Snake: Difference between revisions

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|by              = 2
|by              = 2
|fc              = 13.9
|fc              = 13.9
|symmetry        = .k
|discoverer      = JHC group
|discoverer      = JHC group
|discoveryear    = 1970
|discoveryear    = 1970
|rulemin          = B/S23
|rulemin          = B/S23
|rulemax          = B35678/S012345678
|rulemax          = B35678/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]], {{rl|HighLife}}
|isorulemin      = B/S2ae3n
|isorulemin      = B/S2ae3n
|isorulemax      = B2-ac34-r5678/S012345678
|isorulemax      = B2-ac34-r5678/S012345678
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|viewerconfig    = [[ ZOOM 63 ]]
|viewerconfig    = [[ ZOOM 63 ]]
}}
}}
'''Snake''' is a {{slcells|6|text=6-bit}} [[still life]]. It was discovered by the [[JHC group]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=June 18, 2009}}</ref>
'''Snake''' is a {{slcells|6|text=6-bit}} [[still life]]. It was discovered by the [[JHC group]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=June 18, 2009}}</ref>  


== Use as a rock ==
== Use as a rock ==
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{{EmbedViewer
{{EmbedViewer
|pname        = conduit1
|pname        = conduit1
|viewerconfig = #C [[ GPS 20 THUMBSIZE 2 THEME Book AUTOSTART T 0 PAUSE 2 T 59 PAUSE 1 LOOP 60 ]]
|viewerconfig = #C [[ HEIGHT 360 GPS 20 THUMBSIZE 2 ZOOM 16 THEME Book Y 2 AUTOSTART T 0 PAUSE 2 T 59 PAUSE 1 LOOP 60 ]]
|position    = center
|position    = center
|caption      = Conduit 1, showing the snake as a rock catalyst
|caption      = Conduit 1, showing the snake as a rock catalyst
Line 36: Line 36:
}}
}}


Its ability to act as a rock means that it can also be used as a [[memory cell]], in the form of a [[boat-bit]]:
{{EmbedViewer
|rle = x = 25, y = 21, rule = B3/S23
bo$2bo$3o9$12bo$13bo$11b3o6$21bob2o$21b2obo!
|viewerconfig = #C [[ HEIGHT 360 GPS 20 THUMBSIZE 2 ZOOM 16 THEME Book Y 2 AUTOSTART T 0 PAUSE 2 T 23 GPS 20 PAUSE 3 T 26 GPS 5 PAUSE 4 T 58 GPS 20 PAUSE 5 T 72 GPS 5 PAUSE 1 LOOP 72 ]]
|position    = center
|caption      = The snake acting as a boat-bit
|style        = width:300px;
}}
It is the smallest still life by population that can do this, tied with [[aircraft carrier]], but the snake has a smaller [[bounding box]].
== Use as an induction coil ==
== Use as an induction coil ==
A snake is the cheapest way in both population and bounding box to stabilize a line of three cells, such as in [[cauldron]], and the cheapest in bounding box but not population for a line of five, such as in the [[eater 3]]. Snakes are also the most efficient way to stabilize certain non-flat regions such as those in [[55P10]] and [[28P7.2]], although [[aircraft carrier]]s also work for this purpose.
A snake is the cheapest way in both population and bounding box to stabilize a line of three cells, such as in [[cauldron]], and the cheapest in bounding box but not population for a line of five, such as in the [[eater 3]]. Snakes are also the most efficient way to stabilize certain non-flat regions such as those in [[55P10]] and [[28P7.2]], although [[aircraft carrier]]s also work for this purpose.


== Occurrence ==
== Occurrence ==
{{related|List of common still lifes}}
{{related|List of common still lifes|Most common objects on Catagolue}}
Snake is the twenty-first most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[boat-tie]] but slightly more common than [[big S]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>
Snake is the twenty-first most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[boat-tie]] but slightly more common than [[big S]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>


Line 47: Line 57:
The snake is about twice as common in C2_4 (the symmetry it has) compared to asymmetric soups.
The snake is about twice as common in C2_4 (the symmetry it has) compared to asymmetric soups.


