LifeWiki - User contributions [en]

Pre-block

2011-10-28T23:46:39Z

Bloonsio:

{{Pattern|name=Pre-block|pname=preblock|bx=2|by=2|c=3|discoverer=John Conway|discoveryear=1970|life105=true|life106=true|plaintext=true|rle=true|synthesis=2|synthesisRLE=true}}
'''Pre-block''' (or '''latent block'''), a [[triomino]], is a common [[parent]] of the [[block]]. Given its compactness and distinctive form, it is a recognizable component of many other patterns, such as [[boat]], [[ship]], [[aircraft carrier]], [[block and glider]] or [[snake]]; a mirrored pair comprise one phase of a [[beacon]].

==See also==
*[[Grin]]

==External links==
{{LinkWeisstein|Preblock.html}}
{{LinkLexicon|lex_p.htm#preblock}}

Die hard

2011-10-23T16:02:43Z

Bloonsio:

{{Methuselah|name=Die hard|pname=diehard|bx=8|by=3|c=7|l=130|life105=true|life106=true|plaintext=true|rle=true}}
'''Die hard''' is a [[:Category:Patterns with 7 cells|7-cell]] [[methuselah]] (essentially a collision between a [[block]] and the [[traffic light]] sequence) that vanishes after 130 generations, which is conjectured to be the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells, as eight cells suffice to have a [[glider]] heading towards an arbitrarily distant [[blinker]].

The same exact pattern is also a diehard in [[HighLife]], dying after 119 generations.

Alternatively, die hard may refer to any methuselah that eventually vanishes.

==External links==
[http://www.argentum.freeserve.co.uk/lex_d.htm#diehard Die hard] at the Life Lexicon

B-heptomino

2011-10-22T00:26:36Z

Bloonsio:

{{Methuselah|l=148|name=B-heptomino|pname=bheptomino|c=7|bx=4|by=3|discoverer=John Conway|discoveryear=1970|life105=true|life106=true|plaintext=true|rle=true|synthesis=2|synthesisRLE=true}}
The '''B-heptomino''' is a very common [[methuselah]] that evolves into three [[block]]s, two [[glider]]s and a [[ship]] after 148 generations. Compare with [[Herschel]], which appears at generation 20 of B-heptomino's evolution. It often arises with the cell at top left shifted one space to the left, which does not affect the subsequent evolution. B-heptominoes acquired particular importance in [[:Category:Patterns found in 1996|1996]] due to [[:Category:Patterns found by David Buckingham|David Buckingham]]'s work on [[B track|B tracks]].

==Image gallery==
<gallery>
Image:BheptominoGen20.png|Generation 20 of the B-heptomino
Image:BheptominoFinal.png|Generation 148 of the B-heptomino
Image:Bparent.GIF|A 6-cell parent of the B-heptomino
</gallery>

==See also==
*[[C-heptomino]]
*[[Conduit 1]]
*[[Lifeline Volume 1]]
*[[Omniperiodic]]
*[[Transparent debris effect#Transparent block reaction|Transparent block reaction]]

==External links==
{{LinkWeisstein|B-Heptomino.html}}
{{LinkLexicon|lex_b.htm#bheptomino}}

Pi-heptomino

2011-10-22T00:08:21Z

Bloonsio:

{{Methuselah|name=Pi-heptomino|pname=piheptomino|l=173|c=7|bx=3|by=3|life105=true|life106=true|plaintext=true|rle=true|synthesis=2|synthesisRLE=true}}
'''Pi-heptomino''' (or '''pi''') is a common [[Polyomino#Heptominoes|heptomino]] that stabilizes at [[generation]] 173. The name "pi" is also applied to some slight variations of this object that follow that same evolutionary sequence - in a [[pi ship]], for example, the pi-heptomino itself never actually arises. Forms that are synonymous with the pi-heptomino are displayed below.

