{{Rule|name=2x2|imgname=2x2|s=125|b=36|char=Chaotic|animated=true}}
'''2x2''' 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. Its name comes from the fact that it sends patterns made up of 2x2 blocks to patterns made up of 2x2 blocks.

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.

==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 2x2 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 2x2, For example, the [[beehive]], [[tub]], [[loaf]], [[pond]] and [[mango]].
[[Image:2x2stills.png|framed|center|Some sample still lifes.<br />{{JavaRLE|2x2stills}}]]

====Enumerating the 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 in 2x2===
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! RLE
! No. of Cells
! Approx. Relative Frequency (out of 1.00)
|-
! 1
| 2o!
| 2
| 0.564
|-
! 2
| o$bo!
| 2
| 0.244
|-
! 3
| b2o$o$b2o!
| 5
| 0.0503
|-
! 4
| o$bo$2bo!
| 3
| 0.0482
|-
! 5
| b2o$o$o$b2o!
| 6
| 0.0244
|-
! 6
| b2o$o$o!
| 4
| 0.0185
|-
! 7
| bo$o$obo$bo!
| 5
| 0.00703
|-
! 8
| b2o$o2bo$b2o!
| 6
| 0.00372
|-
! 9
| bo$obo$bo!
| 4
| 0.00312
|-
! 10
| 3bo$2bo$o$2o!
| 5
| 0.00189
|-
! 11
| 3bo$2bo$bo$o!
| 4
| 0.00121
|-
! 12
| b2o$o2bo$bobo$2bo!
| 7
| 5.61×10<sup>-4</sup>
|-
! 13
| bo$obo$o$2bo$3bo!
| 6
| 5.45×10<sup>-4</sup>
|-
! 14
| bo$obo$o$bo$2bo!
| 6
| 3.91×10<sup>-4</sup>
|-
! 15
| bob2o$o3bo$b2o!
| 7
| 2.48×10<sup>-4</sup>
|-
! 16
| 2o$o2bo$2b2o!
| 6
| 2.17×10<sup>-4</sup>
|-
! 17
| b2o$o2bo$o2bo$b2o!
| 8
| 1.88×10<sup>-4</sup>
|-
! 18
| 2bo$bobo$o2bo$obo$bo!
| 8
| 1.24×10<sup>-4</sup>
|-
! 19
| 4bo$3bo$2bo$bo$o!
| 5
| 9.3×10<sup>-5</sup>
|-
! 20
| bo$o$obo$2bo$bo!
| 6
| 7.44×10<sup>-5</sup>
|}
===Oscillators===
A large variety of oscillators of various periods occur naturally in 2x2.

====Period two oscillators====
Many of the [[period]] 2 oscillators in 2x2 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 2x2 rule is the large number of naturally-occurring higher-period oscillators. Oscillators with periods 3, 4, 6, 10, 11, 14, 17, 22 and 26 are all relatively frequent, and oscillators are also known for periods 5, 12, 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. The period of such oscillators for n = 1, 2, 3, ... is given by the sequence 2, 6, 14, 14, 62, 126, 30, 30, 1022, ...

====Naturally occurring Oscillators====
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! [[RLE]]
! [[Period]]
! Minimum No. of [[Cells]]
! Approx. Relative Frequency (out of 1.00)
|-
! 1
| b2o$o$2o!
| 2
| 5
| 0.494
|-
! 2
| 4o$4o!
| 2
| 8
| 0.204
|-
! 3
| 2bo$b2o$2o$o!
| 26
| 6
| 0.0698
|-
! 4
| b2o$o2bo$2o!
| 2
| 5
| 0.0514
|-
! 5
| obo$2bo$2bo$b2o!
| 4
| 6
| 0.0332
|-
! 6
| 2bo$3bo$ob3o$b2o$2bo!
| 14
| 7
| 0.0324
|-
! 7
| o$bo$bo$2bo$2o!
| 4
| 6
| 0.0285
|-
! 8
| o$obo$bo$2b2o!
| 2
| 6
| 0.0217
|-
! 9
| bobo$3bo$2bo$2o!
| 4
| 6
| 0.0169
|-
! 10
| b2o$o3bo$o2b2o!
| 4
| 7
| 0.0152
|-
! 11
| b3o$obobo$obobo!
| 2
| 8
| 0.00848
|-
! 12
| b2o$3bo$2o2bo!
| 2
| 6
| 0.007
|-
! 13
| 5o$b3o2$b3o$5o!
| 10
| 12
| 0.00457
|-
! 14
| b2o$2bo$o$obo$2bo!
| 2
| 7
| 0.00196
|-
! 15
| 3bo$2bo$bo$o$obo$b2o!
| 2
| 7
| 0.00175
|-
! 16
| 4bo$2obo$o$b2o!
| 2
| 6
| 0.00175
|-
! 17
| b2o2$bo$o3bo$5bo!
| 14
| 6
| 0.00156
|-
! 18
| 3b2o$2bobo2$obo$2o!
| 2
| 8
| 0.00106
|-
! 19
| 6o$6o$6o$6o!
| 6
| 16
| 0.00106
|-
! 20
| o$3o3$3o$o!
| 22
| 8
| 0.00043
|}

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

===Spaceships===
There are a number of spaceships known to occur in 2x2 <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.

===Other patterns===
No infinite-growth mechanisms ([[gun|guns]], [[puffer|puffers]] etc.) have yet been discovered in 2x2.