== Construction ==
== Glider synthesis ==
There are known ways to [[Glider synthesis|construct]] a snake with {{gliders|4|text=four gliders}}. A number of different syntheses for the snake can be found in [[Mark Niemiec's database|Mark Niemiec's glider synthesis database]].<ref>{{LinkNiemiec|p1.htm#p1-6|patternname=The 5 six-bit still-lifes|nobullet=nobullet}}</ref>
{{main|Glider synthesis}}
There are known ways to construct a snake with {{gliders|4|text=four gliders}}. A number of different syntheses for the snake can be found in [[Mark Niemiec's database|Mark Niemiec's glider synthesis database]].<ref>{{LinkNiemiec|p1.htm#p1-6|patternname=The 5 six-bit still-lifes|nobullet=nobullet}}</ref>


On February 20, {{year|2022}}, a method was found to construct [[pseudo still life]]s consisting of an arbitrarily large stack of snakes.<ref name="post141897" /> These objects were previously notoriously difficult to synthesize &ndash; a stack of three snakes<ref>A stack of three snakes on Catagolue: {{LinkCatagolue|xs18_bd0db0bd|style=raw}}</ref> formerly cost 67 gliders to construct, making it by far the most expensive pseudo still life with 18 cells.<ref>{{CiteCatagolue|page=census/b3s23/synthesis-costs-2022-02-15/xs18?offset=19000|title=Census|accessdate=February 15, 2022}}</ref>
On February 20, {{year|2022}}, a method was found to construct [[pseudo still life]]s consisting of an arbitrarily large stack of snakes.<ref name="post141897" /> These objects were previously notoriously difficult to synthesize &ndash; a stack of three snakes<ref>A stack of three snakes on Catagolue: {{LinkCatagolue|xs18_bd0db0bd|style=raw}}</ref> formerly cost 67 gliders to construct, making it by far the most expensive pseudo still life with 18 cells.<ref>{{CiteCatagolue|page=census/b3s23/synthesis-costs-2022-02-15/xs18?offset=19000|title=Census|accessdate=February 15, 2022}}</ref>


{|style="margin:auto;width:360px;"
{| style="margin:auto; width:360px"
|-
|{{EmbedViewer
|{{EmbedViewer
|rle          = x = 98, y = 50, rule = B3/S23
|rle          = x = 98, y = 50, rule = B3/S23
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Snake can be infinitely extended, as illustrated below:
Snake can be infinitely extended, as illustrated below:


<gallery widths="92px" style="text-align:center;">
<gallery widths="92px" style="text-align:center">
File:longsnake.png|[[Long snake]]
Longsnake.png|[[Long snake]]
File:verylongsnake.png|[[Very long snake]]
Verylongsnake.png|[[Very long snake]]
File:long3snake.png|[[Long^3 snake|Long<sup>3</sup> snake]]
Long3snake.png|[[Long^3 snake|Long<sup>3</sup> snake]]
File:long4snake.png|[[Long^4 snake|Long<sup>4</sup> snake]]
Long4snake.png|[[Long^4 snake|Long<sup>4</sup> snake]]
File:long5snake.png|[[Long^5 snake|Long<sup>5</sup> snake]]
Long5snake.png|[[Long^5 snake|Long<sup>5</sup> snake]]
File:long6snake.png|[[Long^6 snake|Long<sup>6</sup> snake]]
Long6snake.png|[[Long^6 snake|Long<sup>6</sup> snake]]
File:long7snake.png|[[Long^7 snake|Long<sup>7</sup> snake]]
Long7snake.png|[[Long^7 snake|Long<sup>7</sup> snake]]
File:long9snake.png|[[Long^9 snake|Long<sup>9</sup> snake]]
Long8snake.png|Long<sup>8</sup> snake
Long9snake.png|[[Long^9 snake|Long<sup>9</sup> snake]]
</gallery>
</gallery>


It can also be extended by repeatedly [[siamese|siamising]] it, this forms [[coiled snake]]. This family, together with [[block]], are the only width-2 still lives in Conway's Life.
It can also be extended by repeatedly [[siamese|siamising]] it, this forms [[coiled snake]]. This family, together with [[block]], are the only width-2 still lives in Conway's Life.


<gallery widths="92px" style="text-align:center;">
<gallery widths="92px" style="text-align:center">
File:snake.png|Snake
Snake.png|Snake
File:snakesiamesesnake.png|[[Snake siamese snake]]
Snakesiamesesnake.png|[[Snake siamese snake]]
</gallery>
</gallery>


== See also ==
== See also ==
* [[Aircraft carrier]]
* [[Aircraft carrier]]
* [[Snake siamese snake]]
* [[Snake bridge snake]]
* [[Snake bridge snake]]
* [[Silver's p5]], period 5 oscillator
* [[Silver's p5]], period 5 oscillator
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* {{LinkNiemiec|p1.htm#p1-6|The 5 six-bit still-lifes|rle=0/6sn.rle}}
* {{LinkNiemiec|p1.htm#p1-6|The 5 six-bit still-lifes|rle=0/6sn.rle}}
* {{LinkPentadecathlonObject|id=6.1|archivedate=20221102095932|patternname=Snake}}
* {{LinkPentadecathlonObject|id=6.1|archivedate=20221102095932|patternname=Snake}}
{{Symmetry|180degree}}


[[Category:Catalysts]]
[[Category:Catalysts]]
[[Category:Diagonal line stabilisations]]
[[Category:Diagonal line stabilisations]]