In April [[:Category:Patterns found in 1992|1992]], [[Bill Gosper]] discovered that two [[block]]s can be used to [[eater|eat]] a pi, as shown below. The eating reaction takes 65 [[generation]]s to complete. Gosper also discovered in the same month that a pi, along with two blocks and two [[blinker]]s, can be used to create a [[queen bee shuttle]].

==Image gallery==
{|
|-
|[[Image:Pi2.png|framed|left|Generation 1 of pi-heptomino]]
|[[Image:Pi-parents.gif|framed|left|A grandparent (a pentaplet) and parent (a hexomino) of pi]]
|[[Image:Pi1.png|framed|left|An alternative [[parent]] of generation 1]]
|[[Image:Pi_eater.png|framed|left|A pi eater {{JavaRLE|pieater|brief}}]]
|[[Image:Pi_eater2.png|framed|left|Another pi eater {{JavaRLE|pieater2|brief}}]]
|[[Image:PiWord.GIF|framed|left|This pattern, which resembles the word "Pi", evolves exactly like the Pi-heptomino after two generations, stabilizing at generation 174.]]
|}

==See also==
*[[House]]

==External links==
{{LinkWeisstein|Pi-Heptomino.html}}
{{LinkLexicon|lex_p.htm#piheptomino}}

File:PiWord.GIF

2011-10-22T00:04:25Z

Bloonsio:

T-tetromino

2011-10-22T00:02:32Z

Bloonsio:

{{Pattern|name=T-tetromino|pname=ttetromino|discoverer=John Conway|discoveryear=1970|c=4|bx=3|by=2|life105=true|life106=true|plaintext=true|rle=true}}
'''T-tetromino''' is one of 5 [[Polyomino#Tetrominoes|tetrominoes]]. It is a common [[predecessor]] of the [[traffic light]], and when paired with another T-tetromino it can become a predecessor of the [[pulsar]].

In a cylindrical grid with a width of 6, the T-tetromino is always a [[replicator]]. It copies itself on the 15th and 40th generations of every 40 generations. However, because it leaves behind [[block]]s, [[blinker]]s, and [[spark]]s, it does cleanly replicate itself until after 200 generations. It acts much the same way as the replicator in [[Highlife]] because the two copies of the T-tetromino appear offset in opposite directions of the original. Also, two replicators will destroy each other if they are next to each other. The T-tetromino replicates orthogonally and 35 cells away from the original.
==See also==
*[[Pre-pulsar]]

==External links==
{{LinkLexicon|lex_t.htm#ttetromino}}

Pre-pulsar

2011-10-21T23:42:44Z

Bloonsio:

{{Pattern|name=Pre-pulsar|pname=prepulsar|c=16|bx=9|by=3|life105=true|life106=true|plaintext=true|rle=true}}
The '''pre-pulsar''' is a common [[predecessor]] of the [[pulsar]]. It duplicates itself after 15 generations, although it fails to be a true [[replicator]] because of the way that the two copies then interact.

A pair of [[tub|tubs]] can be placed to eat half of the pre-pulsar as it replicates; this gives the [[period]] [[:Category:Oscillators with period 30|30]] [[oscillator]] [[Eureka]], where the pre-pulsar's replication becomes a movement back and forth. The replication of the pre-pulsar can also be made to occur in just 14 generations as half of it is eaten; this allows the construction of period [[:Category:Oscillators with period 28|28]] and period [[:Category:Oscillators with period 29|29]] oscillators, and is in fact the only known method for creating a period 29 oscillator. The pre-pulsar is also a vital component of the only known method for constructing period [[:Category:Oscillators with period 47|47]] oscillators, and a similar reaction is the key component in the [[168P22.1|first discovered period 22 oscillator]].