==References==
<references />

OCA:2×2

2009-04-18T08:41:08Z

Lewis Patterson:

OCA talk:2×2

2009-04-17T20:36:01Z

Lewis Patterson:

==Text==
We've got a lot of pretty pictures, but this page needs a lot more text to look reasonably balanced. [[User:Elithrion|Elithrion]] 11:00, 19 March 2009 (UTC)

==My changes==
So, I tried to make it more similar to the [[maze]] page layout-wise, simply because consistency is good. Also because (and I mean no offence), the previous layout was horribly confusing with images everywhere. Nath, you need to add the rle/java stuff that I gratuitously linked to without it existing, though. Also, I was lazy, so I just resized 2x2hp via computer (instead of redrawing at a smaller size), but I think with the filter I used it came out okay (although if someone wants to do it properly, that would be better). [[User:Elithrion|Elithrion]] 11:00, 19 March 2009 (UTC)

: I've added the Java/RLE files so that the links now work (well, they work as well as any of the auto-load links work right now). I also swapped out the image of the high-period oscillators for the larger stamp collection image/pattern. [[User:Nathaniel|Nathaniel]] 21:59, 19 March 2009 (UTC)

==2xn box oscillators==
Just wondering if anyone's investigated these semi-thoroughly? I've explored them a little bit this morning, and the period of a 2x(4n) oscillator for n = 1...9 is given by the sequence 2,6,14,14,62,126,30,30,1022. It is not hard to see that each of these is exactly 2 less than a power of 2, which almost surely isn't a coincidence. Indeed, if we add 2 to each term and half the result, we get the sequence 2,4,8,8,32,64,16,16,512. Taking log base 2 of each of these numbers gives 1,2,3,3,5,6,4,4,9, which has a single match in the OEIS ([http://www.research.att.com/~njas/sequences/A003558 here]), which I'm willing to bet gives us the sequence that we want. I'll have a stab at proving it a bit later, I suppose. [[User:Nathaniel|Nathaniel]] 12:37, 19 March 2009 (UTC)

: Well, I just played around with it a little (I would have done it sooner but there's no java link, so I wasn't feeling inspired ;)), and I have to add to your observations that in general, any big box made up by of m×n blocks, where m is even, and n is odd (or to vaguely tie into the pattern you noticed, where m = 0 mod 2, n = 1 mod 2), will be an oscillator. All these boxes are, seemingly, phases of the 2×(4n) series of oscillators (or vice versa!), but they make for a more interesting statement of what's going on, I think. Also, I have proceeded to make no real observations about them thus far. Yay! [[User:Elithrion|Elithrion]] 15:42, 19 March 2009 (UTC)

==Still Life Counts==
How did you find the amount of 8-cell still lifes? [[User:Lewis Patterson|Lewis Patterson]] 18:54, 25 March 2009 (UTC)

: I coded a script in C that counts still lifes in arbitrary rules. I'll upload it to the forums tonight or tomorrow, after I've had a chance to clean up the code a bit. [[User:Nathaniel|Nathaniel]] 20:03, 25 March 2009 (UTC)

==Frequency of common patterns==
Would it be worthwile including a table of the most common patterns on this page, similar to the table at [[List of common still lifes]]. I have some statistics of patterns in this rule (so far around at about 17 million total objects of 300 types) that we could use.
[[User:Lewis Patterson|Lewis Patterson]] 09:54, 14 April 2009 (UTC)

: I don't see why not. The more information the better! [[User:Nathaniel|Nathaniel]] 12:14, 14 April 2009 (UTC)

:: How would we go about naming the patterns? I use codes similar to the ones at http://www.geocities.com/conwaylife/ which would be confusing to anyone who doesn't understand how the codes work. I suppose we could use images for each pattern. [[User:Lewis Patterson|Lewis Patterson]] 14:08, 14 April 2009 (UTC)

::: For still lifes I think the general convention if to do something like (number of cells).(some index). So in standard life, you would set the block and tub to be 4.1 and 4.2 (with the second index chosen more or less arbitrarily, though you certainly ''could'' construct an order on patterns). For oscillators the most common seems to be (minimum number of cells)P(period).index, and omitting the index if only one such pattern exists/is known. So the blinker would be 3P2, for example. I think this would work well enough here as well, though I think images should go along with the table anyways.--[[User:Nathaniel|Nathaniel]] 21:06, 16 April 2009 (UTC)

:::: How many patterns would be best to include in the table? So far, the statistics are at 303 object types. Including all of them would make for a huge table, and a lot of pictures (if we used pictures). Maybe a table of the most common 25 or so objects woud be best.
::::Also, would a seperate table for oscillators be worth making, maybe in the oscillators section of the page?[[User:Lewis Patterson|Lewis Patterson]] 18:03, 17 April 2009 (UTC)

::::: I think a table of 25 on the page itself is probably a good number, possibly with an external link or reference to a plaintext file containing the full 303 (if you have it available in a semi-readable plaintext form? if not that of course is optional). And personally I prefer keeping oscillator counts separate from still-life counts, but I think that's mostly a personal preference thing. [[User:Nathaniel|Nathaniel]] 18:48, 17 April 2009 (UTC)

:::::: Is the RLE text for each pattern OK to put in the table until we get the pictures for each pattern? (eg. Life's beehive would be displayed as b2o$o2bo$b2o!). It can be copied/pasted into most programs easily and I have the RLE codes for all the patterns already. [[User:Lewis Patterson|Lewis Patterson]] 20:36, 17 April 2009 (UTC)

OCA talk:2×2

2009-04-17T20:35:43Z

Lewis Patterson:

==Text==
We've got a lot of pretty pictures, but this page needs a lot more text to look reasonably balanced. [[User:Elithrion|Elithrion]] 11:00, 19 March 2009 (UTC)

==My changes==
So, I tried to make it more similar to the [[maze]] page layout-wise, simply because consistency is good. Also because (and I mean no offence), the previous layout was horribly confusing with images everywhere. Nath, you need to add the rle/java stuff that I gratuitously linked to without it existing, though. Also, I was lazy, so I just resized 2x2hp via computer (instead of redrawing at a smaller size), but I think with the filter I used it came out okay (although if someone wants to do it properly, that would be better). [[User:Elithrion|Elithrion]] 11:00, 19 March 2009 (UTC)

: I've added the Java/RLE files so that the links now work (well, they work as well as any of the auto-load links work right now). I also swapped out the image of the high-period oscillators for the larger stamp collection image/pattern. [[User:Nathaniel|Nathaniel]] 21:59, 19 March 2009 (UTC)

