LifeWiki - User contributions [en]

Kok's galaxy

2015-05-29T17:12:31Z

Vog: Improve link for sparker

{{Oscillator|p=8|c=28|h=39|bx=13|by=13|v=1.00|name=Kok's galaxy|pname=koksgalaxy|discoverer=Jan Kok|discoveryear=1971|life105=true|life106=true|plaintext=true|rle=true|animated=yes|synthesis=12|synthesisRLE=true}}
'''Kok's galaxy''' is a [[period]] [[:Category:Oscillators with period 8|8]] [[oscillator]] found by [[:Category:Patterns found by Jan Kok|Jan Kok]] in [[:Category:Patterns found in 1971|1971]]. It is notable for its uses as a [[Spark#Sparker|sparker]], and can be seen acting as one in [[converter 1]]. In September [[:Category:patterns found in 2003|2003]] [[Jason Summers]] found a [[:Category:patterns that can be constructed with 12 gliders|12]]-[[glider]] [[glider synthesis|synthesis]] of this oscillator.<ref>{{CiteSummersPattern|name=jslife}}</ref>

Kok's galaxy serves as the logo of [[Golly]].

==See also==
*[[Achim's p8]]
*[[Blocker]]
*[[Coe's p8]]
*[[Figure eight]]

==References==
<references/>

==External links==
{{LinkWeisstein|KoksGalaxy.html}}
{{LinkLexicon|lex_k.htm#koksgalaxy}}
[[Category:Patterns with C4 symmetry]]

Spark

2015-05-29T17:10:48Z

Vog: /* Sparker */ fix typo

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

==Sparker==
A '''sparker''' is an oscillator or spaceship that produces sparks.<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_s.htm#sparker|title=Sparker|publisher=The Life Lexicon|author=Stephen Silver|accessdate=May 24, 2009}}</ref>

==Smoke==
'''Smoke''' is debris that is fairly long-lived but eventually dies out completely. Thus, it is basically a large spark, but the term is used especially when talking about the output from a [[spaceship]] (as in a [[Types of spaceships#Smoking ship|smoking ship]]).<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_s.htm#smoke |title=Smoke |work=The Life Lexicon |publisher=Stephen Silver |accessdate=June 10, 2009}}</ref>

==Tail spark==
A '''tail spark''' is a spark that appears at the back of a spaceship.<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_t.htm#tailspark |title=Tail spark |work=The Life Lexicon |publisher=Stephen Silver |accessdate=May 21, 2009}}</ref> For example, there is a one-[[bit]] tail spark at the back of a [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]] in their less dense [[phase]]s.

==References==
<references />

==External links==
{{LinkWeisstein|Spark.html}}
{{LinkLexicon|lex_s.htm#spark}}

Spark

2015-05-29T17:10:33Z

Vog: Move "Sparker" from introduction text into separate section

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

==Sparker==
A '''Sparker''' is an oscillator or spaceship that produces sparks.<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_s.htm#sparker|title=Sparker|publisher=The Life Lexicon|author=Stephen Silver|accessdate=May 24, 2009}}</ref>

==Smoke==
'''Smoke''' is debris that is fairly long-lived but eventually dies out completely. Thus, it is basically a large spark, but the term is used especially when talking about the output from a [[spaceship]] (as in a [[Types of spaceships#Smoking ship|smoking ship]]).<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_s.htm#smoke |title=Smoke |work=The Life Lexicon |publisher=Stephen Silver |accessdate=June 10, 2009}}</ref>

==Tail spark==
A '''tail spark''' is a spark that appears at the back of a spaceship.<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_t.htm#tailspark |title=Tail spark |work=The Life Lexicon |publisher=Stephen Silver |accessdate=May 21, 2009}}</ref> For example, there is a one-[[bit]] tail spark at the back of a [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]] in their less dense [[phase]]s.

==References==
<references />

==External links==
{{LinkWeisstein|Spark.html}}
{{LinkLexicon|lex_s.htm#spark}}

Mark Niemiec

2013-04-23T17:15:37Z

Vog: /* External links */ Remove broken link

{{Person|name=Mark Niemiec|res=United States|alma=University of Waterloo}}
'''Mark D. Niemiec''' is a [[Conway's Game of Life|Life]] enthusiast who has found several [[oscillator]]s, most notably the [[period]] [[:Category:Oscillators with period 9|9]] [[snacker]].