A '''skewed pre-pulsar''' is like a pre-pulsar, however, the pre-traffic lights it is composed of are vertically skewed by two cells. Despite this it manages to replicate itself and becomes two skewed halves of a pulsar. This form, however, is unstable and so is not truly a pulsar predecessor, but it can be hassled similarly to a normal pre-pulsar by oscillators and spaceships

==Image gallery==
{|
|-
|[[Image:Prepulsarpredecessor.png|framed|left|A common four-generation [[predecessor]] of the pre-pulsar that consists of two [[T-tetromino]]es {{JavaRLE|prepulsarpredecessor}}]]
|[[Image:Skewedprepulsar.png|framed|left|A skewed pre-pulsar {{JavaRLE|skewedprepulsar}}]]
|[[Image:minprepulsar.GIF|framed|left|The smallest predecessor of the pulsar has only seven cells.]]
|}

==See also==
*[[Pre-pulsar shuttle 29]]
*[[Pre-pulsar shuttle 47]]
*[[Pre-pulsar spaceship]]
*[[Twirling T-tetsons 2]]

==External links==
*[http://www.argentum.freeserve.co.uk/lex_p.htm#prepulsar Pre-pulsar] at the Life Lexicon

OCA:Move

2011-10-16T04:39:49Z

Bloonsio:

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

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

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

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

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

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| ?
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}

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

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

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

==References==
<references />

OCA:HighLife

2011-10-16T04:38:02Z

Bloonsio:

{{Rule|name=HighLife|imgname=highlife|s=23|b=36|char=Chaotic|animated=true}}
'''HighLife''' 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 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[:Category:Patterns found by John Conway|John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; it's only when patterns get complex that their behavior differs. Nonetheless, it exhibits such rich structure that [[:Category:Patterns found by John Conway|John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."'' <ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s being unstable.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]]. This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:replicator_predecessor.png|framed|right|A 3-generation predecessor of the replicator {{JavaRLE|replicatorpredecessor|brief}}]]
|[[Image:replicator.png|framed|right|The replicator itself {{JavaRLE|replicator|brief}}]]
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with [[:Category:Strict still lifes with 6 cells|6]] cells) and [[hat]] (with [[:Category:Strict still lifes with 9 cells|9]] cells). Also, any pattern involving a [[bun]] or a [[cap]] that is a still life under the standard rules is not a still life in HighLife.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}

===Change in Frequency===
From the same random starting conditions, HighLife usually settles into fewer objects than in [[Conway's Game of Life|Life]]. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, frequency is measured by number of objects per cell rather than total objects. This is because the frequency of total objects also changes between Life and HighLife.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Frequency in Life
! Change in Frequency
! Frequency in HighLife
! Notes
|-
| All Objects
| 6.64×10-3
| -35%
| 4.30×10-3
| The overall decrease of objects causes HighLife to stabilize over twice as fast on average.
|-
| [[Blinker]]
| 2.15×10-3
| -68%
| 6.88×10-4
| Blinkers are much less common (third) since the [[traffic light]] does not form from predecessors in HighLife.
|-
| [[Block]]
| 2.11×10-3
| -13%
| 1.83×10-3
| Although the block are less common in HighLife, it is still the most common object.
|-
| [[Beehive]]
| 1.25×10-3
| -40%
| 7.46×10-4
| Beehives are also less common, but more common than the blinker.
|-
| [[Loaf]]
| 3.89×10-4
| +8%
| 4.19×10-4
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 3.58×10-4
| +16%
| 4.14×10-4
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 8.00×10-5
| +21%
| 9.73×10-5
| Tubs experience a 21% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 7.53×10-5
| -54%
| 3.49×10-5
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife.
|-
| [[Ship]]
| 4.92×10-5
| -100%
| 0
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|-
| [[Aircraft carrier]]
| 5.00×10-7
| +2516%
| 1.30×10-5
| They're 26 times more common. [[Image:Pi1.png]] This evolves into two aircraft carriers and a blinker.
|-
| [[Elevener]]
| 4.55×10-9
| +5395%
| 2.50×10-7
| Eleveners appear 55 times as often in HighLife! It's probably because of a common predecessor.
|}

===Spaceships===
All of the [[standard spacehip]]s from the standard Life rules work in HighLife, but the only non-standard spaceships that are known to work in HighLife are the [[turtle]], [[117P9H3V0|86P9H3V0]], and some [[flotilla]]e of the standard spaceships. There are also several known spaceships that are specific to HighLife<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b36s23/ |title=HighLife (B36/S23) |publisher=David Eppstein|accessdate=April 15, 2009}}</ref>, the most well-known of which is the bomber.