==2xn box oscillators==
Just wondering if anyone's investigated these semi-thoroughly? I've explored them a little bit this morning, and the period of a 2x(4n) oscillator for n = 1...9 is given by the sequence 2,6,14,14,62,126,30,30,1022. It is not hard to see that each of these is exactly 2 less than a power of 2, which almost surely isn't a coincidence. Indeed, if we add 2 to each term and half the result, we get the sequence 2,4,8,8,32,64,16,16,512. Taking log base 2 of each of these numbers gives 1,2,3,3,5,6,4,4,9, which has a single match in the OEIS ([http://www.research.att.com/~njas/sequences/A003558 here]), which I'm willing to bet gives us the sequence that we want. I'll have a stab at proving it a bit later, I suppose. [[User:Nathaniel|Nathaniel]] 12:37, 19 March 2009 (UTC)

: Well, I just played around with it a little (I would have done it sooner but there's no java link, so I wasn't feeling inspired ;)), and I have to add to your observations that in general, any big box made up by of m×n blocks, where m is even, and n is odd (or to vaguely tie into the pattern you noticed, where m = 0 mod 2, n = 1 mod 2), will be an oscillator. All these boxes are, seemingly, phases of the 2×(4n) series of oscillators (or vice versa!), but they make for a more interesting statement of what's going on, I think. Also, I have proceeded to make no real observations about them thus far. Yay! [[User:Elithrion|Elithrion]] 15:42, 19 March 2009 (UTC)

==Still Life Counts==
How did you find the amount of 8-cell still lifes? [[User:Lewis Patterson|Lewis Patterson]] 18:54, 25 March 2009 (UTC)

: I coded a script in C that counts still lifes in arbitrary rules. I'll upload it to the forums tonight or tomorrow, after I've had a chance to clean up the code a bit. [[User:Nathaniel|Nathaniel]] 20:03, 25 March 2009 (UTC)

==Frequency of common patterns==
Would it be worthwile including a table of the most common patterns on this page, similar to the table at [[List of common still lifes]]. I have some statistics of patterns in this rule (so far around at about 17 million total objects of 300 types) that we could use.
[[User:Lewis Patterson|Lewis Patterson]] 09:54, 14 April 2009 (UTC)

: I don't see why not. The more information the better! [[User:Nathaniel|Nathaniel]] 12:14, 14 April 2009 (UTC)

:: How would we go about naming the patterns? I use codes similar to the ones at http://www.geocities.com/conwaylife/ which would be confusing to anyone who doesn't understand how the codes work. I suppose we could use images for each pattern. [[User:Lewis Patterson|Lewis Patterson]] 14:08, 14 April 2009 (UTC)

::: For still lifes I think the general convention if to do something like (number of cells).(some index). So in standard life, you would set the block and tub to be 4.1 and 4.2 (with the second index chosen more or less arbitrarily, though you certainly ''could'' construct an order on patterns). For oscillators the most common seems to be (minimum number of cells)P(period).index, and omitting the index if only one such pattern exists/is known. So the blinker would be 3P2, for example. I think this would work well enough here as well, though I think images should go along with the table anyways.--[[User:Nathaniel|Nathaniel]] 21:06, 16 April 2009 (UTC)

:::: How many patterns would be best to include in the table? So far, the statistics are at 303 object types. Including all of them would make for a huge table, and a lot of pictures (if we used pictures). Maybe a table of the most common 25 or so objects woud be best.
::::Also, would a seperate table for oscillators be worth making, maybe in the oscillators section of the page?[[User:Lewis Patterson|Lewis Patterson]] 18:03, 17 April 2009 (UTC)

::::: I think a table of 25 on the page itself is probably a good number, possibly with an external link or reference to a plaintext file containing the full 303 (if you have it available in a semi-readable plaintext form? if not that of course is optional). And personally I prefer keeping oscillator counts separate from still-life counts, but I think that's mostly a personal preference thing. [[User:Nathaniel|Nathaniel]] 18:48, 17 April 2009 (UTC)

:::::: Is the RLE text for each pattern OK to put in the table until we get the pictures for each pattern? (eg. Life's beehive would be displayed as b2o$o2bo$b2o!). It can be copied/pasted into most programs easily and I have the RLE codes for all the patterns already.

Oscillator

2009-04-17T18:07:31Z

Lewis Patterson:

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] and a [[stator]].

In general [[cellular automaton]] theory the term oscillator usually covers [[spaceship]]s as well, but this usage is not normal in [[Conway's Game of Life]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only [[true period]] oscillators are considered here. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, in which situation a question mark (?) is presented along with the oscillator that has the earliest known date of discovery.

