LifeWiki - User contributions [en]

Slide gun

2015-12-12T20:58:09Z

2x2: typo

[[Image:slide_gun.png|framed|right|A simple slide gun<br/>{{JavaRLE|slidegun}}]] A '''slide gun''' is a [[gun]] that fires [[glider]]s or other [[spaceship]]s sideways from an extending arm. The arm consists of a [[salvo]] of spaceships which are continually pushing a [[still life]] or small [[constellation]], releasing a glider in the process. This releases a wave of spaceships rather than a stream, as each spaceship is on a different path. The first slide gun was constructed by [[Dietrich Leithner]] in July [[:Category:patterns found in 1994|1994]], and was based on a diagonal [[block]]-pushing reaction.

==Tethered rake==
[[Image:tethered_rake.png|framed|right|A [[switch engine]]-based tethered rake<br/>{{JavaRLE|tetheredrake}}]]A '''tethered rake''' is similar to a slide gun in that it has an extending arm, but the end of the arm is in constant motion. This may mean that it has a spaceship or a volatile reaction at its front. Due to the precise timing of gliders or other spaceships required to support such reactions, tethered rakes are often more [[period]]-dependent than slide guns.

==See also==
*[[Blockstacker]]

==External links==
{{LinkLexicon|lex_s.htm#slidegun}}

Talk:Bi-loaf

2015-11-24T01:54:04Z

2x2: /* The new bi-loaf */

==The new bi-loaf==
I found another bi-loaf.
Hint: ▒ is Alt+177 and ▓ is Alt+178. ░ is Alt+176.

<pre><nowiki>
▒▓▓▒▒▒
▓▒▒▓▒▒
▓▒▓▒▓▒
▒▓▒▓▒▓
▒▒▓▒▒▓
▒▒▒▓▓▒
</nowiki></pre>

-wwei23 9:03AM 10/12/2015 NY time

You mean this?:

○●●○○○

●○○●○○

●○●○●○

○●○●○●

○○●○○●

○○○●●○

That is not a bi-loaf, and not even new. It is "loaf bridge loaf".

--[[User:2x2|2x2]] ([[User talk:2x2|talk]]) 01:54, 24 November 2015 (UTC)

User:Tropylium/Vessel

2015-11-20T23:07:52Z

2x2:

__NOTOC__{{Glossary}}
'''Vessels''' are a diagonally [[Long|extensible]] family of [[strict still life]]s. All vessels have a diagonal width of no more than 3 [[lane]]s. The basic structure is a series of diagonally connected pairs of cells.

The basic vessel is the four-cell [[tub]], with two cell pairs. This can be lengthened to produce the [[barge]] (three pairs), [[long barge]] (four pairs), etc.

Adding a single additional cell at one end of a vessel produces the [[boat]] subfamily; adding cells at both ends produces the [[ship]] subfamily.

Boats and ships can be joined as single-point [[tie]]s with each other or with other still lifes featuring a [[pre-block]] protrusion. Tubs/barges and boats can also be joined with each other as two-point ties, but this will only produce a longer vessel.

The [[block]] can be considered a degenerate ship of length 1, aside from the fact that it cannot be used in ties.

While vessels resemble a wider version of single-fuse [[string]]s, crucial differences result from the fact that the cells in the diagonal body already have three neighbors. No components can be attached to the body of a vessel, and although ships/boats can be joined as ties, they cannot be [[siamese|siamized]] in the same way other still lifes with preblock endings can. Sometimes a fuse body can be siamized lengthways with a vessel body though: e.g. a [[loaf]] can be siamized with a barge to result in [[loaf siamese barge]], and a long barge can be siamized with [[cis-fuse with two tails]] to yield a barge with two tails. Larger examples will become increasibly non-intuitive.