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric spaceship]] with [[mod]] equal to 24.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:Bomber_predecessor.png|framed|left|A predecessor of the bomber {{JavaRLE|bomberpredecessor|brief}}]]
|[[Image:Bomber.gif|framed|left|The bomber itself]]
|}

==References==
<references />

OCA:HighLife

2011-10-16T04:35:19Z

Bloonsio:

{{Rule|name=HighLife|imgname=highlife|s=23|b=36|char=Chaotic|animated=true}}
'''HighLife''' 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 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[:Category:Patterns found by John Conway|John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; it's only when patterns get complex that their behavior differs. Nonetheless, it exhibits such rich structure that [[:Category:Patterns found by John Conway|John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."'' <ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s being unstable.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]]. This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:replicator_predecessor.png|framed|right|A 3-generation predecessor of the replicator {{JavaRLE|replicatorpredecessor|brief}}]]
|[[Image:replicator.png|framed|right|The replicator itself {{JavaRLE|replicator|brief}}]]
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with [[:Category:Strict still lifes with 6 cells|6]] cells) and [[hat]] (with [[:Category:Strict still lifes with 9 cells|9]] cells). Also, any pattern involving a [[bun]] or a [[cap]] that is a still life under the standard rules is not a still life in HighLife.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}

===Change in Frequency===
From the same random starting conditions, HighLife usually settles into fewer objects than in [[Conway's Game of Life|Life]]. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, frequency is measured by number of objects per cell rather than total objects. This is because the frequency of total objects also changes between Life and HighLife.

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Frequency in Life
! Change in Frequency
! Frequency in HighLife
! Notes
|-
| All Objects
| 6.64×10-3
| -35%
| 4.30×10-3
| The overall decrease of objects causes HighLife to stabilize over twice as fast on average.
|-
| [[Blinker]]
| 2.15×10-3
| -68%
| 6.88×10-4
| Blinkers are much less common (third) since the [[traffic light]] does not form from predecessors in HighLife.
|-
| [[Block]]
| 2.11×10-3
| -13%
| 1.83×10-3
| Although the block are less common in HighLife, it is still the most common object.
|-
| [[Beehive]]
| 1.25×10-3
| -40%
| 7.46×10-4
| Beehives are also less common, but more common than the blinker.
|-
| [[Loaf]]
| 3.89×10-4
| +8%
| 4.19×10-4
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 3.58×10-4
| +16%
| 4.14×10-4
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 8.00×10-5
| +21%
| 9.73×10-5
| Tubs experience a 21% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 7.53×10-5
| -54%
| 3.49×10-5
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife.
|-
| [[Ship]]
| 4.92×10-5
| -100%
| 0
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|-
| [[Aircraft carrier]]
| 5.00×10-7
| +2516%
| 1.30×10-5
| They're 26 times more common. [[Image:Pi1.png]] This evolves into two aircraft carriers and a blinker.
|-
| [[Elevener]]
| 4.55×10-9
| +5395%
| 2.50×10-7
| Eleveners appear 55 times as often in HighLife! It's probably because of a common predecessor.
|}

===Spaceships===
All of the [[standard spacehip]]s from the standard Life rules work in HighLife, but the only non-standard spaceships that are known to work in HighLife are the [[turtle]], [[117P9H3V0|86P9H3V0]], and some [[flotilla]]e of the standard spaceships. There are also several known spaceships that are specific to HighLife<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b36s23/ |title=HighLife (B36/S23) |publisher=David Eppstein|accessdate=April 15, 2009}}</ref>, the most well-known of which is the bomber.