<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
|-
! [[:Category:Oscillators with period 2|2]]
| [[blinker]]
| [[:Category:Patterns found by John Conway|John Conway]]
| [[:Category:Patterns found in 1970|1970]]
|-
! [[:Category:Oscillators with period 3|3]]
| [[pulsar]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 4|4]]
| [[pinwheel]]
| [[:Category:Patterns found by Simon Norton|Simon Norton]]
| 1970
|-
! [[:Category:Oscillators with period 5|5]]
| [[octagon 2]]
| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]]
| [[:Category:Patterns found in 1971|1971]]
|-
! [[:Category:Oscillators with period 6|6]]
| (?) [[$rats]], [[sombreros]]
| [[:Category:Patterns found by David Buckingham|David Buckingham]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 7|7]]
| [[burloaferimeter]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 8|8]]
| [[figure eight]]
| Simon Norton
| 1970
|-
! [[:Category:Oscillators with period 9|9]]
| [[worker bee]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 10|10]]
| [[42P10.1]]
| David Buckingham
| ≤[[:Category:Patterns found in 1976|1976]]
|-
! [[:Category:Oscillators with period 11|11]]
| [[38P11.1]]
| David Buckingham
| [[:Category:Patterns found in 1977|1977]]
|-
! [[:Category:Oscillators with period 12|12]]
| [[dinner table]]
| [[:Category:Patterns found by Robert Wainwright|Robert Wainwright]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 13|13]]
| [[65P13.1]]
| David Buckingham
| 1976
|-
! [[:Category:Oscillators with period 14|14]]
| [[tumbler]]
| George Collins, Jr.
| 1970
|-
! [[:Category:Oscillators with period 15|15]]
| [[pentadecathlon]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 16|16]]
| [[two pre-L hasslers]]
| Robert Wainwright
| [[:Category:Patterns found in 1983|1983]]
|-
! [[:Category:Oscillators with period 17|17]]
| [[54P17.1]]
| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]]
| [[:Category:Patterns found in 1997|1997]]
|-
! [[:Category:Oscillators with period 18|18]]
| [[117P18]]
| David Buckingham
| ≤[[:Category:Patterns found in 1991|1991]]
|-
! class="red_td" | 19
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 20|20]]
| [[145P20]]
| [[:Category:Patterns found by Noam Elkies|Noam Elkies]]
| [[:Category:Patterns found in 1995|1995]]
|-
! [[:Category:Oscillators with period 21|21]]
| [[124P21]]
| Robert Wainwright
| 1995
|-
! [[:Category:Oscillators with period 22|22]]
| [[168P22.1]]
| Noam Elkies
| 1997
|-
! class="red_td" | 23
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 27|27]]
| [[123P27.1]]
| Noam Elkies
| [[:Category:Patterns found in 2002|2002]]
|-
! [[:Category:Oscillators with period 30|30]]
| [[queen bee shuttle]]
| Bill Gosper
| 1970
|-
! class="red_td" | 31
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 32|32]]
| [[gourmet]]
| David Buckingham
| [[:Category:Patterns found in 1978|1978]]
|-
! [[:Category:Oscillators with period 33|33]]
| (?)
| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]]
| 1997
|-
! class="red_td" | 34
| class="red_td" colspan="3" | ''No non-trivial examples found''
|-
! [[:Category:Oscillators with period 37|37]]
| [[124P37]]
| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]]
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 38
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 39|39]]
| [[134P39.1]]
| David Buckingham, Noam Elkies
| [[:Category:Patterns found in 2000|2000]]
|-
! class="red_td" | 41
| class="red_td" colspan="3" | ''None found''
|-
! class="red_td" | 43
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 46|46]]
| [[twin bees shuttle]]
| Bill Gosper
| 1971
|-
! [[:Category:Oscillators with period 49|49]]
| [[440P49.1]]
| Noam Elkies
| [[:Category:Patterns found in 1999|1999]]
|-
! [[:Category:Oscillators with period 51|51]]
| [[112P51]]
| Nicolay Beluchenko
| 2009
|-
! class="red_td" | 53
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 54|54]]
| [[P54 shuttle]]
| David Buckingham
| 1974
|-
! [[:Category:Oscillators with period 110|110]]
| [[P110 traffic jam]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 144|144]]
| [[Achim's p144]]
| Achim Flammenkamp
| 1994
|}</td><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! Smallest known
! Minimum # of [[cell]]s
|-
! 2
| blinker
| [[:Category:Patterns with 3 cells|3]]
|-
! 3
| [[caterer]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 4
| [[mazing]], [[mold]]
| 12
|-
! 5
| [[pseudo-barberpole]]
| [[:Category:Patterns with 15 cells|15]]
|-
! 6
| [[unix]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 7
| [[28P7.1]], [[28P7.2]], [[burloaferimeter]]
| [[:Category:Patterns with 28 cells|28]]
|-
! 8
| figure eight
| 12
|-
! 9
| [[29P9.1]]
| [[:Category:Patterns with 29 cells|29]]
|-
! 10
| [[37P10.1]], 37P10.2
| [[:Category:Patterns with 37 cells|37]]
|-
! 11
| 38P11.1
| [[:Category:Patterns with 38 cells|38]]
|-
! 12
| dinner table
| [[:Category:Patterns with 33 cells|33]]
|-
! 13
| [[34P13.1]]
| [[:Category:Patterns with 34 cells|34]]
|-
! 14
| [[tumbler]]
| 16
|-
! 15
| [[pentadecathlon]]
| 12
|-
! 16
| [[Achim's p16]]
| [[:Category:Patterns with 32 cells|32]]
|-
! 17
| 54P17.1
| [[:Category:Patterns with 54 cells|54]]
|-
! 18
| [[43P18]]
| [[:Category:Patterns with 43 cells|43]]
|-
! class="red_td" | 19
| class="red_td" colspan="2" | ''None found''
|-
! 20
| [[mold on fumarole]]
| [[:Category:Patterns with 30 cells|30]]
|-
! 21
| [[jam on 44P7.2]]
| [[:Category:Patterns with 57 cells|57]]
|-
! 22
| [[36P22.1]]
| [[:Category:Patterns with 36 cells|36]]
|-
! class="red_td" | 23
| class="red_td" colspan="2" | ''None found''
|-
! 24
| [[Caterer on figure eight]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 27
| [[94P27.1]]
| [[:Category:Patterns with 94 cells|94]]
|-
! 29
| [[pre-pulsar shuttle 29]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 30
| [[queen bee shuttle]]
| [[:Category:Patterns with 20 cells|20]]
|-
! class="red_td" | 31
| class="red_td" colspan="2" | ''None found''
|-
! 33
| [[92P33.1]]
| [[:Category:Patterns with 92 cells|92]]
|-
! class="red_td" | 34
| class="red_td" colspan="2" | ''None found''
|-
! 37
| 124P37
| [[:Category:Patterns with 124 cells|124]]
|-
! class="red_td" | 38
| class="red_td" colspan="2" | ''None found''
|-
! 39
| [[jam on 34P13.1]]
| [[:Category:Patterns with 47 cells|47]]
|-
! class="red_td" | 41
| class="red_td" colspan="2" | ''None found''
|-
! class="red_td" | 43
| class="red_td" colspan="2" | ''None found''
|-
! 49
| 440P49.1
| [[:Category:Patterns with 440 cells|440]]
|-
! 51
| 112P51
| [[:Category:Patterns with 112 cells|112]]
|-
! class="red_td" | 53
| class="red_td" colspan="2" | ''None found''
|-
! 54
| [[P54 shuttle]]
| [[:Category:Patterns with 48 cells|48]]
|-
! 100
| [[centinal]]
| [[:Category:Patterns with 70 cells|70]]
|}
</td></tr></table>