===Tub series===
<gallery>
Image:tub.png|a simple tub
Image:barge.png|but now it's a barge
Image:longbarge.png|and a barge for ever after
</gallery>

===Boat series===
<gallery>
Image:boat.png|row row row your boat
Image:longboat.png|gently down the stream
Image:longlongboat.png|merrily merrily merrily merrily life is but a dream
</gallery>

===Ship series===
<gallery>
Image:ship.png|a simple ship
Image:longship.png|but this one's grown a bit
Image:longlongship.png|very long ship
</gallery>

Phoenix 1

2015-11-14T16:11:53Z

2x2:

__NOTOC__{{Oscillator|p=2|c=12|bx=8|by=8|h=24|v=1.00|name=Phoenix 1|pname=phoenix1|discoverer=MIT group|discoveryear=1971|life105=true|life106=true|plaintext=true|rle=true|animated=true|synthesis=10|synthesisRLE=true|rulemin=B3/S|rulemax=B345678/S2345678|rulespecial=[[Conway's Game of Life|Conway Life]], [[HighLife]]|v=1.00}}
'''Phoenix 1''' (or '''flip-flops'''<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_f.htm#flipflops |title=Flip-flops| work=The Life Lexicon |publisher=Stephen Silver |accessdate=June 21, 2011}}</ref>) is a [[period]] [[:Category:Oscillators with period 2|2]] [[oscillator]] that was discovered by the [[MIT group]] in December [[:Category:Patterns found in 1971|1971]]. It is the smallest known [[phoenix]] as well as the first discovered phoenix, and is thus sometimes simply referred to as ''the'' phoenix.

Phoenix 1 consists of four identical three-cell segments, chained in a loop. Other arrangements are possible, to generate larger period 2 phoenices as shown below. A single copy of this rotor can also be supported by a [[stator]]: this is an oscillator known as the [[griddle]]. The same rotor segment also appears in [[by flops]] and [[why not]].

Despite its small size, it had not shown up naturally in soup until October 5th, 2015, and another soup turned up with this object shortly after.

==Image gallery==
{|
|-
|[[Image:Phoenix1extended.png|framed|left|An extension of phoenix 1<br />{{JavaRLE|phoenix1extended|brief}}]]
|}

==See also==
*[[Almosymmetric]]
*[[Revolver]]

==References==
<references />

==External links==
{{LinkWeisstein|filename=Phoenix.html}}
{{LinkLexicon|filename=lex_p.htm#phoenix}}

Switch engine/Snippet

2015-10-26T01:19:32Z

2x2: Yl1152

<noinclude>{{Snippet}}</noinclude>[[Image:Switchengine.png|left]]A '''switch engine''' is a [[methuselah]] that was found by [[Charles Corderman]] in [[:Category:Patterns found in 1971|1971]]. It is unstable by itself, but it can be used to make [[:Category:Spaceships with speed c/12|c/12]] diagonal [[puffer]]s and [[spaceship]]s.

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 the only ones (besides combinations of them) ever seen to occur from non-symmetric [[soup|random starting patterns]].

OCA:Move

2015-10-18T01:35:59Z

2x2: http://catagolue.appspot.com/census/b368s245/C1 speed 4,10 too

{{Rule|name=Move|imgname=move|s=245|b=368|char=Stable|animated=true}}
'''Move''' (or '''Morley'''<ref>The name given to this rule in [[Golly]], in reference to Stephen Morley, who has extensively studied it.</ref>) is a [[Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have 2, 4, or 5 [[Moore neighbourhood|neighbours]]. Cells are born if they have 3, 6, or 8 neighbours. Random starting patterns tend to stabilize into [[ash]] consisting of small [[still life]]s and [[period]] 2 and 4 [[oscillator]]s. It also contains one commonly-occurring slow-moving [[spaceship]] and slow-moving [[puffer]]. The time required to stabilize is generally much shorter than in the [[Conway's Game of Life|Game of Life]].

==Notable patterns==
The move rule contains a large variety of known patterns, including many [[gun]]s, spaceships<ref name="Eppstein">{{cite web|url=http://fano.ics.uci.edu/ca/rules/b368s245/ |title=Move (B368/S245) |publisher=David Eppstein|accessdate=March 28, 2009}}</ref>, and puffers.