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric spaceship]] with [[mod]] equal to 24.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:Bomber_predecessor.png|framed|left|A predecessor of the bomber {{JavaRLE|bomberpredecessor|brief}}]]
|[[Image:Bomber.gif|framed|left|The bomber itself]]
|}

==References==
<references />

OCA:HighLife

2011-10-15T05:06:57Z

Bloonsio:

{{Rule|name=HighLife|imgname=highlife|s=23|b=36|char=Chaotic|animated=true}}
'''HighLife''' 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 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[:Category:Patterns found by John Conway|John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; it's only when patterns get complex that their behavior differs. Nonetheless, it exhibits such rich structure that [[:Category:Patterns found by John Conway|John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."'' <ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s being unstable.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]]. This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:replicator_predecessor.png|framed|right|A 3-generation predecessor of the replicator {{JavaRLE|replicatorpredecessor|brief}}]]
|[[Image:replicator.png|framed|right|The replicator itself {{JavaRLE|replicator|brief}}]]
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with [[:Category:Strict still lifes with 6 cells|6]] cells) and [[hat]] (with [[:Category:Strict still lifes with 9 cells|9]] cells). Also, any pattern involving a [[bun]] or a [[cap]] that is a still life under the standard rules is not a still life in HighLife.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}

===Change in Frequency===
From the same random starting conditions, HighLife usually settles into fewer objects than in [[Conway's Game of Life|Life]]. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, frequency is measured by number of objects per cell rather than total objects. This is because the frequency of total objects also changes between Life and HighLife.

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Frequency in Life
! Change in Frequency
! Frequency in HighLife
! Notes
|-
| All Objects
| 6.64×10-3
| -35%
| 4.30×10-3
| The overall decrease of objects causes HighLife to stabilize over twice as fast on average.
|-
| [[Blinker]]
| 2.15×10-3
| -68%
| 6.88×10-4
| Blinkers are much less common (third) since the [[traffic light]] does not form from predecessors in HighLife.
|-
| [[Block]]
| 2.11×10-3
| -13%
| 1.83×10-3
| Although the block are less common in HighLife, it is still the most common object.
|-
| [[Beehive]]
| 1.25×10-3
| -40%
| 7.46×10-4
| Beehives are also less common, but more common than the blinker.
|-
| [[Loaf]]
| 3.89×10-4
| +8%
| 4.19×10-4
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 3.58×10-4
| +16%
| 4.14×10-4
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 8.00×10-5
| +21%
| 9.73×10-5
| Tubs experience a 17% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 7.53×10-5
| -54%
| 3.49×10-5
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife.
|-
| [[Ship]]
| 4.92×10-5
| -100%
| 0
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|-
| [[Aircraft carrier]]
| 5.00×10-7
| +2516%
| 1.30×10-5
| They're 26 times more common. [[Image:Pi1.png]] This evolves into two aircraft carriers and a blinker.
|-
| [[Elevener]]
| 4.55×10-9
| +5395%
| 2.50×10-7
| Eleveners appear 55 times as often in HighLife! It's probably because of a common predecessor.
|}

===Spaceships===
All of the [[standard spacehip]]s from the standard Life rules work in HighLife, but the only non-standard spaceships that are known to work in HighLife are the [[turtle]], [[117P9H3V0|86P9H3V0]], and some [[flotilla]]e of the standard spaceships. There are also several known spaceships that are specific to HighLife<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b36s23/ |title=HighLife (B36/S23) |publisher=David Eppstein|accessdate=April 15, 2009}}</ref>, the most well-known of which is the bomber.