He expanded on [[David Buckingham]]'s [[still life]] enumeration results, generating complete lists of still lifes and [[pseudo still life]]s up to 24 [[cell]]s, as well as period [[:Category:Oscillators with period 2|2]] oscillators and pseudo oscillators up to 19 cells.

He also expanded on Buckingham's [[glider synthesis]] results, generating syntheses of many 15-cell still lifes, all pseudo still lifes up to 15 cells, many remaining period 2 oscillators of 15 - 18 cells, most period 2 pseudo oscillators up to 19 cells, and most higher-period oscillators and pseudo oscillators up to 20 cells.

{{PatternsFoundBy|name=Mark Niemiec}}

==References==
*{{cite web|url=http://home.interserv.com/~mniemiec/lifecred.htm#niemiec|publisher=Mark D. Niemiec |title=Life Credits |accessdate=May 5, 2009}}

{{DEFAULTSORT:Niemiec, Mark}}

Glider synthesis

2013-04-23T17:15:16Z

Vog: /* External links */ Remove broken link

{{Glossary}}
'''Glider synthesis''' (or '''glider construction''') is the construction of an object by means of [[glider]] collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement.

Glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[:Category:Patterns found by David Buckingham|David Buckingham]].

==Syntheses of note==
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[:Category:Spaceships with speed c/2|c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[:Category:Patterns found by Mark Niemiec|Mark Niemiec]]. In June [[:Category:Patterns found in 1998|1998]], [[:Category:Patterns found by Stephen Silver|Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July [[:Category:Patterns found in 1999|1999]] that [[:Category:Patterns found by Jason Summers|Jason Summers]] used this to build a Cordership gun). In May [[:Category:Patterns found in 2000|2000]], [[Noam Elkies]] suggested that a [[:Category:Spaceships with speed 2c/5|2c/5]] spaceship ([[60P5H2V0]]) found by [[:Category:Patterns found by Tim Coe|Tim Coe]] in May [[:Category:Patterns found in 1996|1996]] might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March [[:Category:Patterns found in 2003|2003]] that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.

A 3-glider synthesis of a [[pentadecathlon]] was found in April [[:Category:Patterns found in 1997|1997]] by [[:Category:Patterns found by Heinrich Koenig|Heinrich Koenig]], which came as a surprise because it was widely assumed that anything using just three gliders would already be known.

===2-glider syntheses===
There are 71 distinct 2-glider collisions, of which 28 produce nothing, six produce a [[block]], five produce a [[honey farm]], three produce a [[B-heptomino]], three produce a [[pi-heptomino]], three produce a [[blinker]], three produce a [[traffic light]], two produce a [[glider]], two produce a [[pond]], two produce a [[loaf]] and a [[blinker]], one produces a [[boat]], one produces a [[beehive]], one produces a [[loaf]], one produces an [[eater 1]], one produces [[lumps of muck]], one produces a [[teardrop]], one produces an [[interchange]], one produces a traffic light and a glider, one produces an [[Polyomino#Octominoes|octomino]], one produces a [[bi-block]], one produces four blocks, one produces two blocks, one produces a blinker, loaf, [[tub]] and block, and one produces the so-called [[two-glider mess]], a [[methuselah]] stabilizing after 530 generations and consisting of four gliders, eight blinkers (including a traffic light), four blocks, a beehive and a [[ship]].

All 71 such syntheses can be seen below in a pattern put together by [[:Category:Patterns found by Jason Summers|Jason Summers]] on January 29, [[:Category:Patterns found in 2005|2005]].

[[Image:2glidersyntheses.png|framed|center|All 71 distinct 2-glider collisions, arranged by what they synthesize.<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=twoglidersyntheses.rle click here] ]]

==See also==
*[[:Category:Pattern_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]

==External links==
*[http://radicaleye.com/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses
{{LinkWeisstein|GliderSynthesis.html}}
{{LinkLexicon|lex_g.htm#glidersynthesis}}

Infinite LWSS hotel

2013-01-11T13:11:49Z

Vog: Spam

{{Pattern|name=Infinite LWSS hotel|pname=infinitelwsshotel|c=3357|bx=515|by=298|discoverer=Jason Summers|discoveryear=2002|life105=true|life106=true|rle=true}}
The '''infinite LWSS hotel''' is a [[pattern]] that was found by [[Jason Summers]] on October 20, [[:Category:Patterns found in 2002|2002]] that contains an ever-expanding [[lightweight spaceship]] [[track]]. One new lightweight spaceship is added to the loop every 250 [[generation]]s. The preexisting lightweight spaceships reenter the stream at a point 12/25ths of the way between two new lightweight spaceships; unlike earlier patterns of this type, this one will not work (for long) if the old spaceships re-enter exactly halfway between the new ones. <ref>{{CiteSummersPattern|name=jslife|accessdate=May 21, 2009}}</ref>

==See also==
*[[Infinite glider hotel]]

==References==
<references />

OCA:2×2

2013-01-10T22:46:12Z

Vog: Undo revision 17642 by Funfriend123 (talk)

{{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.