===Still lifes===
Below is an enumeration of small still lifes in the move rule.<ref>Computed using the ''EnumStillLifes.c'' script located [http://www.conwaylife.com/forums/viewtopic.php?f=9&t=44 here].</ref> Despite the abundance of interesting moving patterns in this rule, there are relatively few still lifes. It can be seen that there are still lifes of arbitrarily large size by noting that for every odd number of [[cell]]s greater than 5, there is an obvious extension of the [[Polyomino#Pentominoes|Z-pentomino]] for that number of cells that is a still life. Also, every [[lake]] is a still life, so for any n ≥ 3, there is at least one still life with 8n cells.

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
|-
| ≤ 3
| 0
|-
| 4
| 1
|-
| 5
| 1
|-
| 6
| 2
|-
| 7
| 2
|-
| 8
| 4
|-
| 9
| 1
|-
| 10
| 3
|}
</td><td align="center" style="padding-left:12px;">
[[Image:Move_SL.png|framed|right|Small still lifes in the move rule<br />{{JavaRLE|movestilllifes|brief}}]]
</td></tr></table>

===Common Objects===
Random starting patterns tend to stabilize into a much lower density (around 0.4%) than in [[Conway's Game of Life|Game of Life]] (around 3%). There are many more [[oscillator]]s than [[still life]]s in Move. About five sixths of objects in random settled areas are oscillators.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|51 px|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|51 px|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| R-Pentomino
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}
The R-pentomino is a P4 oscillator whose evolution can be seen at http://pixelartmaker.com/art/eff70a0fbd389b9.

===Spaceships===
[[Image:move_glider.gif|framed|right|The jellyfish<br />{{JavaRLE|jellyfish|brief}}]]There are at least 16 spaceships known in the move rule.<ref name="Eppstein" /> Of these, by far the most well-known is the '''jellyfish''', which travels at [[speed]] c/7 diagonally.

===Guns===
[[Image:Jasonsbow.png|framed|right|Jason's bow, a period 404 double-barreled gun<br />{{JavaRLE|jasonsbow}}]]At least 11 guns have been found, most of them by Stephen Morley and Jason Summers.<ref>{{cite web|url=http://safalra.com/special/b368s245/guns/ |title=b368s245 Guns |publisher=Stephen Morley|accessdate=March 28, 2009}}</ref> The first gun to be constructed was called Safalra's bow and was discovered on September 21, 2002 by Stephen Morley. It shoots two c/7 diagonal spaceships in opposite directions every 404 generations. Jason's bow, shown to the right, is a smaller version of Safalra's bow that was found by Jason Summers.

===Other patterns===
One [[puffer]] that commonly appears from random starting configurations is shown below. Its period is 170 and it travels at [[speed]] 13c/170. It is formed by a common six-cell pattern, which is the smallest pattern that exhibits [[infinite growth]] in this rule.
{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:move_pufpred.png|framed|center|A six-cell starting configuration of the puffer]]
|[[Image:move_puffer.gif|framed|center|A common puffer<br />{{JavaRLE|movepuffer}}]]
|}

==References==
<references />

Talk:Eater 1

2015-10-18T01:30:54Z

2x2: /* Reflector */

==Smallest non-symmetric still life?==
I believe that this is this smallest still life that is neither symmetric through a line nor radially symmetric. I'll add something to the article after I go through a list of the smallest still lifes to confirm. [[User:Nathaniel|Nathaniel]] 01:03, 23 January 2009 (UTC)
:Yes, this is the case. I will add this to the article now. [[User:Nathaniel|Nathaniel]] 01:48, 29 January 2009 (UTC)
==Reflector==
I found that an Eater 1 is a one-time reflector.

x = 10, y = 4, rule = B3/S23
o$3o5bo$3bo3bo$2b2o3b3o!