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric spaceship]] with [[mod]] equal to 24.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:Bomber_predecessor.png|framed|left|A predecessor of the bomber {{JavaRLE|bomberpredecessor|brief}}]]
|[[Image:Bomber.gif|framed|left|The bomber itself]]
|}

==References==
<references />

OCA:HighLife

2011-10-15T04:57:48Z

Bloonsio:

{{Rule|name=HighLife|imgname=highlife|s=23|b=36|char=Chaotic|animated=true}}
'''HighLife''' 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 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[:Category:Patterns found by John Conway|John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; it's only when patterns get complex that their behavior differs. Nonetheless, it exhibits such rich structure that [[:Category:Patterns found by John Conway|John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."'' <ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s being unstable.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]]. This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:replicator_predecessor.png|framed|right|A 3-generation predecessor of the replicator {{JavaRLE|replicatorpredecessor|brief}}]]
|[[Image:replicator.png|framed|right|The replicator itself {{JavaRLE|replicator|brief}}]]
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with [[:Category:Strict still lifes with 6 cells|6]] cells) and [[hat]] (with [[:Category:Strict still lifes with 9 cells|9]] cells). Also, any pattern involving a [[bun]] or a [[cap]] that is a still life under the standard rules is not a still life in HighLife.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}

===Change in Frequency===
From the same random starting conditions, HighLife usually settles into fewer objects than [[Conway's Game of Life|Life]]. In this chart, frequency is measured by number of objects per cell rather than total objects because the frequency of total objects changes between Life and HighLife.

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Frequency in Life
! Change in Frequency
! Frequency in HighLife
!
|-
| All Objects
| 6.64×10-3
| -35%
| 4.30×10-3
| The overall decrease of objects causes HighLife to stabilize over twice as fast on average.
|-
| [[Blinker]]
| 2.15×10-3
| -68%
| 6.88×10-4
| Blinkers are much less common (third) since the [[traffic light]] does not form from predecessors in HighLife.
|-
| [[Block]]
| 2.11×10-3
| -13%
| 1.83×10-3
| Although blocks are less common in HighLife, they are the most common object.
|-
| [[Beehive]]
| 1.25×10-3
| -40%
| 7.46×10-4
| Beehives are also less common, but more common than the blinker.
|-
| [[Loaf]]
| 3.89×10-4
| +8%
| 4.19×10-4
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 3.58×10-4
| +16%
| 4.14×10-4
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 8.00×10-5
| +21%
| 9.73×10-5
| Tubs experience a 17% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 7.53×10-5
| -54%
| 3.49×10-5
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife.
|-
| [[Ship]]
| 4.92×10-5
| -100%
| 0
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|-
| [[Aircraft carrier]]
| 5.00×10-7
| +2516%
| 1.30×10-5
| They're 26 times more common. [[Image:Pi1.png]] This evolves into two aircraft carriers and a blinker.
|-
| [[Elevener]]
| 4.55×10-9
| +5395%
| 2.50×10-7
| Eleveners appear 55 times as often in HighLife! It's probably because of a common predecessor.
|}

===Spaceships===
All of the [[standard spacehip]]s from the standard Life rules work in HighLife, but the only non-standard spaceships that are known to work in HighLife are the [[turtle]], [[117P9H3V0|86P9H3V0]], and some [[flotilla]]e of the standard spaceships. There are also several known spaceships that are specific to HighLife<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b36s23/ |title=HighLife (B36/S23) |publisher=David Eppstein|accessdate=April 15, 2009}}</ref>, the most well-known of which is the bomber.

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric spaceship]] with [[mod]] equal to 24.

