Difference between revisions of "Block"

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{{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}}
{{Stilllife
'''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]].
|name             = Block
|pname           = block
|c               = 4
|bx               = 2
|by               = 2
|fc              = 0.0
|discoverer       = John Conway
|discoveryear    = 1970
|rulemin          = B/S3
|rulemax          = B345678/S012345678
|rulespecial     = [[Conway's Game of Life|Conway Life]], [[HighLife]], [[Maze]]
|isorulemin      = B/S3a
|isorulemax      = B1e2-a345678/S012345678
|synthesis        = 2
|synthesisRLE    = true
|plaintext        = true
|rle              = true
|apgcode          = xs4_33
|pentadecathlonid = 4.1
}}
'''Block''' is an extremely well-known and common [[still life]] that was found by [[John Conway]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> In terms of its {{slcells|4}} [[cell]]s it is tied with [[tub]] as the smallest still life, and in terms of its 2&times;2 [[bounding box]] it is the outright smallest.  It is also the only known still life that is a [[polyomino]], and the only still life where all cells have three neighbors.


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 can also work as a [[reflector]] for two gliders via the [[interchange]] synthesis.
Due to its small size, its ability to act as an [[eater]], and its simple [[glider syntheses]], it is extremely useful in the construction of large patterns. It can be used as an [[induction coil]] as in [[block on dock]], [[block on table]] and [[block on griddle]]. It [[glider-block cycle|can also work]] as a [[reflector]] for two gliders via the [[interchange]] synthesis, as can be seen in [[106P135]].


Block is the most common still life (or any object at all) 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 [[Game of Life]] to the world.


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.
==[[List of common still lifes|Commonness]]==
The block is the most common still life (and indeed object) that occurs as a result of [[soup|random starting patterns]]. In [[Achim Flammenkamp's census]] it occurred almost twice as often as [[beehive]], the next most common still life.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>; it is also the most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref> It is also the most common object produced by [[2-glider collision]]s (six different ways).


==Eater==
==Eater==
There are multiple ways in which the block may act as an eater. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a [[rock]], except through induction, such as the [[p47 pre-pulsar shuttle]].). Oscillators such as [[blocker]], [[p56 B-heptomino shuttle]], [[queen bee shuttle]], [[twin bees shuttle]] and [[unix]] showcase mechanisms which leave a [[pre-block]] or a [[hook]], while the mechanisms seen in [[Coe's p8]], [[eater 5]] and [[octagon 4]] leave a [[grin]]. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in [[37P7.1]]. It has been seen eating [[mango]]s, [[boat]]s, [[loaf|loaves]], and [[beehive]]s.


There are multiple ways in which the block may act as an eater. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a [[rock]]). Oscillators such as [[blocker]], [[p56 B-heptomino shuttle]], [[queen bee shuttle]], [[twin bees shuttle]] and [[unix]] showcase mechanisms which leave a [[pre-block]], while the mechanisms seen in [[Coe's p8]], [[eater 5]] and [[octagon 4]] leave a [[grin]]. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in [[37P7.1]]. It has been seen eating [[mango]]s, [[boat]]s, [[loaf|loaves]], and [[beehive]]s.
Some more complex eaters can be based on the block as well. [[Eater 2]] is a construction allowing a block to eat [[glider]]s: while the collision would normally destroy both, the addition of further still life(s) or [[inductee]]s allows the remaining three-cell [[spark]] to regenerate into a block.


Some more complex eaters can be based on the block as well. [[Eater 2]] is a construction allowing a block to eat [[glider]]s: while the collision would normally destroy both, the addition of further still life(s) or [[inductee]]s allows the remaining three-cell [[spark]] to regenerate into a block.
Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]]. Several larger oscillators including [[p54 shuttle]], [[78P70]], [[two blockers hassling R-pentomino]] and [[Achim's p144]] are examples. A particular reaction with a [[B-heptomino]] is commonly used in the construction of [[Herschel track]]s.
 