-wwei23 7:27PM 10/17/2015 NY time

:No, the glider is in a different place [[User:2x2|2x2]] ([[User talk:2x2|talk]]) 01:30, 18 October 2015 (UTC)

OCA:Move

2015-10-15T00:55:34Z

2x2: /* Common Objects */

{{Rule|name=Move|imgname=move|s=245|b=368|char=Stable|animated=true}}
'''Move''' (or '''Morley'''<ref>The name given to this rule in [[Golly]], in reference to Stephen Morley, who has extensively studied it.</ref>) is a [[Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have 2, 4, or 5 [[Moore neighbourhood|neighbours]]. Cells are born if they have 3, 6, or 8 neighbours. Random starting patterns tend to stabilize into [[ash]] consisting of small [[still life]]s and [[period]] 2 and 4 [[oscillator]]s. It also contains one commonly-occurring slow-moving [[spaceship]] and slow-moving [[puffer]]. The time required to stabilize is generally much shorter than in the [[Conway's Game of Life|Game of Life]].

==Notable patterns==
The move rule contains a large variety of known patterns, including many [[gun]]s, spaceships<ref name="Eppstein">{{cite web|url=http://fano.ics.uci.edu/ca/rules/b368s245/ |title=Move (B368/S245) |publisher=David Eppstein|accessdate=March 28, 2009}}</ref>, and puffers.

===Still lifes===
Below is an enumeration of small still lifes in the move rule.<ref>Computed using the ''EnumStillLifes.c'' script located [http://www.conwaylife.com/forums/viewtopic.php?f=9&t=44 here].</ref> Despite the abundance of interesting moving patterns in this rule, there are relatively few still lifes. It can be seen that there are still lifes of arbitrarily large size by noting that for every odd number of [[cell]]s greater than 5, there is an obvious extension of the [[Polyomino#Pentominoes|Z-pentomino]] for that number of cells that is a still life. Also, every [[lake]] is a still life, so for any n ≥ 3, there is at least one still life with 8n cells.

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
|-
| ≤ 3
| 0
|-
| 4
| 1
|-
| 5
| 1
|-
| 6
| 2
|-
| 7
| 2
|-
| 8
| 4
|-
| 9
| 1
|-
| 10
| 3
|}
</td><td align="center" style="padding-left:12px;">
[[Image:Move_SL.png|framed|right|Small still lifes in the move rule<br />{{JavaRLE|movestilllifes|brief}}]]
</td></tr></table>

===Common Objects===
Random starting patterns tend to stabilize into a much lower density (around 0.4%) than in [[Conway's Game of Life|Game of Life]] (around 3%). There are many more [[oscillator]]s than [[still life]]s in Move. About five sixths of objects in random settled areas are oscillators.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|51 px|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|51 px|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| R-Pentomino
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}
The R-pentomino is a P4 oscillator whose evolution can be seen at http://pixelartmaker.com/art/eff70a0fbd389b9.

===Spaceships===
[[Image:move_glider.gif|framed|right|The jellyfish<br />{{JavaRLE|jellyfish|brief}}]]There are at least 16 spaceships known in the move rule.<ref name="Eppstein" /> Of these, by far the most well-known is the '''jellyfish''', which is only one known to occur naturally from [[soup]] and travels at [[speed]] c/7 diagonally.

===Guns===
[[Image:Jasonsbow.png|framed|right|Jason's bow, a period 404 double-barreled gun<br />{{JavaRLE|jasonsbow}}]]At least 11 guns have been found, most of them by Stephen Morley and Jason Summers.<ref>{{cite web|url=http://safalra.com/special/b368s245/guns/ |title=b368s245 Guns |publisher=Stephen Morley|accessdate=March 28, 2009}}</ref> The first gun to be constructed was called Safalra's bow and was discovered on September 21, 2002 by Stephen Morley. It shoots two c/7 diagonal spaceships in opposite directions every 404 generations. Jason's bow, shown to the right, is a smaller version of Safalra's bow that was found by Jason Summers.