{| style="margin-left:auto;margin-right:auto;"
|-
|[[Image:Bomber_predecessor.png|framed|left|A predecessor of the bomber {{JavaRLE|bomberpredecessor|brief}}]]
|[[Image:Bomber.gif|framed|left|The bomber itself]]
|}

==References==
<references />

OCA:Move

2011-10-15T04:10:48Z

Bloonsio:

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

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

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

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

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

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| ?
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}

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

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

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

==References==
<references />

OCA:Move

2011-10-15T03:57:46Z

Bloonsio:

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

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

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

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

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

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| ?
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}

</td></tr></table>

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

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

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

==References==
<references />

OCA:Move

2011-10-15T03:56:38Z

Bloonsio:

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

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

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

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

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

<table border="0" cellpadding="0" cellspacing="0" style="margin-left:auto;margin-right:auto;"><tr><td align="center">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Rank
! Object
! Name
! Period
! Relative Frequency
|-
| 1
| [[Blinker]]
| [[Image:blinker.png‎|center]]
| 2
| 0.305
|-
| 2
| P-pentomino
| [[Image:Move2.GIF‎|center]]
| 4
| 0.155
|-
| 3
| [[Tub]]
| [[Image:tub.png|center]]
| 1
| 0.128
|-
| 4
| Long blinker
| [[Image:Move4.GIF|center]]
| 2
| 0.108
|-
| 5
| ?
| [[Image:Move5.GIF|center]]
| 4
| 0.078
|-
| 6
| ?
| [[Image:Move6.GIF|center]]
| 2
| 0.058
|-
| 7
| Big blinker
| [[Image:Move7.GIF|center]]
| 2
| 0.056
|-
| 8
| Z-pentomino
| [[Image:Move8.GIF|center]]
| 1
| 0.047
|-
| 9
| Spinning Glider
| [[Image:Move9.GIF|center]]
| 4
| 0.025
|-
| 10
| ?
| [[Image:Move10.GIF|center]]
| 1
| 0.014
|}

</td></tr></table>

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

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

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

==References==
<references />

File:Move10.GIF

2011-10-15T03:45:10Z

Bloonsio: Tenth most common object in the Life-like cellular automaton Move.

Tenth most common object in the Life-like cellular automaton Move.

File:Move9.GIF

2011-10-15T03:44:54Z

Bloonsio: Ninth most common object in the Life-like cellular automaton Move.

Ninth most common object in the Life-like cellular automaton Move.

File:Move8.GIF

2011-10-15T03:44:38Z

Bloonsio: Eighth most common object in the Life-like cellular automaton Move.

Eighth most common object in the Life-like cellular automaton Move.

File:Move7.GIF

2011-10-15T03:44:09Z

Bloonsio: Seventh most common object in the Life-like cellular automaton Move.

Seventh most common object in the Life-like cellular automaton Move.

File:Move6.GIF

2011-10-15T03:43:48Z

Bloonsio: Sixth most common object in the Life-like cellular automaton Move.

Sixth most common object in the Life-like cellular automaton Move.

File:Move5.GIF

2011-10-15T03:43:31Z

Bloonsio: Fifth most common object in the Life-like cellular automaton Move.

Fifth most common object in the Life-like cellular automaton Move.

File:Move4.GIF

2011-10-15T03:42:56Z

Bloonsio: Fourth most common object in the Life-like cellular automaton Move.

Fourth most common object in the Life-like cellular automaton Move.

File:Move2.GIF

2011-10-15T03:37:09Z

Bloonsio: uploaded a new version of "File:Move2.GIF"

Second most common object in the Life-like cellular automaton Move.

File:Move2.GIF

2011-10-15T03:35:57Z

Bloonsio: Second most common object in the Life-like cellular automaton Move.

Second most common object in the Life-like cellular automaton Move.

Talk:Fred

2011-10-08T21:51:56Z

Bloonsio:

Hey, I realized, there are two dots (single cells) that are a bit to the right of the center. It looks to me that the lower one doesn't affect Fred's evolution. Is it necessary? If not, can it be removed?

Talk:Fred

2011-10-08T21:48:26Z

Bloonsio:

Hey, I realized, there are two dots (single cells) that are a bit to the right of the center. It looks to me that they don't affect Fred's evolution. Are they necessary? If not, can they be removed?

Talk:Fred

2011-10-08T21:43:55Z

Bloonsio: Created page with "h"