LifeWiki - User contributions [en]

Infinite growth

2011-05-08T13:32:15Z

Gemini III: /* Growth rates */

A finite [[pattern]] is said to exhibit '''infinite growth''' if it is such that its population is unbounded. That is, for any number N there exists a generation n such that the population in [[generation]] n is greater than N. The first known pattern to exhibit infinite growth was the [[Gosper glider gun]].

==Small infinite growth patterns==
[[Image:10cellinfinitegrowth.png|framed|right|10-cell infinite growth {{JavaRLE|10cellinfinitegrowth|brief}}]]A natural question to ask is what the smallest starting size of an infinite growth pattern can be (either in terms of number of [[cell]]s or [[bounding box]]). In [[:Category:Patterns found in 1971|1971]], [[Charles Corderman]] found that a [[switch engine]] could be stabilized by a [[pre-block]] in a number of different ways to produce either a [[block-laying switch engine]] or a [[glider-producing switch engine]], giving several 11-cell patterns with infinite growth. This record stood for more than quarter of a century until [[Paul Callahan]] found, in November [[:Category:Patterns found in 1997|1997]], two 10-cell patterns with infinite growth. The following month he found the one shown to the right, which is much neater, being a single [[cluster]]. It produces a block-laying switch engine. [[Nick Gotts]] and Paul Callahan have since shown that there is no infinite growth pattern with fewer than 10 cells, so that the question of the smallest infinite growth pattern in terms of number of cells has been answered completely.

Also of interest are some infinite growth patterns with particularly small bounding boxes. The following pattern is the smallest [[one cell thick pattern]] that exhibits infinite growth, found via computer search in October [[:Category:Patterns found in 1998|1998]] by Callahan:

[[Image:Unidimensional_infinite.png|framed|center|Paul Callahan's one cell thick infinite growth pattern {{JavaRLE|unidimensionalinfinitegrowth}}]]

Indeed, this pattern produces two [[block-laying switch engine]]s at about [[generation]] 700. The following pattern (also found by Callahan) is the only pattern with infinite growth that fits inside a 5×5 bounding box. It too emits a block-laying switch engine.

[[Image:5x5_infinite.png|framed|center|Paul Callahan's 5×5 infinite growth pattern {{JavaRLE|5x5infinitegrowth|brief}}]]

Paul Callahan's pattern shows that infinite growth patterns exist in bounding boxes with area 25, but whether or not infinite growth patterns could exist in smaller boxes was not known until [[:Category:Patterns found in 2009|2009]], when exhaustive computer searches were conducted to show that there is an infinite growth pattern with bounding box 2×12 (area 24), and that this area is minimal.<ref>{{cite web|url=http://infinitegrowth.wordpress.com/2009/06/05/n-cell-thick-patterns-1/|title=n-Cell Thick Patterns|publisher=Infinite Growth|accessdate=June 12, 2009|date=June 5, 2009}}</ref><ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=78|title=n-cell thick patterns & infinite growth|publisher=ConwayLife.com Forums|accessdate=June 12, 2009|date=June 5, 2009}}</ref> This pattern is shown below.

[[Image:2x12_infinite.png|framed|center|The minimally sized 2×12 infinite growth pattern {{JavaRLE|2x12infinitegrowth|brief}}]]

==Growth rates==
Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other growth rates are possible. The following table summarizes asymptotic growth rates that have been explicitly constructed in [[Conway's Game of Life|Life]]:

{| class="wikitable" style="margin-left:auto;margin-right:auto;" |
|-
! Growth rate f(t)
! Examples
|-
| t (linear)
| [[block-laying switch engine]], [[Gosper glider gun]], [[space rake]], [[puffer 2]]
|-
| t2 (quadratic)
| [[breeder 1]], [[max]], [[mosquito 5]], [[metacatacryst]]
|-
| sqrt(t)
| [[sqrtgun]]
|-
| t3/2
| ?
|-
| log(t) (logarithmic)
| [[Caber tosser 1]]
|-
| log(t)2
| [[log(t)^2 growth]]
|-
| tlog(t)
| [[tlog(t) growth]], [[Gotts dots]]
|-
| tlog(t)2
| ?
|}

It is not difficult to see that quadratic growth is the fastest possible growth rate, and many patterns that grow at such speed are now known. There are patterns that exhibit infinite growth but whose population does not tend toward infinity – see [[sawtooth]]. By combining a sawtooth with a pattern that grows infinitely at a different rate, it is possible to construct patterns that grow (for example) logarithmically at some times and linearly at other times. There are even patterns, such as the [[Fermat prime calculator]], for which it is not known if they grow infinitely or not.