==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]]
| 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]]
| 6
| 0.00384
|-
! 9
| [[Image:2x2_stilllife_rank9.png]]
| 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]]
| 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]]
| 6
| 2.23×10<sup>-4</sup>
|-
! 17
| [[Image:2x2_stilllife_rank17.png]]
| 8
| 1.94×10<sup>-4</sup>
|-
! 18
| [[Image:2x2_stilllife_rank18.png]]
| 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 [http://www.research.att.com/~njas/sequences/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> No [[gun]]s have yet been discovered in 2×2.

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

==References==
<references />

C/4 diagonal

2013-01-09T10:31:24Z

Vog: Mark claim that comes with neither pattern file nor citation

{{Speed|speed=c/4 diagonal|image=glider|ss=yes|puff=yes|rake=yes|wick=yes|gun=yes}}
'''c/4 diagonal''' is a diagonal [[speed]] that is equivalent to one fourth of the speed of light.

==Spaceships==
c/4 diagonal was the first [[spaceship]] speed to be discovered when [[Richard Guy]] found the [[glider]] in [[:Category:patterns found in 1970|1970]]. The glider was the only known c/4 diagonal spaceship until [[Dean Hickerson]]'s [[computer search|searches]] discovered the [[big glider]] in December [[:Category:patterns found in 1989|1989]]. [[Robert Wainwright]] then found a few small [[tagalong]]s for this spaceship, including one that could connect two or more big gliders, giving arbitrarily large c/4 diagonal spaceships. Since then many c/4 diagonal spaceships have been found, and there has been a continual search for the second smallest spaceship of this speed, the current record holder being [[crab]], with [[:Category:patterns with 25 cells|25]] [[cell]]s. Of particular note are those spaceships that produce [[spark]]s, such as [[Tim Coe]]'s [[swan]]. The first higher [[period]] c/4 diagonal spaceship used two swans to pull a period [[:Category:spaceships with period 8|8]] tagalong and was discovered by [[Jason Summers]] in November [[:Category:patterns found in 2000|2000]]. In September [[:Category:patterns found in 2005|2005]] [[Hartmut Holzwart]] found a c/4 diagonal period [[:Category:spaceships with period 12|12]] spaceship. There is a severe lack of higher period c/4 diagonal spaceship technology until period 4508, for which [[David Bell]] has constructed a [[rake]] with an adjustable period of 4508 + 32N, which can easily be turned into a spaceship by deleting the outgoing glider with a swan.

==Puffers==
[[Image:c4diagonalpuffer1.png|framed|right|The first c/4 diagonal puffer<br/>{{JavaRLE|c4diagonalpuffer1}}]]
The first c/4 diagonal [[puffer]] was discovered by Hartmut Holzwart on February 9, [[:Category:patterns found in 2004|2004]], which creates a [[tub]] and [[beehive]] every 28 generations. On September 30, [[:Category:patterns found in 2005|2005]] Jason Summers constructed a period 4284 puffer that was the basis of David Bell's adjustable rake.

===Rakes===
On October 14, 2005 David Bell constructed an adjustable period sideways rake with period 4508 + 32N based on Jason Summers' period 4284 puffer.

==Wickstretchers==
Hartmut Holzwart discovered the first c/4 diagonal [[wickstretcher]], [[boatstretcher 1]], on June 1, [[:Category:patterns found in 1993|1993]]. Holzwart also found a c/4 diagonal linestretcher on November 19, 2004. An incomplete [[wickstretcher]] was found by [[Paul Tooke]] in September 2004 for a period 6 wick, and in January 2013, Jason Summers and [[Matthias Merzenich]] found a stationary termination {{Requestpatternfile}} that completes the wickstretcher. In October 2004 Hartmut Holzwart found a c/4 diagonal eater for this wick.

==Guns==
Many [[gun]]s have been made that shoot gliders, but no gun has yet been constructed for any other c/4 diagonal spaceship.