==See also==
*[[List of common oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]

==External links==
*[http://web.archive.org/web/20070918210303/www.math.ucdavis.edu/~dean/RLE/stamps.html Oscillator Stamp Collection] by Dean Hickerson, via [http://www.archive.org Archive.org]
*[http://www.argentum.freeserve.co.uk/lex_o.htm#oscillator Oscillator] at the Life Lexicon

OCA talk:2×2

2009-04-17T18:03:52Z

Lewis Patterson:

OCA talk:HighLife

2009-04-16T18:30:06Z

Lewis Patterson:

==Pattern pages for non-standard rules?==
What do people think about having pattern pages for rules other than Conway's Life (such as HighLife, provided there's actually quite a few patterns for that rule of course)? The reason I ask is that there are probably 50 or so complex constructed patterns for the HighLife rule, most of which are probably worth a mention, and they certainly won't all fit on one page.

If we do make pattern pages for another rule, the issue arises of distinguishing them from standard Conway patterns. We could of course add to the pattern box at the right a "rules" section that lists the rules that the pattern works in, but should the page names be altered as well? As an example, if we had a page for the Bomber spaceship, should we name it [[Bomber_(HighLife)]] or just [[Bomber]]? Any other thoughts/concerns? [[User:Nathaniel|Nathaniel]] 15:02, 16 April 2009 (UTC)

* The idea of putting the rules in the pattern box seems a good idea, although changing the names of the pages to show the rule may be difficult if patterns work in more than one rule, and not necessary unless there are 2 different patterns in different rules with the same name. [[User:Lewis Patterson|Lewis Patterson]] 18:30, 16 April 2009 (UTC)

Omniperiodic

2009-04-15T13:43:48Z

Lewis Patterson:

{{Glossary}}
A [[cellular automaton]] is said to be '''omniperiodic''' if it has [[oscillator]]s of all [[period]]s. It is not known if [[Conway's Game of Life]] is omniperiodic, although that is widely believed to be the case.

The only periods for which no oscillator is known are 19, 23, 31, 38, 41, 43 and 53. If it is insisted that the oscillator must contain a [[cell]] oscillating at the full period, then period 34 is also unknown (see [[period#Pseudo period|pseudo period]]). The most recently achieved periods were all found by [[:Category:Patterns found by Noam Elkies|Noam Elkies]]: period 49 in August [[:Category:Patterns found in 1999|1999]] (a glider loop using period 7 reflectors built from his new period 7 pipsquirter), period 39 in July [[:Category:Patterns found in 2000|2000]], and period 27 in November [[:Category:Patterns found in 2002|2002]].

Note that if infinite oscillators are allowed, then all periods are possible because any period of 14 or more can be obtained using a stream of [[glider]]s or [[lightweight spaceship]]s.

==Large-period oscillators==
In October [[:Category:Patterns found in 1996|1996]], [[:Category:Patterns found by David Buckingham|David Buckingham]] wrote the article [http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html ''My Experience with B-heptominos in Oscillators''] that describes his discovery of [[Conduit 1|Herschel conduits]], including sufficient stable [[conduit]]s to enable, for the first time, the construction of [[period]] n [[oscillator]]s - and true period n [[gun]]s - for every n ≥ 54.

==See also==
*[[Emu]]
*[[Herschel loop]]

==External links==
*[http://www.argentum.freeserve.co.uk/lex_m.htm#myexperiencewithbheptominosinoscillators My Experience with B-heptominos in Oscillators] at the Life Lexicon
*[http://www.argentum.freeserve.co.uk/lex_o.htm#omniperiodic Omniperiodic] at the Life Lexicon

Oscillator

2009-04-15T11:38:34Z

Lewis Patterson: Added P37 Oscillator

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] and a [[stator]].

In general [[cellular automaton]] theory the term oscillator usually covers [[spaceship]]s as well, but this usage is not normal in [[Conway's Game of Life]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only [[true period]] oscillators are considered here. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, in which situation a question mark (?) is presented along with the oscillator that has the earliest known date of discovery.