Latest revision as of 20:25, 17 January 2026

Snake
x = 4, y = 2, rule = B3/S23 ob2o$2obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 63 ]]
View static image
Pattern type Strict still life
Number of cells 6
Bounding box 4 × 2
Frequency class 13.9
Static symmetry .k (C2_4)
Discovered by JHC group
Year of discovery 1970

Snake is a 6-bit still life. It was discovered by the JHC group in 1970.[1]

Use as a rock

Main article: Tutorials/Catalyses#Snake

The snake can act as a rock. An example is shown below in Conduit 1.

x = 24, y = 13, rule = B3/S23 b2o$2bo$bo$b2o6$o3b2o15bo$2o2b2o15bo$b2o18b3o$2o21bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 360 GPS 20 THUMBSIZE 2 ZOOM 16 THEME Book Y 2 AUTOSTART T 0 PAUSE 2 T 59 PAUSE 1 LOOP 60 ]]
Conduit 1, showing the snake as a rock catalyst
(click above to open LifeViewer)
RLE: here Plaintext: here

Its ability to act as a rock means that it can also be used as a memory cell, in the form of a boat-bit:

x = 25, y = 21, rule = B3/S23 bo$2bo$3o9$12bo$13bo$11b3o6$21bob2o$21b2obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 360 GPS 20 THUMBSIZE 2 ZOOM 16 THEME Book Y 2 AUTOSTART T 0 PAUSE 2 T 23 GPS 20 PAUSE 3 T 26 GPS 5 PAUSE 4 T 58 GPS 20 PAUSE 5 T 72 GPS 5 PAUSE 1 LOOP 72 ]]
The snake acting as a boat-bit
(click above to open LifeViewer)

It is the smallest still life by population that can do this, tied with aircraft carrier, but the snake has a smaller bounding box.

Use as an induction coil

A snake is the cheapest way in both population and bounding box to stabilize a line of three cells, such as in cauldron, and the cheapest in bounding box but not population for a line of five, such as in the eater 3. Snakes are also the most efficient way to stabilize certain non-flat regions such as those in 55P10 and 28P7.2, although aircraft carriers also work for this purpose.

Occurrence

See also: List of common still lifes, Most common objects on Catagolue

Snake is the twenty-first most common still life in Achim Flammenkamp's census, being less common than boat-tie but slightly more common than big S.[2]

It is the 21st most common still life on Adam P. Goucher's Catagolue, being less common than boat-tie but more common than big S. It is the rarest still life with 6 cells, being 3.6 times rarer than carrier.[3]

The snake is about twice as common in C2_4 (the symmetry it has) compared to asymmetric soups.

Glider synthesis

Main article: Glider synthesis

There are known ways to construct a snake with four gliders. A number of different syntheses for the snake can be found in Mark Niemiec's glider synthesis database.[4]

On February 20, 2022, a method was found to construct pseudo still lifes consisting of an arbitrarily large stack of snakes.[5] These objects were previously notoriously difficult to synthesize – a stack of three snakes[6] formerly cost 67 gliders to construct, making it by far the most expensive pseudo still life with 18 cells.[7]

x = 98, y = 50, rule = B3/S23 bo$2bo$3o13$95bo$95bobo$95b2o27$63bo$64b2o$63b2o$68bo$67b2o$67bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 420 ZOOM 10 X 6 Y 27 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 164 PAUSE 1 T 208 PAUSE 1 LOOP 209 ]]
A two-stage four-glider synthesis for the snake[8]
(click above to open LifeViewer)
x = 34, y = 37, rule = B3/S23 15bo$16bo$14b3o18$32b2o$32bo$25b2o3bobo$24bo2bo2b2o$25bobo$26bo$8b2o$ 7bobo$7b2o3$2o$b2o$o$8bo$7bobo$7b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 420 ZOOM 8 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 108 PAUSE 1 LOOP 109 ]]
Two one-glider seed constellations for the snake from the octohash database
(click above to open LifeViewer)

Extensibility

Snake can be infinitely extended, as illustrated below:

It can also be extended by repeatedly siamising it, this forms coiled snake. This family, together with block, are the only width-2 still lives in Conway's Life.

See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on June 18, 2009.
  2. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on May 5, 2023.
  4. ↑ The 5 six-bit still-lifes at Mark D. Niemiec's Life Page
  5. ↑ iNoMed (February 20, 2022). Re: Still Life Synthesis Thread (discussion thread) at the ConwayLife.com forums
  6. ↑ A stack of three snakes on Catagolue: xs18_bd0db0bd
  7. ↑ Adam P. Goucher. "Census". Catagolue. Retrieved on February 15, 2022.
  8. ↑ GUYTU6J (February 21, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
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