==See also==
*[[c/4 orthogonal]]
*[[:Category:speeds|List of important speeds]]

==References==
*Jason Summers' ''Status of Life page''
*{{CiteSummersPattern|name=jslife}}

Oscillator

2013-01-03T17:16:22Z

Vog: Remove spam: Undo revision 17633 by Ipodsoft (talk)

{{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]].

[[cellular automaton|Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[glider]] or [[spaceship]]. Strictly speaking "glider" means the little figure so prevalent in [[Conway's Game of Life]], but the more general usage has now become popular.
==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 non-trivial oscillators are considered here, in the sense that there must be at least one [[cell]] that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method.

<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]]
| [[: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]]
| [[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]]
| [[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 24|24]]
| [[186P24]]
| [[Bill Gosper]]
| [[:Category:Patterns found in 1994|1994]]
|-
! [[:Category:Oscillators with period 25|25]]
| [[134P25]]
| Noam Elkies
| 1994
|-
! [[:Category:Oscillators with period 26|26]]
| [[pre-pulsar shuttle 26]]
| David Buckingham
| 1983
|-
! [[:Category:Oscillators with period 27|27]]
| [[123P27.1]]
| Noam Elkies
| [[:Category:Patterns found in 2002|2002]]
|-
! [[:Category:Oscillators with period 28|28]]
| [[Newshuttle]]
| David Buckingham
| [[:Category:patterns found in 1973|1973]]
|-
! [[:Category:Oscillators with period 29|29]]
| [[pre-pulsar shuttle 29]]
| David Buckingham
| [[:Category:patterns found in 1980|1980]]
|-
! [[:Category:Oscillators with period 30|30]]
| [[queen bee shuttle]]
| Bill Gosper
| 1970
|-
! [[:Category:oscillators with period 31|31]]
| [[48P31]]
| [[Matthias Merzenich]]
| [[:Category:patterns found in 2010|2010]]
|-
! [[:Category:Oscillators with period 32|32]]
| [[gourmet]]
| David Buckingham
| [[:Category:Patterns found in 1978|1978]]
|-
! [[:Category:Oscillators with period 33|33]]
| [[258P3 on Achim's p11]]
| 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 35|35]]
| [[P35 beehive hassler]]
| Dean Hickerson
| 1995
|-
! [[:Category:oscillators with period 36|36]]
| [[P36 toad hassler]]
| Robert Wainwright
| 1984
|-
! [[: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]]
|-
! [[:Category:oscillators with period 40|40]]
| [[P40 B-heptomino shuttle]]
| David Buckingham
| ≤1991
|-
! class="red_td" | 41
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:oscillators with period 42|42]]
| [[P42 glider shuttle]]
| Noam Elkies
| 1994
|-
! class="red_td" | 43
| class="red_td" colspan="3" | ''None found''
|-
! [[:Category:oscillators with period 44|44]]
| [[P44 pi-heptomino hassler]]
| David Buckingham
| 1992
|-
! [[:Category:Oscillators with period 45|45]]
| [[pentadecathlon on snacker]]
| ?
| ≤1995
|-
! [[:Category:Oscillators with period 46|46]]
| [[twin bees shuttle]]
| Bill Gosper
| 1971
|-
! [[:Category:oscillators with period 47|47]]
| [[pre-pulsar shuttle 47]]
| David Buckingham
| [[:Category:patterns found in 1982|1982]]
|-
! [[:Category:oscillators with period 48|48]]
| [[P48 toad hassler]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 49|49]]
| [[p49 glider shuttle]]
| Noam Elkies
| [[:Category:Patterns found in 1999|1999]]
|-
! [[:Category:oscillators with period 50|50]]
| [[P50 glider shuttle]]
| Dean Hickerson
| 1992
|-
! [[:Category:Oscillators with period 51|51]]
| [[112P51]]