<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
|-
! [[:Category:Oscillators with period 2|2]]
| [[blinker]]
| [[:Category:Patterns found by John Conway|John Conway]]
| [[:Category:Patterns found in 1970|1970]]
|-
! [[:Category:Oscillators with period 3|3]]
| [[pulsar]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 4|4]]
| [[pinwheel]]
| [[:Category:Patterns found by Simon Norton|Simon Norton]]
| 1970
|-
! [[:Category:Oscillators with period 5|5]]
| [[octagon 2]]
| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]]
| [[:Category:Patterns found in 1971|1971]]
|-
! [[:Category:Oscillators with period 6|6]]
| (?) [[$rats]], [[sombreros]]
| [[:Category:Patterns found by David Buckingham|David Buckingham]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 7|7]]
| [[burloaferimeter]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 8|8]]
| [[figure eight]]
| Simon Norton
| 1970
|-
! [[:Category:Oscillators with period 9|9]]
| [[worker bee]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 10|10]]
| [[42P10.1]]
| David Buckingham
| ≤[[:Category:Patterns found in 1976|1976]]
|-
! [[:Category:Oscillators with period 11|11]]
| [[38P11.1]]
| David Buckingham
| [[:Category:Patterns found in 1977|1977]]
|-
! [[:Category:Oscillators with period 12|12]]
| [[dinner table]]
| [[:Category:Patterns found by Robert Wainwright|Robert Wainwright]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 13|13]]
| [[65P13.1]]
| David Buckingham
| 1976
|-
! [[:Category:Oscillators with period 14|14]]
| [[tumbler]]
| George Collins, Jr.
| 1970
|-
! [[:Category:Oscillators with period 15|15]]
| [[pentadecathlon]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 16|16]]
| [[two pre-L hasslers]]
| Robert Wainwright
| [[:Category:Patterns found in 1983|1983]]
|-
! [[:Category:Oscillators with period 17|17]]
| [[54P17.1]]
| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]]
| [[:Category:Patterns found in 1997|1997]]
|-
! [[:Category:Oscillators with period 18|18]]
| [[117P18]]
| David Buckingham
| ≤[[:Category:Patterns found in 1991|1991]]
|-
! class="red_td" | 19
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 20|20]]
| [[145P20]]
| [[:Category:Patterns found by Noam Elkies|Noam Elkies]]
| [[:Category:Patterns found in 1995|1995]]
|-
! [[:Category:Oscillators with period 21|21]]
| [[124P21]]
| Robert Wainwright
| 1995
|-
! [[:Category:Oscillators with period 22|22]]
| [[168P22.1]]
| Noam Elkies
| 1997
|-
! class="red_td" | 23
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 27|27]]
| [[123P27.1]]
| Noam Elkies
| [[:Category:Patterns found in 2002|2002]]
|-
! [[:Category:Oscillators with period 30|30]]
| [[queen bee shuttle]]
| Bill Gosper
| 1970
|-
! class="red_td" | 31
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 32|32]]
| [[gourmet]]
| David Buckingham
| [[:Category:Patterns found in 1978|1978]]
|-
! [[:Category:Oscillators with period 33|33]]
| (?)
| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]]
| [[:Category:Patterns found in 1997|1997]]
|-
! class="red_td" | 34
| class="red_td" colspan="3" | ''No non-trivial examples found''
|-
! [[:Category:Oscillators with period 37|37]]
| 124P37
| [[:Category:Patterns found by Niolay Beluchenko|Nicolay Beluchenko]]
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 38
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 39|39]]
| [[134P39.1]]
| David Buckingham, Noam Elkies
| [[:Category:Patterns found in 2000|2000]]
|-
! class="red_td" | 41
| class="red_td" colspan="3" | ''None found''
|-
! class="red_td" | 43
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 46|46]]
| [[twin bees shuttle]]
| Bill Gosper
| 1971
|-
! [[:Category:Oscillators with period 49|49]]
| [[440P49.1]]
| Noam Elkies
| [[:Category:Patterns found in 1999|1999]]
|-
! [[:Category:Oscillators with period 51|51]]
| [[112P51]]
| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]]
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 53
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 54|54]]
| [[P54 shuttle]]
| David Buckingham
| 1974
|-
! [[:Category:Oscillators with period 110|110]]
| [[P110 traffic jam]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 144|144]]
| [[Achim's p144]]
| Achim Flammenkamp
| 1994
|}</td><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! Smallest known
! Minimum # of [[cell]]s
|-
! 2
| blinker
| [[:Category:Patterns with 3 cells|3]]
|-
! 3
| [[caterer]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 4
| [[mazing]], [[mold]]
| 12
|-
! 5
| [[pseudo-barberpole]]
| [[:Category:Patterns with 15 cells|15]]
|-
! 6
| [[unix]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 7
| [[28P7.1]], [[28P7.2]], [[burloaferimeter]]
| [[:Category:Patterns with 28 cells|28]]
|-
! 8
| figure eight
| 12
|-
! 9
| [[29P9.1]]
| [[:Category:Patterns with 29 cells|29]]
|-
! 10
| [[37P10.1]], 37P10.2
| [[:Category:Patterns with 37 cells|37]]
|-
! 11
| 38P11.1
| [[:Category:Patterns with 38 cells|38]]
|-
! 12
| dinner table
| [[:Category:Patterns with 33 cells|33]]
|-
! 13
| [[34P13.1]]
| [[:Category:Patterns with 34 cells|34]]
|-
! 14
| [[tumbler]]
| 16
|-
! 15
| [[pentadecathlon]]
| 12
|-
! 16
| [[Achim's p16]]
| [[:Category:Patterns with 32 cells|32]]
|-
! 17
| 54P17.1
| [[:Category:Patterns with 54 cells|54]]
|-
! 18
| [[43P18]]
| [[:Category:Patterns with 43 cells|43]]
|-
! class="red_td" | 19
| class="red_td" colspan="2" | ''None found''
|-
! 20
| [[mold on fumarole]]
| [[:Category:Patterns with 30 cells|30]]
|-
! 21
| [[jam on 44P7.2]]
| [[:Category:Patterns with 57 cells|57]]
|-
! 22
| [[36P22.1]]
| [[:Category:Patterns with 36 cells|36]]
|-
! class="red_td" | 23
| class="red_td" colspan="2" | ''None found''
|-
! 27
| [[94P27.1]]
| [[:Category:Patterns with 94 cells|94]]
|-
! 29
| [[pre-pulsar shuttle 29]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 30
| [[queen bee shuttle]]
| [[:Category:Patterns with 20 cells|20]]
|-
! 33
| [[92P33.1]]
| [[:Category:Patterns with 92 cells|92]]
|-
! 39
| [[jam on 34P13.1]]
| [[:Category:Patterns with 47 cells|47]]
|-
! 49
| 440P49.1
| [[:Category:Patterns with 440 cells|440]]
|-
! 51
| 112P51
| [[:Category:Patterns with 112 cells|112]]
|-
! 54
| [[P54 shuttle]]
| [[:Category:Patterns with 48 cells|48]]
|-
! 100
| [[centinal]]
| [[:Category:Patterns with 70 cells|70]]
|}
</td></tr></table>

==See also==
*[[List of common oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]

==External links==
*[http://web.archive.org/web/20070918210303/www.math.ucdavis.edu/~dean/RLE/stamps.html Oscillator Stamp Collection] by Dean Hickerson, via [http://www.archive.org Archive.org]
*[http://www.argentum.freeserve.co.uk/lex_o.htm#oscillator Oscillator] at the Life Lexicon

Oscillator

2009-04-15T11:34:55Z

Lewis Patterson:

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] and a [[stator]].