===Other patterns===
One [[puffer]] that commonly appears from random starting configurations is shown below. Its period is 170 and it travels at [[speed]] 13c/170. It is formed by a common six-cell pattern, which is the smallest pattern that exhibits [[infinite growth]] in this rule.
{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:move_pufpred.png|framed|center|A six-cell starting configuration of the puffer]]
|[[Image:move_puffer.gif|framed|center|A common puffer<br />{{JavaRLE|movepuffer}}]]
|}

==References==
<references />

Talk:Switch engine

2015-10-10T00:55:35Z

2x2:

[[User:Kiran.|Kiran]] ([[User talk:Kiran.|talk]]) 02:29, 13 July 2015 (UTC)What is the decomino seed?
==Misc.==
Look what I found!

x = 27, y = 27, rule = B3/S23

22bobo$21bo$22bo2bo$24b3o18$bo$obo2$o2bo$2b2o$3bo!

-wwei23 5:56PM 10/9/2015 NY time

Long barge with 2 tails? [[User:2x2|2x2]] ([[User talk:2x2|talk]]) 00:55, 10 October 2015 (UTC)

Talk:Puffer

2015-08-10T18:22:59Z

2x2: Created page with "==New puffer I found== I don't know where to put this, but I seem to have found a puffer made of 2 glider puffers and a blinker puffer. It may be used because it creats ash th..."

==New puffer I found==
I don't know where to put this, but I seem to have found a puffer made of 2 glider puffers and a blinker puffer. It may be used because it creats ash that interupts the front stream of gliders at certain intervals:

a_n=44+175(9^n+1)

Where n>3. I was thinking of putting 2 one-time eaters (blocks, perhaps) at the first two intervals (gen 165, gen 1535), then making a c/8 spaceship interact with the gliders.

Again, I don't know if this is notable, but the RLE is at [http://pastebin.com/YbHGTa94]

Thanks, and let me know if this is in the wrong section --[[User:2x2|2x2]] ([[User talk:2x2|talk]]) 18:22, 10 August 2015 (UTC)

OCA:2×2

2015-08-10T00:23:45Z

2x2: I set up a wiki!

{{Rule|name=2×2|imgname=2x2|s=125|b=36|char=Chaotic|animated=true}}
'''2×2''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s survive from one generation to the next if they have 1, 2 or 5 [[neighbours]], and are born if they have 3 or 6 neighbours. It thus has rulestring "B36/S125". Patterns under the rule have a chaotic evolution similar to those under the [[Conway's Game of Life|standard Life rules]], but the chaos tends to die out much more quickly.

Its name comes from the fact that patterns made up of 2×2 blocks continue to evolve as patterns made up of 2×2 blocks.

A 2×2 wiki has been set up at [http://2x2.wikia.com].

==Block evolution==
The 2×2 rule can emulate a simpler cellular automaton that acts on each 2×2 block. The emulated automaton is a [[block cellular automaton]] that makes use of the [[Margolus neighbourhood]] and evolves according to the following six rules:

[[Image:2x2block_evolve.png|framed|center|The 2x2 block evolution rule]]

Note that, as this emulates a Margolus neighbourhood, the resulting block appears at the center of the original four blocks. Thus, patterns that are originally made up of 2×2 blocks will forever be made up of 2×2 blocks, but the block partition will be offset by one [[cell]] in the odd [[generation]]s from the even generations. By examining the image above, one can see that a Life-like cellular automaton will emulate a Margolus block cellular automaton if and only if the following four equations are satisfied: B4 = S4, B5 = S6 = S7, B3 = S5, B1 = B2 = S3, where the first equation for example means that the birth condition for cells with four neighbours must equal the survival condition for cells with four neighbours. There are 2<sup>12</sup> = 4096 such rules, which emulate 2<sup>6</sup> = 64 different block cellular automata.

This rule can be seen to satisfy the above equations because 4 is neither a birth condition nor a survival condition, 5 is not a birth condition and 6 and 7 are not survival conditions, 3 is a birth condition and 5 is a survival condition, and 3 is not a survival condition and 1 and 2 are not birth conditions.

==Notable patterns==
A large variety of [[still life]]s and [[oscillators]] appear spontaneously from randomly generated starting states. There is also a somewhat rare naturally-occurring [[spaceship]], which travels at c/8 diagonally.