| Nicolay Beluchenko
| 2009
|-
! [[:Category:Oscillators with period 52|52]]
| [[35P52]]
| David Buckingham
| 1977
|-
! 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 55|55]]
| [[pre-pulsar hassler 55]]
| David Buckingham
| [[:Category:patterns found in 1986|1986]]
|-
! [[:Category:oscillators with period 56|56]]
| [[P56 B-heptomino shuttle]]
| David Buckingham
| ≤1991
|-
! [[:Category:Oscillators with period 57|57]]
| [[P57 Herschel loop 1]]
| [[:Category:patterns found by Dietrich Leithner|Dietrich Leithner]]
| 1997
|-
! [[:Category:oscillators with period 58|58]]
| [[P58 toadsucker]]
| Bill Gosper
| 1994
|-
! [[:Category:oscillators with period 59|59]]
| [[P59 Herschel loop 1]]
| David Buckingham
| 1997
|-
! [[:Category:oscillators with period 60|60]]
| [[P60 glider shuttle]]
| David Buckingham
| ≤ 1971
|-
! [[:Category:oscillators with period 61|61]]
| [[P61 Herschel loop 1]]
| David Buckingham
| [[:Category:patterns found in 1996|1996]]
|-
! [[:Category:Oscillators with period 72|72]]
| [[47P72]]
| Robert Wainwright
| 1990
|-
! [[:Category:oscillators with period 88|88]]
| [[P44 pi-heptomino hassler#Image gallery|P88 pi-heptomino hassler]]
| Dean Hickerson
| 1994
|-
! [[:Category:Oscillators with period 100|100]]
| [[Centinal]]
| Bill Gosper
| ≤[[:Category:patterns found in 1987|1987]]
|-
! [[:Category:Oscillators with period 110|110]]
| [[P110 traffic jam]]
| Bill Gosper
| 1994
|-
! [[:Category:Oscillators with period 124|124]]
| [[P124 lumps of muck hassler]]
| Dean Hickerson
| 1994
|-
! [[:Category:Oscillators with period 132|132]]
| [[P132 pi-heptomino hassler]]
| David Buckingham
| ≤1994
|-
! [[:Category:Oscillators with period 144|144]]
| [[Achim's p144]]
| Achim Flammenkamp
| 1994
|-
! [[:Category:Oscillators with period 156|156]]
| [[P156 Hans Leo hassler]]
| Noam Elkies
| 1995
|-
! [[:Category:Oscillators with period 200|200]]
| [[P200 traffic jam]]
| Bill Gosper
| 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]]
| [[:Category:Patterns with 12 cells|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]]
| [[:Category:Patterns with 12 cells|12]]
|-
! 9
| [[29P9]]
| [[:Category:Patterns with 29 cells|29]]
|-
! 10
| [[24P10]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 11
| [[38P11.1]]
| [[:Category:Patterns with 38 cells|38]]
|-
! 12
| [[dinner table]]
| [[:Category:Patterns with 33 cells|33]]
|-
! 13
| [[34P13]]
| [[:Category:Patterns with 34 cells|34]]
|-
! 14
| [[tumbler]]
| [[:Category:Patterns with 16 cells|16]]
|-
! 15
| [[pentadecathlon]]
| [[:Category:Patterns with 12 cells|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
| [[caterer on 44P7.2]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 22
| [[36P22]]
| [[: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]]
|-
! 25
| [[98P25]]
| [[:Category:Patterns with 98 cells|98]]
|-
! 26
| [[p26 glider loop]]
| [[:Category:Patterns with 156 cells|156]]
|-
! 27
| [[56P27]]
| [[:Category:Patterns with 56 cells|56]]
|-
! 28
| [[mold on 41P7.2]]
| [[:Category:Patterns with 53 cells|53]]
|-
! 29
| [[pre-pulsar shuttle 29]]
| [[:Category:Patterns with 54 cells|54]]
|-
! 30
| [[queen bee shuttle]]
| [[:Category:Patterns with 20 cells|20]]
|-
! 31
| [[48P31]]
| [[:Category:patterns with 48 cells|48]]
|-
! 32
| [[gourmet]]
| [[:Category:Patterns with 66 cells|66]]
|-
! 33
| [[92P33.1]]
| [[:Category:Patterns with 92 cells|92]]
|-
! class="red_td" | 34
| class="red_td" colspan="2" | ''No non-trivial examples found''
|-
! 35
| [[50P35]]
| [[:Category:patterns with 50 cells|50]]