In general [[cellular automaton]] theory the term oscillator usually covers [[spaceship]]s as well, but this usage is not normal in [[Conway's Game of Life]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only [[true period]] oscillators are considered here. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, in which situation a question mark (?) is presented along with the oscillator that has the earliest known date of discovery.

<table border="0" cellpadding="0" cellspacing="0" width="100%"><tr><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
|-
! [[:Category:Oscillators with period 2|2]]
| [[blinker]]
| [[:Category:Patterns found by John Conway|John Conway]]
| [[:Category:Patterns found in 1970|1970]]
|-
! [[:Category:Oscillators with period 3|3]]
| [[pulsar]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 4|4]]
| [[pinwheel]]
| [[:Category:Patterns found by Simon Norton|Simon Norton]]
| 1970
|-
! [[:Category:Oscillators with period 5|5]]
| [[octagon 2]]
| [[:Category:Patterns found by Sol Goodman|Sol Goodman]], [[:Category:Patterns found by Arthur Taber|Arthur Taber]]
| [[:Category:Patterns found in 1971|1971]]
|-
! [[:Category:Oscillators with period 6|6]]
| (?) [[$rats]], [[sombreros]]
| [[:Category:Patterns found by David Buckingham|David Buckingham]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 7|7]]
| [[burloaferimeter]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 8|8]]
| [[figure eight]]
| Simon Norton
| 1970
|-
! [[:Category:Oscillators with period 9|9]]
| [[worker bee]]
| David Buckingham
| 1972
|-
! [[:Category:Oscillators with period 10|10]]
| [[42P10.1]]
| David Buckingham
| ≤[[:Category:Patterns found in 1976|1976]]
|-
! [[:Category:Oscillators with period 11|11]]
| [[38P11.1]]
| David Buckingham
| [[:Category:Patterns found in 1977|1977]]
|-
! [[:Category:Oscillators with period 12|12]]
| [[dinner table]]
| [[:Category:Patterns found by Robert Wainwright|Robert Wainwright]]
| [[:Category:Patterns found in 1972|1972]]
|-
! [[:Category:Oscillators with period 13|13]]
| [[65P13.1]]
| David Buckingham
| 1976
|-
! [[:Category:Oscillators with period 14|14]]
| [[tumbler]]
| George Collins, Jr.
| 1970
|-
! [[:Category:Oscillators with period 15|15]]
| [[pentadecathlon]]
| John Conway
| 1970
|-
! [[:Category:Oscillators with period 16|16]]
| [[two pre-L hasslers]]
| Robert Wainwright
| [[:Category:Patterns found in 1983|1983]]
|-
! [[:Category:Oscillators with period 17|17]]
| [[54P17.1]]
| [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]]
| [[:Category:Patterns found in 1997|1997]]
|-
! [[:Category:Oscillators with period 18|18]]
| [[117P18]]
| David Buckingham
| ≤[[:Category:Patterns found in 1991|1991]]
|-
! class="red_td" | 19
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 20|20]]
| [[145P20]]
| [[:Category:Patterns found by Noam Elkies|Noam Elkies]]
| [[:Category:Patterns found in 1995|1995]]
|-
! [[:Category:Oscillators with period 21|21]]
| [[124P21]]
| Robert Wainwright
| 1995
|-
! [[:Category:Oscillators with period 22|22]]
| [[168P22.1]]
| Noam Elkies
| 1997
|-
! class="red_td" | 23
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 27|27]]
| [[123P27.1]]
| Noam Elkies
| [[:Category:Patterns found in 2002|2002]]
|-
! [[:Category:Oscillators with period 30|30]]
| [[queen bee shuttle]]
| Bill Gosper
| 1970
|-
! class="red_td" | 31
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 32|32]]
| [[gourmet]]
| David Buckingham
| [[:Category:Patterns found in 1978|1978]]
|-
! [[:Category:Oscillators with period 33|33]]
| (?)
| Noam Elkies, [[:Category:Patterns found by Achim Flammenkamp|Achim Flammenkamp]]
| [[:Category:Patterns found in 1997|1997]]
|-
! class="red_td" | 34
| class="red_td" colspan="3" | ''No non-trivial examples found''
|-
! 37
| ?
| Nicolay Beluchenko
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 38
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 39|39]]
| [[134P39.1]]
| David Buckingham, Noam Elkies
| [[:Category:Patterns found in 2000|2000]]
|-
! class="red_td" | 41
| class="red_td" colspan="3" | ''None found''
|-
! class="red_td" | 43
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 46|46]]
| [[twin bees shuttle]]
| Bill Gosper
| 1971
|-
! [[:Category:Oscillators with period 49|49]]
| [[440P49.1]]
| Noam Elkies
| [[:Category:Patterns found in 1999|1999]]
|-
! [[:Category:Oscillators with period 51|51]]
| [[112P51]]
| [[:Category:Patterns found by Nicolay Beluchenko|Nicolay Beluchenko]]
| [[:Category:Patterns found in 2009|2009]]
|-
! class="red_td" | 53
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:Oscillators with period 54|54]]
| [[P54 shuttle]]
| David Buckingham
| 1974
|-
! [[:Category:Oscillators with period 110|110]]
| [[P110 traffic jam]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 144|144]]
| [[Achim's p144]]
| Achim Flammenkamp
| 1994
|}</td><td align="center" width="50%">
{| class="wikitable"
|-
! Period
! Smallest known
! Minimum # of [[cell]]s
|-
! 2
| blinker
| [[:Category:Patterns with 3 cells|3]]
|-
! 3
| [[caterer]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 4
| [[mazing]], [[mold]]
| 12
|-
! 5
| [[pseudo-barberpole]]
| [[:Category:Patterns with 15 cells|15]]
|-
! 6
| [[unix]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 7
| [[28P7.1]], [[28P7.2]], [[burloaferimeter]]
| [[:Category:Patterns with 28 cells|28]]
|-
! 8
| figure eight
| 12
|-
! 9
| [[29P9.1]]
| [[:Category:Patterns with 29 cells|29]]
|-
! 10
| [[37P10.1]], 37P10.2
| [[:Category:Patterns with 37 cells|37]]
|-
! 11
| 38P11.1
| [[:Category:Patterns with 38 cells|38]]
|-
! 12
| dinner table
| [[:Category:Patterns with 33 cells|33]]
|-
! 13
| [[34P13.1]]
| [[:Category:Patterns with 34 cells|34]]
|-
! 14
| [[tumbler]]
| 16
|-
! 15
| [[pentadecathlon]]
| 12
|-
! 16
| [[Achim's p16]]
| [[:Category:Patterns with 32 cells|32]]
|-
! 17
| 54P17.1
| [[:Category:Patterns with 54 cells|54]]
|-
! 18
| [[43P18]]
| [[:Category:Patterns with 43 cells|43]]
|-
! class="red_td" | 19
| class="red_td" colspan="2" | ''None found''
|-
! 20
| [[mold on fumarole]]
| [[:Category:Patterns with 30 cells|30]]
|-
! 21
| [[jam on 44P7.2]]
| [[:Category:Patterns with 57 cells|57]]
|-
! 22
| [[36P22.1]]
| [[:Category:Patterns with 36 cells|36]]
|-
! class="red_td" | 23
| class="red_td" colspan="2" | ''None found''
|-
! 27
| [[94P27.1]]
| [[:Category:Patterns with 94 cells|94]]
|-
! 29
| [[pre-pulsar shuttle 29]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 30
| [[queen bee shuttle]]
| [[:Category:Patterns with 20 cells|20]]
|-
! 33
| [[92P33.1]]
| [[:Category:Patterns with 92 cells|92]]
|-
! 39
| [[jam on 34P13.1]]
| [[:Category:Patterns with 47 cells|47]]
|-
! 49
| 440P49.1
| [[:Category:Patterns with 440 cells|440]]
|-
! 51
| 112P51
| [[:Category:Patterns with 112 cells|112]]
|-
! 54
| [[P54 shuttle]]
| [[:Category:Patterns with 48 cells|48]]
|-
! 100
| [[centinal]]
| [[:Category:Patterns with 70 cells|70]]
|}
</td></tr></table>