===Quadratic growth===
The first quadratic growth pattern constructed was the [[breeder 1|original breeder]], found in [[:Category:Patterns found in 1971|1971]] by [[Bill Gosper]]. Since then, many other [[breeder]]s have been found, and even some [[spacefiller]]s have been constructed. It is unknown how small quadratic growth patterns can be, and a race has been taking place since the early 1990's to construct the smallest such pattern. The current record holder is [[26-cell quadratic growth]]. Previous record holders include [[catacryst]], [[metacatacryst]], and the [[mosquito]]es.

==References==
<references />

==External links==
{{LinkWeisstein|InfiniteGrowth.html}}
{{LinkLexicon|lex_i.htm#infinitegrowth}}
[[Category:Everything else]]

Eater 4

2011-05-08T13:18:21Z

Gemini III:

{{Stilllife|type=eater|name=Eater 4|pname=eater4|bx=14|by=14|c=40|discoverer=David Buckingham|discoveryear=1971|life105=true|life106=true|plaintext=true|rle=true}}
'''Eater 4''' is an [[eater]] that was found by [[:Category:Patterns found by David Buckingham|David Buckingham]] in [[:Category:Patterns found in 1971|1971]], but was not recognized as an eater until 1975 or 1976. It can't eat [[glider]]s, but it can be used for various other purposes. The four northeast-most center cells regrow in a few generations after being destroyed by taking a bite out of something.

==See also==
*[[Eater 1]]
*[[Eater 2]]
*[[Eater 3]]
*[[Eater 5]]

==External links==
{{LinkWeisstein|filename=Eater4.html}}
{{LinkLexicon|filename=lex_e.htm#eater4}}
[[Category:Strict still lifes]][[Category:Strict still lifes with 40 cells]]

Eater 4

2011-05-07T21:24:08Z

Gemini III:

{{Stilllife|type=eater|name=Eater 4|pname=eater4|bx=14|by=14|c=40|discoverer=David Buckingham|discoveryear=1971|life105=true|life106=true|plaintext=true|rle=true}}
'''Eater 4''' is an [[eater]] that was found by [[:Category:Patterns found by David Buckingham|David Buckingham]] in [[:Category:Patterns found in 1971|1971]], but was not recognized as an eater until 1975 or 1976. It can't eat [[glider]]s, but it can be used for various other purposes. The four northeast-most centre cells regrow in a few generations after being destroyed by taking a bite out of something.

==See also==
*[[Eater 1]]
*[[Eater 2]]
*[[Eater 3]]
*[[Eater 5]]

==External links==
{{LinkWeisstein|filename=Eater4.html}}
{{LinkLexicon|filename=lex_e.htm#eater4}}
[[Category:Strict still lifes]][[Category:Strict still lifes with 40 cells]]

Glider-producing switch engine

2011-05-06T00:34:11Z

Gemini III:

{{Puffer|name=Glider-producing switch engine|bx=67|by=60|pname=gliderproducingswitchengine|c=123|p=384|s=c/12|dir=Diagonal|discoverer=Charles Corderman|life105=true|life106=true|plaintext=true|rle=true|synthesis=5|synthesisRLE=true}}
The '''glider-producing switch engine''' (or '''glider-making switch engine''') is a [[puffer]] that was found by [[:Category:Patterns found by Charles Corderman|Charles Corderman]] in the early 1970s. It consists of a [[switch engine]] reacting with [[block]]s to produce various [[still life]]s, several [[blinker]]s, and a [[glider]] every 384 [[generation]]s.

It is the second most common naturally-occurring pattern that exhibits [[infinite growth]], and is one of only two patterns that exhibits infinite growth that has been known to occur naturally (the other being the [[block-laying switch engine]]).

Because of its easy construction (see its predecessors below), it has appeared in some superlinear growth patterns including [[mosquito 3]].<ref>{{Cite web|url=http://www.argentum.freeserve.co.uk/lex_m.htm#mosquito3|title=Mosquito 3|author=Stephen Silver|publisher=The Life Lexicon|accessdate=June 1, 2009}}</ref>

==Time bomb==
The '''time bomb''' (shown below) is a 17-[[cell]] [[pattern]] that was found by [[Doug Petrie]] that evolves into a glider-producing switch engine.<ref>{{Cite web|url=http://www.argentum.freeserve.co.uk/lex_t.htm#timebomb|title=Time bomb|author=Stephen Silver|publisher=The Life Lexicon|accessdate=May 16, 2009}}</ref>

==Image gallery==
{|
|-
|[[Image:Gliderproducingswitchengine_debris.png|thumb|231px|left|The debris left behind by the glider-producing switch engine]]
|[[Image:Timebomb.png|framed|left|The time bomb is a predecessor of the glider-producing switch engine {{JavaRLE|timebomb|brief}}]]
|[[Image:Gliderproducingswitchengine_pred.png|framed|left|Another simple [[predecessor]] of the glider-producing switch engine {{JavaRLE|gliderproducingswitchenginepredecessor}}]]
|}