|-
! 36
| [[22P36]]
| [[:Category:patterns with 22 cells|22]]
|-
! 37
| [[124P37]]
| [[:Category:Patterns with 124 cells|124]]
|-
! class="red_td" | 38
| class="red_td" colspan="2" | ''None found''
|-
! 39
| [[caterer on 34P13]]
| [[:Category:Patterns with 46 cells|46]]
|-
! 40
| [[26P40]]
| [[:Category:patterns with 26 cells|26]]
|-
! class="red_td" | 41
| class="red_td" colspan="2" | ''None found''
|-
! 42
| [[unix on 41P7.2]]
| [[:Category:Patterns with 57 cells|57]]
|-
! class="red_td" | 43
| class="red_td" colspan="2" | ''None found''
|-
! 44
| [[mold on 36P22]]
| [[:Category:patterns with 50 cells|50]]
|-
! 45
| [[pentadecathlon on thumb 1]]
| [[:Category:patterns with 48 cells|48]]
|-
! 46
| [[twin bees shuttle]]
| [[:Category:patterns with 28 cells|28]]
|-
! 47
| [[pre-pulsar shuttle 47]]
| [[:Category:patterns with 84 cells|84]]
|-
! 48
| [[69P48]]
| [[:Category:patterns with 69 cells|69]]
|-
! 49
| [[p49 glider shuttle]]
| [[:Category:Patterns with 400 cells|400]]
|-
! 50
| [[P50 traffic jam]]
| [[:Category:patterns with 92 cells|92]]
|-
! 51
| [[112P51]]
| [[:Category:Patterns with 112 cells|112]]
|-
! 52
| [[35P52]]
| [[:Category:Patterns with 35 cells|35]]
|-
! class="red_td" | 53
| class="red_td" colspan="2" | ''None found''
|-
! 54
| [[P54 shuttle]]
| [[:Category:Patterns with 48 cells|48]]
|-
! 55
| [[fumarole on Achim's p11]]
| [[:Category:patterns with 90 cells|90]]
|-
! 56
| [[P56 B-heptomino shuttle]]
| [[:Category:patterns with 45 cells|45]]
|-
! 57
| [[P57 Herschel loop 1]]
| [[:Category:patterns with 1000 or more cells|3004]]
|-
! 58
| [[P58 toadsucker]]
| [[:Category:patterns with 258 cells|258]]
|-
! 59
| [[P59_Herschel_loop_2|P59 Herschel loop 2]]
| 5822
|-
! 60
| [[mold on pentadecathlon]]
| [[:Category:patterns with 24 cells|24]]
|-
! 61
| [[P61 herschel loop 2]]
| 1596
|-
! 63
| [[snacker on 38P7.2]]
| [[:Category:patterns with 78 cells|78]]
|-
! 65
| [[fumarole on 34P13]]
| [[:Category:patterns with 52 cells|52]]
|-
! 66
| [[caterer on 36P22]]
| [[:Category:patterns with 48 cells|48]]
|-
! 70
| [[78P70]]
| [[:Category:patterns with 78 cells|78]]
|-
! 72
| [[47P72]]
| [[:Category:Patterns with 47 cells|47]]
|-
! 75
| [[6 bits]]
| [[:Category:Patterns with 49 cells|49]]
|-
! 88
| [[49P88]]
| [[:Category:patterns with 49 cells|49]]
|-
! 90
| [[fumarole on 43P18]]
| [[:Category:patterns with 61 cells|61]]
|-
! 96
| [[caterer on 68P32]]
| [[:Category:patterns with 80 cells|80]]
|-
! 99
| [[extended snacker on Achim's p11]]
| [[:Category:patterns with 124 cells|124]]
|-
! 100
| [[centinal]]
| [[:Category:Patterns with 70 cells|70]]
|-
! 104
| [[figure eight on 34P13]]
| [[:Category:Patterns with 46 cells|46]]
|-
! 105
| [[pentadecathlon on 37P7.1]]
| [[:Category:patterns with 49 cells|49]]
|-
! 108
| [[T-nosed p4 on 56P27]]
| [[:Category:patterns with 87 cells|87]]
|-
! 110
| [[pseudo-barberpole on 36P22]]
| [[:Category:Patterns with 51 cells|51]]
|-
! 120
| [[figure eight on pentadecathlon]]
| [[:Category:Patterns with 24 cells|24]]
|-
! 138
| [[Gabriel's p138]]
| [[:Category:patterns with 36 cells|36]]
|-
! 144
| [[Achim's p144]]
| [[:Category:Patterns with 42 cells|42]]
|-
! 156
| [[92P156]]
| [[:Category:Patterns with 92 cells|92]]
|-
! 177
| [[104P177]]
| [[:Category:patterns with 104 cells|104]]
|-
! 312
| [[60P312]]
| [[:Category:Patterns with 60 cells|60]]
|}
</td></tr></table>

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

==External links==
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkWeisstein|Oscillator.html}}