Difference between revisions of "OCA:HighLife"

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<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>
<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==
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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]], [[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 2<sup>n</sup> copies of the replicator at generation 12(2<sup>n</sup> - 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<br />{{JavaRLE|replicatorpredecessor|brief}}]]
|[[Image:replicator.png|framed|right|The replicator itself<br />{{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
|-
| &le;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}}
|}
 
===Spaceships===
All of the [[standard spacehip]]s from the standard Life rules work in HighLife, but the only non-standard spaceship which is known to work in HighLife is [[turtle]]. 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<br />{{JavaRLE|bomberpredecessor|brief}}]]
|[[Image:Bomber.gif|framed|left|The bomber itself]]
|}


==References==
==References==
<references />
<references />

Revision as of 21:41, 5 August 2010

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HighLife
x=0, y = 0, rule = B36/S23 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 23/36
B36/S23
Character Chaotic

HighLife is a Life-like cellular automaton in which cells 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 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 John Conway himself stated

"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things." [1]

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References