==References==
<references />

==External links==
*[http://www.pentadecathlon.com/objects/class4/typeB/SwitchEngine1/switchEngine1.php Single switch engine puffer trains] at the Life Objects Catalog

Switch engine

2011-05-06T00:32:37Z

Gemini III:

__NOTOC__{{Methuselah|name=Switch engine|bx=6|by=4|pname=switchengine|c=8|l=3911|discoverer=Charles Corderman|discoveryear=1971|life105=true|life106=true|plaintext=true|rle=true}}
A '''switch engine''' (or '''Corder engine'''<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_c.htm#corderengine |title=Corder engine |work=The Life Lexicon |publisher=Stephen Silver |accessdate=June 10, 2009}}</ref>) 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 ever seen to occur from [[soup|random starting patterns]].

Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the [[mosquito]]es, [[catacryst]], [[metacatacryst]], [[Gotts dots]], and [[26-cell quadratic growth]].

In addition to the puffers based on a single switch engine, puffers such as [[Noah's ark]] can be created by combining two switch engines. Such puffers are generally quite [[dirty]]. By combining even more switch engines, it is possible to create [[Cordership]]s, which move at [[:Category:Spaceships with speed c/12|c/12]] diagonally and are thus the slowest known spaceships in Life other than [[Gemini|Geminoids]]. Such spaceships can be constructed by combining as few as [[3-engine Cordership|three]] switch engines.

==Stable pattern==
The stable pattern that results from the switch engine has 842 [[cell]]s. It consists of 60 [[block]]s, 33 [[beehive]]s (including one [[honey farm]]), 50 [[blinker]]s (including eight [[traffic light]]s), 12 [[glider]]s, 11 [[boat]]s, 11 [[loaf|loaves]], four [[ship]]s, two [[long boat]]s, two [[pond]]s, and two [[tub]]s.
{|
|-
|[[Image:Switchengine_final.png|thumb|left|Generation 3911]]
|}

==See also==
*[[Ark]]
*[[Cordership]]
*[[Infinite growth]]
*[[Time bomb]]

==References==
<references />

==External links==
{{LinkWeisstein|SwitchEngine.html}}
{{LinkLexicon|lex_s.htm#switchengine}}
*[http://www.calcyman.co.uk/life/corder.htm Corderships and Switch Engines] at [http://www.calcyman.co.uk/ www.calcyman.co.uk]

[[Category:Puffer engines]]

Schick engine

2011-05-06T00:31:09Z

Gemini III:

{{Spaceship|name=Schick engine|discoverer=Paul Schick|discoveryear=1972|pname=schickengine|bx=20|by=11|h=43.2|dir=Orthogonal|p=12|s=c/2|c=39|life105=true|life106=true|plaintext=true|rle=true|animated=true|synthesis=10|synthesisRLE=true}}
'''Schick engine''' (or '''Schick ship''') is an orthogonal [[c/2 orthogonal|c/2]] [[spaceship]] that was found by [[:Category:Patterns found by Paul Schick|Paul Schick]] in [[:Category:Patterns found in 1972|1972]]. Alternatively, it may refer just to the [[tagalong]] (displayed in green) that is attached to the back of the two [[lightweight spaceship]]s. The tagalong may also be attached to the back of two [[middleweight spaceship]]s, two [[heavyweight spaceship]]s, or a lightweight spaceship and a heavyweight spaceship.

Its eleven-cell rear [[spark]] can be perturbed by other c/2 spaceships to form a variety of [[puffer]]s and thus it is a [[puffer engine]].

==See also==
*[[Blinker ship 1]]

==External links==
{{LinkWeisstein|SchickEngine.html}}
{{LinkLexicon|lex_s.htm#schickengine}}
[[Category:Tagalongs]]
[[Category:Smoking ships]]
[[Category:Puffer engines]]

Spaceship terminology

2011-05-06T00:21:08Z

Gemini III: /* Edge spark */

{{Glossary}}
There are many different '''terms''' used when describing specific aspects of [[spaceships]] in [[Conway's Game of Life]] and related [[cellular automaton|cellular automata]]. The following are the terminology that are in common use. This page contains only very general terminology that applies to wide varieties of spaceships.

==Arm==
An '''arm''' is a long extension hanging off from the main body of a spaceship (or [[puffer]]) that is perpendicular to the direction of travel. Many known spaceships have multiple arms. This is an artifact of the search methods used to find such spaceships, rather than an indication of what a "typical" spaceship might look like.

==Edge spark==
An '''edge spark''' is a [[spark]] that appears at the side of a spaceship that can be used to perturb things as the spaceship passes by. For instance, a [[Heavyweight spaceship|heavyweight spaceship]] produces a domino edge spark that can be used to perturb or eat things.

==Heat==
{{main|Heat}}
The '''heat''' of a spaceship (or [[oscillator]]) is the average number of [[cell]]s that change state in each [[generation]]. For example, the heat of a [[glider]] is 4, because 2 cells are born and 2 cells die every generation.