==Blockic constellation==
A '''blockic constellation''' is a [[constellation]] consisting entirely of blocks. It's possible to arrange blocks in [[seed|a way]] that can be triggered by a single glider to produce any glider constructible pattern.{{citation needed}}


Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]]. Several larger oscillators including [[p54 shuttle]], [[78P70]], [[47P72]] and [[Achim's p144]] are examples. A particular reaction with a [[B-heptomino]] is commonly used in the construction of [[Herschel track]]s.
==Block arrays==
[[Pseudo still life]]s exist consisting of an arbitrary array of blocks placed next to each other, which may be referred to as '''block [[agar]]s'''. On December 3, {{year|2015}}, [[Martin Grant]] found a method of constructing a 3&times;''n'' array via [[glider synthesis]],<ref name="post25637" /> and on May 6, {{year|2020}}, [[Goldtiger997]] found a method of constructing a 4&times;''n'' array.<ref name="post96210" />


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


==References==
==References==
<references />
<references>
<ref name="post25637">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 25637
|author = Martin Grant
|date  = December 3, 2015
}}</ref>
<ref name="post96210">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 96210
|author = Goldtiger997
|date  = May 6, 2020
}}</ref>
</references>


==External links==
==External links==
{{LinkWeisstein|Block.html}}
{{LinkLexicon|lex_b.htm#block}}
{{LinkLexicon|lex_b.htm#block}}
{{LinkLexicon|lex_b.htm#blockic|patternname=Blockic}}
{{LinkCatagolue|xs4_33}}
{{LinkCatagolue|xs4_33}}
{{LinkNiemiec|p1.htm#p1-4|patternname=The 2 four-bit still-lifes}}
{{LinkNiemiec|p1.htm#p1-4|patternname=The 2 four-bit still-lifes}}
*[http://www.ibiblio.org/lifepatterns/october1970.html The fantastic combinations of John Conway's new solitaire game "life"] by Martin Gardner
*[http://www.ibiblio.org/lifepatterns/october1970.html The fantastic combinations of John Conway's new solitaire game "life"] by Martin Gardner
{{LinkForumThread|f=2|t=1065|title=Blockic splitters}}
{{LinkForumThread|f=2|t=1134|title=Blockic Seeds}}


[[Category:Eaters]]
[[Category:Eaters]]
{{Symmetry|full}}
{{Symmetry|full}}
__NOTOC__

Revision as of 03:12, 8 December 2020

Block
x = 2, y = 2, rule = B3/S23 2o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]]
View static image
Pattern type Strict still life
Number of cells 4
Bounding box 2 × 2
Frequency class 0.0
Discovered by John Conway
Year of discovery 1970

Block is an extremely well-known and common still life that was found by John Conway in 1970.[1] In terms of its 4 cells 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, and the only still life where all cells have three neighbors.

Due to its small size, its ability to act as an eater, and its simple glider syntheses, it is extremely useful in the construction of large patterns. It can be used as an induction coil as in block on dock, block on table and block on griddle. It can also work as a reflector for two gliders via the interchange synthesis, as can be seen in 106P135.

The block was one of the patterns described in the original 1970 article by Martin Gardner that introduced the Game of Life to the world.

Commonness

The block is the most common still life (and indeed object) that occurs as a result of random starting patterns. In Achim Flammenkamp's census it occurred almost twice as often as beehive, the next most common still life.[2]; it is also the most common object on Adam P. Goucher's Catagolue.[3] It is also the most common object produced by 2-glider collisions (six different ways).

Eater

There are multiple ways in which the block may act as an eater. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a rock, except through induction, such as the p47 pre-pulsar shuttle.). Oscillators such as blocker, p56 B-heptomino shuttle, queen bee shuttle, twin bees shuttle and unix showcase mechanisms which leave a pre-block or a hook, while the mechanisms seen in Coe's p8, eater 5 and octagon 4 leave a grin. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in 37P7.1. It has been seen eating mangos, boats, loaves, and beehives.

Some more complex eaters can be based on the block as well. Eater 2 is a construction allowing a block to eat gliders: while the collision would normally destroy both, the addition of further still life(s) or inductees allows the remaining three-cell spark to regenerate into a block.

Since the block is the most common object to emerge from soups, it is also the most common object to show transparent debris effect. Several larger oscillators including p54 shuttle, 78P70, two blockers hassling R-pentomino and Achim's p144 are examples. A particular reaction with a B-heptomino is commonly used in the construction of Herschel tracks.

Blockic constellation

A blockic constellation is a constellation consisting entirely of blocks. It's possible to arrange blocks in a way that can be triggered by a single glider to produce any glider constructible pattern.[citation needed]

Block arrays

Pseudo still lifes exist consisting of an arbitrary array of blocks placed next to each other, which may be referred to as block agars. On December 3, 2015, Martin Grant found a method of constructing a 3×n array via glider synthesis,[4] and on May 6, 2020, Goldtiger997 found a method of constructing a 4×n array.[5]

See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  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 June 24, 2016.
  4. ↑ Martin Grant (December 3, 2015). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. ↑ Goldtiger997 (May 6, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums

External links


Retrieved from "https://conwaylife.com/w/index.php?title=Block&oldid=75627"