===Still lifes===
Still lifes are generally smaller in 2×2 than in Life, with the smallest occurring having a
population of just 2 cells. These still life patterns still tend to be similar to Life patterns in terms
of structure, for example often having islands that stabilise each other.
Many still lifes from Life are also still lifes in 2×2, For example, the [[beehive]], [[tub]], [[loaf]], [[pond]] and [[mango]].
[[Image:2x2stills.png|framed|center|Some sample still lifes.<br />{{JavaRLE|2x2stills}}]]

====Enumerating still lifes====
The following table catalogs all still lifes in the 2x2 rule with 10 or fewer [[cell]]s.<ref>Computed using the ''EnumStillLifes.c'' script located [http://www.conwaylife.com/forums/viewtopic.php?f=9&t=44 here].</ref>

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| 1
| 0
|
|
|-
| 2
| 2
| [[Image:2x22cellstilllifes.png]]
| {{JavaRLE|2x22cellstilllifes}}
|-
| 3
| 1
| [[Image:2x23cellstilllifes.png]]
| {{JavaRLE|2x23cellstilllifes}}
|-
| 4
| 3
| [[Image:2x24cellstilllifes.png]]
| {{JavaRLE|2x24cellstilllifes}}
|-
| 5
| 4
| [[Image:2x25cellstilllifes.png]]
| {{JavaRLE|2x25cellstilllifes}}
|-
| 6
| 9
| [[Image:2x26cellstilllifes.png]]
| {{JavaRLE|2x26cellstilllifes}}
|-
| 7
| 10
| [[Image:2x27cellstilllifes.png]]
| {{JavaRLE|2x27cellstilllifes}}
|-
| 8
| 27
| [[Image:2x28cellstilllifes.png]]
| {{JavaRLE|2x28cellstilllifes}}
|-
| 9
| 48
| [[Image:2x29cellstilllifes.png]]
| {{JavaRLE|2x29cellstilllifes}}
|-
| 10
| 126
| [[Image:2x210cellstilllifes.png]]
| {{JavaRLE|2x210cellstilllifes}}
|}

===Common still lifes===
The following table lists the twenty most common [[strict still life]]s that arise after several generations of a [[soup|random starting pattern]].<ref name="freqres">Full results are located [http://www.conwaylife.com/forums/download/file.php?id=18 here].</ref> The "approx. rel. freq." column gives an estimate of the proportion of all randomly-occurring still lifes that will be of the given type.
<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%" valign="top">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Pattern
! # of cells
! Approx. rel. freq. (out of 1.00)
|-
! 1
| [[Image:2x2_stilllife_rank1.png]] ([[domino]])
| 2
| 0.582
|-
! 2
| [[Image:2x2_stilllife_rank2.png]]
| 2
| 0.251
|-
! 3
| [[Image:2x2_stilllife_rank3.png]]
| 5
| 0.052
|-
! 4
| [[Image:2x2_stilllife_rank4.png]]
| 3
| 0.0498
|-
! 5
| [[Image:2x2_stilllife_rank5.png]]
| 6
| 0.0252
|-
! 6
| [[Image:2x2_stilllife_rank6.png]]
| 4
| 0.019
|-
! 7
| [[Image:2x2_stilllife_rank7.png]]
| 5
| 0.00725
|-
! 8
| [[Image:2x2_stilllife_rank8.png]] ([[beehive]])
| 6
| 0.00384
|-
! 9
| [[Image:2x2_stilllife_rank9.png]] ([[tub]])
| 4
| 0.00322
|-
! 10
| [[Image:2x2_stilllife_rank10.png]]
| 5
| 0.00195
|}
</td><td align="center" width="50%">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Pattern
! # of cells
! Approx. rel. freq. (out of 1.00)
|-
! 11
| [[Image:2x2_stilllife_rank11.png]]
| 4
| 0.00124
|-
! 12
| [[Image:2x2_stilllife_rank12.png]] ([[loaf]])
| 7
| 5.8×10<sup>-4</sup>
|-
! 13
| [[Image:2x2_stilllife_rank13.png]]
| 6
| 5.63×10<sup>-4</sup>
|-
! 14
| [[Image:2x2_stilllife_rank14.png]]
| 6
| 4.04×10<sup>-4</sup>
|-
! 15
| [[Image:2x2_stilllife_rank15.png]]
| 7
| 2.56×10<sup>-4</sup>
|-
! 16
| [[Image:2x2_stilllife_rank16.png]] ([[aircraft carrier]])
| 6
| 2.23×10<sup>-4</sup>
|-
! 17
| [[Image:2x2_stilllife_rank17.png]] ([[pond]])
| 8
| 1.94×10<sup>-4</sup>
|-
! 18
| [[Image:2x2_stilllife_rank18.png]] ([[mango]])
| 8
| 1.28×10<sup>-4</sup>
|-
! 19
| [[Image:2x2_stilllife_rank19.png]]
| 5
| 9.6×10<sup>-5</sup>
|-
! 20
| [[Image:2x2_stilllife_rank20.png]]
| 6
| 7.68×10<sup>-5</sup>
|}
</td></tr></table>