==Mod==
{{main|Mod}}
The '''mod''' of a spaceship (or [[oscillator]]) is the least number of generations that it takes for it to reappear in its original form, possibly reflected or rotated in some way.

==Period==
{{main|Period}}
The '''period''' of a spaceship is the smallest number of generations that it takes for it to reappear in its original form, translated by a non-zero amount.

==Speed==
{{main|Speed}}
The '''speed''' of a spaceship is a measure of the number of generations that it takes for it to travel some given distance.

==See also==
* [[Types of spaceships]]

==External links==
*[http://www.argentum.freeserve.co.uk/lex.htm The Life Lexicon]
[[Category:Everything else]]

Wing (spaceship)

2011-05-06T00:17:05Z

Gemini III:

{{Spaceship|name=Wing (spaceship)|pname=wingspaceship|dir=Diagonal|p=4|s=c/4|c=72|bx=23|by=23|h=58.0|discoverer=Hartmut Holzwart|discoveryear=1993|life105=true|life106=true|plaintext=true|rle=true|animated=true}}
'''Wing''' is a diagonal [[spaceship]] that was discovered by [[:Category:Patterns found by Hartmut Holzwart|Hartmut Holzwart]] in [[:Category:Patterns found in 1993|1993]], consisting of two gliders pulling a large tagalong. It was the first extensible [[:Category:Spaceships with speed c/4|c/4]] spaceship to be found.<ref>[[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifep.zip pattern collection].</ref>

==Image gallery==
{|
|-
|[[Image:Wing_extended.png|framed|left|An extended version of the spaceship {{JavaRLE|wingextended}}]]
|}

==References==
<references />

Sparky

2011-05-06T00:13:51Z

Gemini III: /* Image gallery */

{{Spaceship|name=Sparky|pname=sparky|bx=30|by=11|h=100|dir=Orthogonal|p=4|s=c/4|c=101|life105=true|life106=true|plaintext=true|rle=true|animated=true}}
'''Sparky''' is an orthogonal [[:Category:Spaceships with speed c/4|c/4]] [[spaceship]]. Alternatively, it may refer just to the [[tagalong]] (displayed in green) that is attached to the back of [[non-monotonic spaceship 1]]. Its name is due to the several [[spark]]s that it produces at its rear in one of its [[phase]]s.

==Image gallery==
{|
|-
|[[Image:Sparky_gen3.png|framed|left|Generation 3 reveals the many sparks at the back]]
|}

==External links==
{{LinkWeisstein|filename=Sparky.html}}
{{LinkLexicon|filename=lex_s.htm#sparky}}
[[Category:Tagalongs]]

Heavyweight spaceship

2011-05-06T00:05:48Z

Gemini III:

{{Spaceship|name=Heavyweight Spaceship|pname=hwss|bx=7|by=7|h=19|dir=Orthogonal|p=4|s=c/2|c=13|discoverer=John Conway|discoveryear=1970|life105=true|life106=true|plaintext=true|rle=true|animated=true|synthesis=3|synthesisRLE=true|rulemin=B3/S23|rulemax=B3468/S23|rulespecial=[[Conway's Game of Life|Conway Life]], [[HighLife]]}}
The '''heavyweight spaceship''' (or '''HWSS''' for short) is the fourth most common spaceship (after the [[glider]], [[lightweight spaceship]] and [[middleweight spaceship]]). It was found by [[:Category:Patterns found by John Conway|John Conway]] in [[:Category:Patterns found in 1970|1970]] and travels at a speed of [[c/2 orthogonal|c/2]] orthogonally. Its [[polyomino#Dominoes|domino]] [[spark]] can be used to stabilize several [[tagalong]]s, including [[sidecar]] and half of [[x66]]. It is one of only three known spaceships that is a [[Polyomino|polyomino]] in any of its phases.

==Image gallery==
{|
|-
|[[Image:HWSS_eaters.png|framed|left|Three Heavyweight spaceship eaters {{JavaRLE|hwsseaters}}]]
|}

==See also==
*[[Overweight spaceship]]

==External links==
{{LinkWeisstein|HeavyweightSpaceship.html}}
{{LinkLexicon|lex_h.htm#hwss}}
[[Category:Glide symmetric spaceships]]

Star

2011-05-06T00:02:57Z

Gemini III:

{{Oscillator|name=Star|pname=star|p=3|h=37.3|c=24|bx=13|by=13|discoverer=Hartmut Holzwart|discoveryear=1993|life105=true|life106=true|plaintext=true|rle=true|animated=true|synthesis=20|synthesisRLE=true}}
'''Star''' is a [[period]] [[:Category:Oscillators with period 3|3]] [[oscillator]] that was found by [[:Category:Patterns found by Hartmut Holzwart|Hartmut Holzwart]] on February 16, [[:Category:Patterns found in 1993|1993]].<ref>{{CiteHickersonOscillators}}</ref> It is one of the few known oscillators that is a [[polyomino]] in one of its [[phase]]s. In August, [[:Category:patterns found in 2004|2004]] Jason Summers found a [[:Category:patterns that can be constructed with 20 gliders|20-glider]] [[Glider synthesis|Synthesis]] of this oscillator.<ref>{{CiteSummersPattern|name=jslife}}</ref>

==Image gallery==
{|
|-
|[[Image:star_gen2.png|framed|left|Star is named after [[generation]] 2 of its evolution]]
|[[Image:star_with_blocks.png|framed|left|A related period 3 oscillator. Any or all of the blocks are optional; if present they are lethargic beacons. {{JavaRLE|starwithblocks|brief}}]]
|}

==See also==
*[[Cross]]

==References==
<references/>

==External links==
{{LinkWeisstein|Star.html}}
{{LinkLexicon|lex_s.htm#star}}

Block

2011-05-06T00:02:19Z

Gemini III:

{{Stilllife|name=Block|pname=block|c=4|bx=2|by=2|discoveryear=1970|discoverer=John Conway|life105=true|life106=true|plaintext=true|rle=true|synthesis=2|synthesisRLE=true|rulespecial=[[Conway's Game of Life|Conway Life]], [[HighLife]], [[Maze]]|rulemin=B/S3|rulemax=B345678/S012345678}}
'''Block''' is an extremely well-known and common [[still life]] that was found by [[John Conway]] in [[:Category:Patterns found in 1970|1970]]. In terms of its [[:Category:Strict still lifes with 4 cells|4]] [[cell]]s it is tied with [[tub]] as the smallest still life, and in terms of its 2×2 [[bounding box]] it is the outright smallest. It is also the only known still life that is a [[Polyomino|polyomino]].

Due to its small size, its ability to act as an [[eater]], and its simple [[glider synthesis|glider syntheses]], it is extremely useful in the construction of large patterns. It can be used as an [[induction coil]] as in [[block and dock]], [[block on table]] and [[griddle and block]].

It is also the most common still life that occurs as a result of [[soup|random starting patterns]], occurring almost twice as often as [[beehive]], the next most common still life.<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html |title=Most seen natural occurring ash objects in Game of Life |author=Achim Flammenkamp |date=September 7, 2004 |accessdate=January 15, 2009}}</ref>

The block was one of the patterns described in the original 1970 article by [[Martin Gardner]] that introduced the [[Conway's Game of Life|Game of Life]] to the world.

==See also==
*[[Bi-block]]
*[[Blockade]]
*[[Blockstacker]]
*[[Grin]]
*[[List of common still lifes]]
*[[Pre-block]]

==References==
<references />

==External links==
{{LinkWeisstein|Block.html}}
{{LinkLexicon|lex_b.htm#block}}
*[http://home.interserv.com/~mniemiec/still.htm#4-bit%20still Four-bit still lifes] by Mark Niemiec
*[http://www.ibiblio.org/lifepatterns/october1970.html The fantastic combinations of John Conway's new solitaire game "life"] by Martin Gardner

Eater 2

2011-05-05T23:59:53Z

Gemini III: OOPS!

{{Stilllife|type=eater|name=Eater 2|pname=eater2|c=19|bx=7|by=7|discoverer=David Buckingham|life105=true|life106=true|plaintext=true|rle=true|synthesis=9|synthesisRLE=true|rulemin=B/S23|rulemax=B378/S012345678|rulespecial=[[Conway's Game of Life|Conway Life]]}}
'''Eater 2''' is an [[eater]] that was found by [[:Category:Patterns found by David Buckingham|David Buckingham]] in the 1970s. Mostly it works like the standard eater (see [[eater 1]]) but with two slight differences that make it useful despite its size; it takes longer to recover from each bite and it acts like an eater in two directions. The first property means that, among other things, it can eat a [[glider]] in a position that would destroy an eater 1. This novel glider-eating action is occasionally of use in itself, and combined with the symmetry means that an eater 2 can eat gliders along four different paths.

An eater 2 variant noticed by [[:Category:Patterns found by Stephen Silver|Stephen Silver]] in May [[:Category:Patterns found in 1998|1998]] that is useful for obtaining smaller bounding boxes is shown below. Note that eater 2 is a [[strict still life]] because the outside cells are not stable without the [[block]], but the eater 2 variant below is a [[pseudo still life]] because it is made up of an [[aircraft carrier]], [[block]] and [[hat]], each of which are stable.

Eater 2 can also be used to eater objects other than gliders. For example, one of them can eat a [[Lightweight spaceship|lightweight]] or [[Middleweight spaceship|middleweight]] spaceship, two of them can eat a [[60P5H2V0]], three of them can eat the bulk of a [[3-engine Cordership]], and seven of them can be arranged to eat the majority of the [[7-in-a-row Cordership]].

