separated still lifes. These 'swimmer tracks' were first constructed by David Bell in 2005. Stable converters have since been constructed that convert Herschels or gliders to switch engines and back.

Final pattern

Generation 3911

The final pattern that results from a lone switch engine has 842 cells. It consists of 60 blocks, 33 beehives (including one honey farm), 50 blinkers (including eight traffic lights), 12 gliders, 11 boats, 11 loaves, four ships, two long boats, two ponds, and two tubs.

Synthesis

In 1973, Douglas G. Petrie employed a 4-glider recipe of a switch engine in his synthesis for a block-laying switch engine.[6] Decades later, Luka Okanishi discovered a surprisingly small 3-glider synthesis for a clean switch engine on March 12, 2017.[7]

Other rules

The only two-state isotropic alien rule where the main mechanism of the switch engine still works is B3/S236e. No single-engine orbits are known in that rule despite searches being done[8][9], but there are known Corderships that work.[9]

x = 47, y = 68, rule = B3/S23 3o$obo$3o$obo$3o16$3o18bo18b2o$bo2bo16bo2bo17bo$5bo14bobobo17bo$2bobo 38b4o$24b2o16$3o$obo$3o$2bo$2bo16$2o18bo21bo$20b2o18bo$bo39bo$2b2obobo 13b3o17bo$24bo$4bobo15b2o16bob3o2$43bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
8-cell 0, 1, 2 and 9-cell 3, 4, 5-generation switch engine predecessors[10]
(click above to open LifeViewer)
RLE: here Plaintext: here

References

  1. ↑ "Corder engine". The Life Lexicon. Stephen Silver. Retrieved on June 10, 2009.
  2. ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 2.
  3. ↑ Dave Greene (July 17, 2015). Re: CMD shape switch engine (discussion thread) at the ConwayLife.com forums
  4. ↑ Dave Greene (July 18, 2015). Re: CMD shape switch engine (discussion thread) at the ConwayLife.com forums
  5. ↑ Adam P. Goucher. "Statistics". Catagolue.
  6. ↑ Robert Wainwright (June 1973). Lifeline, vol 10, page 5.
  7. ↑ Luka Okanishi (March 12, 2017). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
  8. ↑ dani (November 8, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
  9. ↑ 9.0 9.1 Schiaparelliorbust (October 23, 2020). Re: Thread for basic non-CGOL questions (discussion thread) at the ConwayLife.com forums
  10. ↑ dani (March 17, 2022). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
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