==See also==
*[[List of common oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]

==External links==
*[http://web.archive.org/web/20070918210303/www.math.ucdavis.edu/~dean/RLE/stamps.html Oscillator Stamp Collection] by Dean Hickerson, via [http://www.archive.org Archive.org]
*[http://www.argentum.freeserve.co.uk/lex_o.htm#oscillator Oscillator] at the Life Lexicon

OCA talk:2×2

2009-04-14T14:08:48Z

Lewis Patterson:

2009-04-03T19:52:13Z

Lewis Patterson:

Oscillator

2009-04-03T19:17:12Z

Lewis Patterson:

Talk:Oscillator

2009-04-03T16:04:15Z

2009-04-01T20:51:26Z

Lewis Patterson: New page: ==P51 Oscillator== A p51 oscillator has been found. It is the 3rd one down here: http://pentadecathlon.com/lifeNews/2009/03/new_oscillators_4.html ~~~~

==P51 Oscillator==
A p51 oscillator has been found. It is the 3rd one down here: http://pentadecathlon.com/lifeNews/2009/03/new_oscillators_4.html
[[User:Lewis Patterson|Lewis Patterson]] 20:51, 1 April 2009 (UTC)

OCA talk:Maze

2009-03-26T16:20:14Z

Lewis Patterson: New page: ==Mistake in the still lifes== The 6th pattern along on the bottom row of the size 7 still lifes. It looks like 2 smaller still lifes; a domino and a 5-cell arrow-shaped pattern made up of...

==Mistake in the still lifes==
The 6th pattern along on the bottom row of the size 7 still lifes. It looks like 2 smaller still lifes; a domino and a 5-cell arrow-shaped pattern made up of 2 islands.

2009-03-18T18:37:06Z

Lewis Patterson:

'''2x2''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which cell birth occurs with 3 or 6 neighbors, and survival occurs on 1, 2 or 5. Patterns in the rule have a similar chaotic evolution to the standard Life rules, although the chaos dies out much sooner.

==Notable Patterns==
A large variety of still lifes and oscillators appear spontaneously from randomly generated starting states. There is also a rare spaceship, which travels at c/8 diagonally.

[[Image:2x2stills.png|framed|left|Some example still lifes in 2x2.]]
===Still Lifes===
Still patterns are generally smaller in 2x2 than in Life; the smallest occuring have populations of only 2 cells. In 2x2, still patterns tend to be similar to Life in terms of structure; ie. forming patterns with islands stabilising each other.
Many still patterns from life also work in 2x2, For example, the [[beehive]], [[tub]], [[loaf]], [[pond]] and [[mango]].

===Oscillators===
A large variety of patterns of many periods occur naturally in 2x2. Naturally occuring oscillator periods include 2, 3, 4, 5, 6, 10, 14, 17, 22 and 26.
[[Image:2x2_p2s.gif|framed|left|Naturally occurring P2's.]]

Other oscillators can be made from 2xn boxes. For example, when n=4 a p2 oscillator is formed, and when n=8, the rectangle oscillates at p6.

===Spaceships===
There are a selection of ships known in 2x2 <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 random soups. It travels at c/8 diagonally.
[[Image:2x2glider.png|framed|right|The c/8 gilder.]]

===Other patterns===
No infinite-growth mechanisms ([[gun|guns]], [[puffer|puffers]] etc.) have yet been discovered in 2x2.

==References==
<references />