On January 29, [[:Category:patterns found in 2004|2004]] [[Mark Niemiec]] found a [[:Category:patterns that can be constructed with 9 gliders|9]]-[[glider]] [[glider synthesis|synthesis]] of a variation of eater 2 that consists of a hat, a block, and a [[table]].

==Image gallery==
{|
|-
|[[Image:Eater2_2.png|framed|Eater 2 variant]]
|}

==See also==
*[[65P13.1]]
*[[Eater 3]]
*[[Eater 4]]
*[[Eater 5]]
*[[Gliderless gun 1]]

==External links==
{{LinkWeisstein|Eater2.html}}
{{LinkLexicon|lex_e.htm#eater2}}
[[Category:Strict still lifes]][[Category:Strict still lifes with 19 cells]]

Eater 2

2011-05-05T23:58:12Z

Gemini III:

{{Stilllife|type=eater|name=Eater 2|pname=eater2|c=19|bx=7|by=7|discoverer=David Buckingham|life105=true|life106=true|plaintext=true|rle=true|synthesis=9|synthesisRLE=true|rulemin=B/S23|rulemax=B378/S012345678|rulespecial=[[Conway's Game of Life|Conway Life]]}}
'''Eater 2''' is an [[eater]] that was found by [[:Category:Patterns found by David Buckingham|David Buckingham]] in the 1970s. Mostly it works like the standard eater (see [[eater 1]]) but with two slight differences that make it useful despite its size; it takes longer to recover from each bite and it acts like an eater in two directions. The first property means that, among other things, it can eat a [[glider]] in a position that would destroy an eater 1. This novel glider-eating action is occasionally of use in itself, and combined with the symmetry means that an eater 2 can eat gliders along four different paths.

An eater 2 variant noticed by [[:Category:Patterns found by Stephen Silver|Stephen Silver]] in May [[:Category:Patterns found in 1998|1998]] that is useful for obtaining smaller bounding boxes is shown below. Note that eater 2 is a [[strict still life]] because the outside cells are not stable without the [[block]], but the eater 2 variant below is a [[pseudo still life]] because it is made up of an [[aircraft carrier]], [[block]] and [[hat]], each of which are stable.

Eater 2 can also be used to eater objects other than gliders. For example, one of them can eat a [[lightweight|Lightweight spaceship]] or [[middleweight|Middleweight spaceship]] two of them can eat a [[60P5H2V0]], three of them can eat the bulk of a [[3-engine Cordership]], and seven of them can be arranged to eat the majority of the [[7-in-a-row Cordership]].

On January 29, [[:Category:patterns found in 2004|2004]] [[Mark Niemiec]] found a [[:Category:patterns that can be constructed with 9 gliders|9]]-[[glider]] [[glider synthesis|synthesis]] of a variation of eater 2 that consists of a hat, a block, and a [[table]].

==Image gallery==
{|
|-
|[[Image:Eater2_2.png|framed|Eater 2 variant]]
|}

==See also==
*[[65P13.1]]
*[[Eater 3]]
*[[Eater 4]]
*[[Eater 5]]
*[[Gliderless gun 1]]

==External links==
{{LinkWeisstein|Eater2.html}}
{{LinkLexicon|lex_e.htm#eater2}}
[[Category:Strict still lifes]][[Category:Strict still lifes with 19 cells]]

Boatstretcher 1

2011-04-16T00:03:05Z

Gemini III: Undo revision 14176 by 187.39.188.10 (Talk); vandalism

{{Wickstretcher|dir=Diagonal|p=4|s=c/4|name=Boatstretcher 1|pname=boatstretcher1|c=77|discoverer=Hartmut Holzwart|discoveryear=1993|animated=true|life105=true|life106=true|plaintext=true|rle=true}}
'''Boatstretcher 1''' is a [[c/4 diagonal|c/4]] diagonal [[boatstretcher]] that was discovered by [[Hartmut Holzwart]] on June 1, [[:Category:Patterns found in 1993|1993]]. It was the first diagonal wickstretcher to be found.<ref>{{CiteLexicon|lex_t.htm#tubstretcher|name=Tubstretcher}}</ref>

==References==
<references/>

Catacryst

2011-04-15T20:49:19Z

Gemini III:

{{Pattern|name=Catacryst|pname=catacryst|c=58|bx=2555|by=1772|discoverer=Nick Gotts|discoveryear=2000|life105=true|life106=true|rle=true}}
'''Catacryst''' is a [[:Category:Patterns with 58 cells|58]]-cell quadratic growth pattern found by [[:Category:Patterns found by Nick Gotts|Nick Gotts]] in April [[:Category:Patterns found in 2000|2000]]. This was formerly the smallest known pattern with superlinear growth, but has since been superseded by the related [[metacatacryst]] and [[26-cell quadratic growth]]. The catacryst consists of three [[ark|arks]] plus a [[glider]]-producing [[switch engine]]. It produces a [[block]]-laying switch engine every 47616 generations. Each block-laying switch engine has only a finite life, but the length of this life increases linearly with each new switch engine, so that the pattern overall grows quadratically, as an unusual type of MMS [[breeder]].