===Oscillators===
A large variety of oscillators of various periods occur naturally in 2×2.

====Period two oscillators====
Many of the [[period]] 2 oscillators in 2×2 have a single-cell 'on-off' [[rotor]], with small variations in the
[[stator]] of the oscillator. These occur fairly frequently naturally.
[[Image:2x2_p2s.gif|framed|center|Some period 2 oscillators.<br />{{JavaRLE|2x2period2oscillators}} ]]

====Higher-period oscillators====
One of the most interesting aspects of the 2×2 rule is the large number of naturally-occurring higher-period oscillators. Oscillators with periods 3, 4, 5, 6, 10, 14, 22 and 26 are all relatively frequent, and oscillators are also known for periods 8, 11, 12, 17, 24 and 60.
[[Image:2x2_oscillator_stamp.png|framed|center|Many oscillators with different periods from 2 through 60.<br />{{JavaRLE|2x2oscillators}} ]]

One simple infinite family of oscillators is given by the 2×(4n) boxes of alive [[cell]]s.<ref>{{Cite web|url=http://www.nathanieljohnston.com/index.php/2009/05/rectangular-oscillators-in-the-2x2-b36s125-cellular-automaton/|title=Rectangular Oscillators in the 2×2 (B36/S125) Cellular Automaton|author=Nathaniel Johnston|date=May 22, 2009|accessdate=May 24, 2009}}</ref> Such oscillators can be analyzed by noting that each [[phase]] of their oscillation can be represented as an exclusive or (XOR) of rectangles of different sizes that emulate the [[Rule 90]] cellular automaton.<ref>{{Cite web|url=http://groups.google.tk/group/comp.theory.cell-automata/browse_frm/thread/b059a5fb0c796743/c5683380affb8068?lnk=gst&q=2x2#c5683380affb8068|title=Life 2x2: long oscillator|publisher=comp.theory.cell-automata|accessdate=May 24, 2009|date=November 2, 2001}}</ref> The period of these oscillators for n = 1, 2, 3, ... is given by the sequence 2, 6, 14, 14, 62, 126, 30, 30, 1022, ... (Sloane's [https://oeis.org/A160657 A160657]).