==Image gallery==
<gallery>
Image:Catacryst_gen1000000.png|Generation 1,000,000 of catacryst
Image:Catacryst1.png|The top portion of the catacryst (an [[ark]])
Image:Catacryst2.png|The top-right portion of the catacryst (a [[glider]]-producing [[switch engine]])
Image:Catacryst3.png|The bottom-middle portion of the catacryst (an ark)
Image:Catacryst4.png|The bottom-left portion of the catacryst (an ark)
</gallery>

==External links==
{{LinkLexicon|lex_c.htm#catacryst}}

Eater 3

2011-04-15T20:41:30Z

Gemini III:

{{Stilllife|type=eater|name=Eater 3|pname=eater3|bx=12|by=12|c=31|discoverer=David Buckingham|life105=true|life106=true|plaintext=true|rle=true}}
'''Eater 3''' is a large symmetric [[eater]] that was found by [[:Category:Patterns found by David Buckingham|David Buckingham]] and has a very different eating action from [[eater 1]] and [[eater 2]]; however, it shares with those two eaters the ability to eat [[glider|gliders]]. The [[loaf]] can take bites out things, being flipped over in the process. The rest of the object simply flips it back again. Two copies of the eater 3 can share a loaf, forming the period 8 [[oscillator]] shown below.

The eater 3 can be reduced in area by replacing the [[tub]]s with [[snake]]s; this property is used to compact the [[rectifier]].

==Image gallery==
{|
|-
|[[Image:Eater3_p8.png|framed|left|A related period 8 oscillator {{JavaRLE|period8eater3}}]]
|}

==See also==
*[[38P11.1]]
*[[Eater 4]]
*[[Eater 5]]

==External links==
{{LinkWeisstein|filename=Eater3.html}}
{{LinkLexicon|filename=lex_e.htm#eater3}}

Ark

2011-04-10T17:14:40Z

Gemini III:

{{Glossary}}
An '''ark''' is a pair of mutually stabilizing [[switch engine]]s. The most popular ark is [[Noah's ark]]; however, there are five known arks in total, two of which (including Noah's ark) are symmetric.

==External links==
*[http://www.argentum.freeserve.co.uk/lex_a.htm#ark Ark] at the Life Lexicon
*[http://pentadecathlon.com/objects/class4/typeB/SwitchEngine2/switchEngine2.php Double Switch Engine Puffers] at Pentadecathlon

Talk:Ark

2011-04-10T17:12:06Z

Gemini III: Other arks

== Other arks ==

What about arks ''other'' than [[Noah's ark]]? --[[User:Gemini III|Gemini III]] 17:12, 10 April 2011 (UTC)

Mosquito 1

2011-04-03T22:27:14Z

Gemini III:

{{Pattern|name=Mosquito 1|pname=mosquito1|c=103|bx=1794|by=412|discoverer=Nick Gotts|discoveryear=1998|rle=true|life105=true|life106=true}}
'''Mosquito 1''' is a [[:Category:Patterns with 103 cells|103]]-cell quadratic growth pattern that was found by [[Nick Gotts]] on September 29, [[:Category:Patterns found in 1998|1998]]. At the time of its discovery, it was the smallest known pattern exhibiting superlinear growth (passing the former record holder [[jaws]]), but it was surpassed one week later by a 97-cell pattern found by [[Stephen Silver]], and then almost immediately by the [[:Category:Patterns with 85 cells|85]]-cell [[mosquito 2]].

It consists of the classic [[puffer 2]] plus four [[lightweight spaceship]]s and four [[middleweight spaceship]]s. Once it gets going it produces a new [[block-laying switch engine]] (plus a lot of junk) every 280 [[generation]]s. It is therefore an MMS [[breeder]], albeit a messy one.