====Naturally occurring oscillators====
The following table lists the twenty most common oscillators that arise after several generations of a [[soup|random starting pattern]].<ref name="freqres" /> Of particular interest are some quite high-period oscillators that appear abnormally frequently (in particular, the period 26 [[stairstep hexomino]] is the third most common oscillator). The "approx. rel. freq." column gives an estimate of the proportion of all randomly-occurring oscillators that will be of the given type.
<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%" valign="top">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Pattern
! [[Period]]
! Minimum # of [[cell]]s
! Approx. rel. freq. (out of 1.00)
|-
! 1
| [[Image:2x2_oscillator_rank1.gif]]
| 2
| 5
| 0.494
|-
! 2
| [[Image:2x2_oscillator_rank2.gif]]
| 2
| 8
| 0.204
|-
! 3
| [[Image:2x2_oscillator_rank3.gif]]
| 26
| 6
| 0.0698
|-
! 4
| [[Image:2x2_oscillator_rank4.gif]]
| 2
| 5
| 0.0514
|-
! 5
| [[Image:2x2_oscillator_rank5.gif]]
| 4
| 6
| 0.0332
|-
! 6
| [[Image:2x2_oscillator_rank6.gif]]
| 14
| 7
| 0.0324
|-
! 7
| [[Image:2x2_oscillator_rank7.gif]]
| 4
| 6
| 0.0285
|-
! 8
| [[Image:2x2_oscillator_rank8.gif]]
| 2
| 6
| 0.0217
|-
! 9
| [[Image:2x2_oscillator_rank9.gif]]
| 4
| 6
| 0.0169
|-
! 10
| [[Image:2x2_oscillator_rank10.gif]]
| 4
| 7
| 0.0152
|}
</td><td align="center" width="50%">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Pattern
! [[Period]]
! Minimum # of [[cell]]s
! Approx. rel. freq. (out of 1.00)
|-
! 11
| [[Image:2x2_oscillator_rank11.gif]]
| 2
| 8
| 0.00848
|-
! 12
| [[Image:2x2_oscillator_rank12.gif]]
| 2
| 6
| 0.007
|-
! 13
| [[Image:2x2_oscillator_rank13.gif]]
| 10
| 12
| 0.00457
|-
! 14
| [[Image:2x2_oscillator_rank14.gif]]
| 2
| 7
| 0.00196
|-
! 15
| [[Image:2x2_oscillator_rank15.gif]]
| 2
| 7
| 0.00175
|-
! 16
| [[Image:2x2_oscillator_rank16.gif]]
| 2
| 6
| 0.00175
|-
! 17
| [[Image:2x2_oscillator_rank17.gif]]
| 14
| 6
| 0.00156
|-
! 18
| [[Image:2x2_oscillator_rank18.gif]]
| 2
| 8
| 0.00106
|-
! 19
| [[Image:2x2_oscillator_rank19.gif]]
| 6
| 16
| 0.00106
|-
! 20
| [[Image:2x2_oscillator_rank20.gif]]
| 22
| 8
| 0.00043
|}
</td></tr></table>

[[Image:2x2glider.gif|framed|right|The c/8 glider.<br />{{JavaRLE|2x2glider|brief}} ]]

===Spaceships===
There are a number of spaceships known to occur in 2×2 <ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b36s125/ |title=2x2 (B36/S125) |publisher=David Eppstein|accessdate=March 18, 2009}}</ref>. Of these, only one is known to occur naturally from [[soup]]. It travels at c/8 diagonally.

===Infinite growth===
The first known infinitely-growing pattern in 2×2 was discovered in June 2009 by Nathaniel Johnston while testing the [http://www.conwaylife.com/soup/ Online Life-Like CA Soup Search] -- a c/8 diagonal [[wickstretcher]] based on the above c/8 glider.<ref>{{Cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=114|title=First infinite growth in 2x2 (B36/S125)?|publisher=ConwayLife.com forums|accessdate=July 13, 2009}}</ref><ref>{{Cite web|url=http://www.nathanieljohnston.com/index.php/2009/07/the-online-life-like-ca-soup-search/|title=The Online Life-Like CA Soup Search|publisher=NathanielJohnston.com|date=July 11, 2009|accessdate=July 13, 2009}}</ref> Multiple C/2 [[puffers]] have been discovered by Paul Tooke in 2010 including p60 forward and backward c/8 glider [[rakes]], a 2c/5 [[puffer]] was also discovered. No [[gun]]s have yet been discovered in 2×2. An MMS [[breeder]] was [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=39&start=25#p20740 discovered] by wildmyron on June 25, 2015.

[[Image:2x2linepuffer.gif|center|framed|The c/8 wickstretcher<br />{{JavaRLE|2x2linepuffer|brief}}]]

==References==
<references />