==Image gallery==
{|
|-
|[[Image:Mosquito_1b.png|thumb|left|A 97-cell improvement of mosquito 1 by Stephen Silver {{JavaRLE|mosquito1b}}]]
|[[Image:Mosquito_gen35000.png|thumb|left|Generation 35000 of mosquito 1]]
|}

==See also==
*[[Mosquito 2]]
*[[Mosquito 3]]
*[[Mosquito 4]]
*[[Mosquito 5]]

==External links==
{{LinkWeisstein|Mosquito1.html}}
{{LinkLexicon|lex_m.htm#mosquito1}}

Mosquito 1

2011-04-03T22:26:49Z

Gemini III:

{{Pattern|name=Mosquito 1|pname=mosquito1|c=103|bx=1794|by=412|discoverer=Nick Gotts|discoveryear=1998|rle=true|life105=true|life106=true}}
'''Mosquito 1''' is a [[:Category:Patterns with 103 cells|103]]-cell quadratic growth pattern that was found by [[Nick Gotts]] on September 29, [[:Category:Patterns found in 1998|1998]]. At the time of its discovery, it was the smallest known pattern exhibiting superlinear growth (passing the former record holder [[jaws]]), but it was surpassed one week later by a 97-cell pattern found by [[Stephen Silver]], and then almost immediately by the [[:Category:Patterns with 85 cells|85]]-cell [[mosquito 2]].

It consists of the classic [[puffer 2]] plus four [[lightweight spaceship]]s and four [[middleweight spaceship]]s. Once it gets going it produces a new [[block-laying switch engine]] (plus a lot of junk) every 280 [[generation]]s. It is therefore an MMS [[breeder]], albeit a messy one.

==Image gallery==
{|
|-
|[[Image:Mosquito_1b.png|thumb|left|A 97-cell improvement of mosquito 1 by Stephen Silver {{JavaRLE|mosquito1b}}]]
|[[Image:Mosquito_gen35000.png|thumb|left|Generation 35000 of mosquito 1]]
|}

==See also==
*[[Mosquito 3]]
*[[Mosquito 4]]
*[[Mosquito 5]]

==External links==
{{LinkWeisstein|Mosquito1.html}}
{{LinkLexicon|lex_m.htm#mosquito1}}

Dead spark coil

2011-04-03T22:14:12Z

Gemini III:

{{Stilllife|name=Dead spark coil|pname=deadsparkcoil|bx=7|by=5|c=18|life105=true|life106=true|plaintext=true|rle=true|synthesis=4|synthesisRLE=true}}
'''Dead spark coil''' (or '''cis-house on house''' or '''JC''') is the forty-fifth most common [[still life]], being less common than [[trans-mirrored R-bee]] but more common than [[cis-mirrored hook]].<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html |title=Most seen natural occurring ash objects in Game of Life |author=Achim Flammenkamp |date=September 7, 2004 |accessdate=January 15, 2009}}</ref> It is composed of two [[house]]s that are acting as [[induction coil]]s to stabilize each other. It is an oscillator in [[Highlife]].

==See also==
*[[List of common still lifes]]
*[[Mirrored dock]]
*[[Spark coil]]

==References==
<references />

==External links==
{{LinkWeisstein|filename=DeadSparkCoil.html}}
{{LinkLexicon|filename=lex_d.htm#deadsparkcoil}}

User:Gemini III

2010-11-06T15:34:12Z

Gemini III: New page: Hello. I am '''Gemini III.'''

Hello. I am '''Gemini III.'''

Methuselah

2010-11-05T23:49:58Z

Gemini III: /* Examples */

{{Glossary}}
A '''methuselah''' is, roughly speaking, a [[pattern]] that takes a large number of [[generation]]s in order to stabilize (known as its lifespan) and becomes much larger than its initial configuration at some point during its evolution. In particular, patterns that grow forever are not methuselahs. Their exact definition is not completely agreed upon, and most definitions place restrictions on the number of [[cell]]s in the initial pattern.

[[Martin Gardner]] defined methuselahs as patterns of fewer than ten cells that take longer than 50 generations to stabilize,<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=246}}</ref> though some sources allow for more cells or require a longer lifespan.

==Examples==
The smallest methuselah is the [[R-pentomino]], a pattern of five cells first considered by [[:Category:Patterns found by John Conway|John Conway]]<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=219, 223}}</ref> that takes 1103 generations before stabilizing. The [[acorn]], a pattern of seven cells developed by [[:Category:Patterns found by Charles Corderman|Charles Corderman]], takes 5206 generations to stabilize. Some other popular examples include [[B-heptomino]], [[bunnies]], [[die hard]] and [[rabbits]].
{|
|-
|[[Image:Acorn.png|framed|Acorn]]
|[[Image:Bheptomino.png|framed|B-heptomino]]
|[[Image:Rpentomino.png|framed|R-pentomino]]
|[[Image:Rabbits.png|framed|Rabbits]]
|}

The longest-lived methuselah known to date, [[Fred]], was discovered by [[:Category:Patterns found by Schneelocke|Schneelocke]]. It has an initial population of 150, a final population of 2924, takes 35426 generations to stabilize, and fits within a 20×20 [[bounding box]].

==See also==
*[[List of long-lived methuselahs]]
*[[:Category:Methuselahs|List of methuselahs]]

==References==
<references />

==External links==
[http://www.argentum.freeserve.co.uk/lex_m.htm#methuselah Methuselah] at the Life Lexicon