Block: Difference between revisions
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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 [[Game of Life]] to the world. | ||
== 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]], 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. | ||
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Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]], as described above. 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. | Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]], as described above. 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== | == 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}} | 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}} | ||
==Block arrays== | == 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×''n'' array via [[glider synthesis]],<ref name="post25637" /> and on May 6, {{year|2020}}, [[Goldtiger997]] found a method of constructing a 4×''n'' array.<ref name="post96210" /> | [[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×''n'' array via [[glider synthesis]],<ref name="post25637" /> and on May 6, {{year|2020}}, [[Goldtiger997]] found a method of constructing a 4×''n'' array.<ref name="post96210" /> | ||
==See also== | == [[List of common still lifes|Commonness]] == | ||
*[[Bi-block]] | 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). | ||
*[[Blockade]] | |||
*[[Bricklayer]] | The chance of a block in a specific location in an infinite random soup is approximately 1 in 473. This number is the frequency of on cells (0.0287) divided by the average object size (4.388) times the chance that a particular object will be a block (0.323). As blocks have 8-way symmetry, there is no symmetry factor to take into account. This number is helpful in determining how often transparent blocks occur; transparent blocks are twice as common as transparent blinkers, almost four times as common as transparent beehives, and more than twenty times as common as anything else. | ||
*[[Blockstacker]] | |||
== [[Glider synthesis]] == | |||
{{Small constructible periodic object}} | |||
== See also == | |||
* [[Bi-block]] | |||
* [[Blockade]] | |||
* [[Bricklayer]] | |||
* [[Blockstacker]] | |||
==References== | == References == | ||
<references> | <references> | ||
<ref name="post25637">{{LinkForumThread | <ref name="post25637">{{LinkForumThread | ||
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</references> | </references> | ||
==External links== | == External links == | ||
{{LinkLexicon|lex_b.htm#block}} | {{LinkLexicon|lex_b.htm#block}} | ||
{{LinkLexicon|lex_b.htm#blockic|patternname=Blockic}} | {{LinkLexicon|lex_b.htm#blockic|patternname=Blockic}} | ||
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[[Category:Eaters]] | [[Category:Eaters]] | ||
{{Symmetry|full}} | {{Symmetry|full}} | ||
Revision as of 02:34, 24 December 2021
| Block | |||||||||
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| Pattern type | Strict still life | ||||||||
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| Number of cells | 4 | ||||||||
| Bounding box | 2 × 2 | ||||||||
| Frequency class | 0.0 | ||||||||
| Static symmetry | Unspecified | ||||||||
| Discovered by | John Conway | ||||||||
| Year of discovery | 1969 | ||||||||
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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 strict 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.
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, as described above. 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,[2] and on May 6, 2020, Goldtiger997 found a method of constructing a 4×n array.[3]
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.[4]; it is also the most common object on Adam P. Goucher's Catagolue.[5] It is also the most common object produced by 2-glider collisions (six different ways).
The chance of a block in a specific location in an infinite random soup is approximately 1 in 473. This number is the frequency of on cells (0.0287) divided by the average object size (4.388) times the chance that a particular object will be a block (0.323). As blocks have 8-way symmetry, there is no symmetry factor to take into account. This number is helpful in determining how often transparent blocks occur; transparent blocks are twice as common as transparent blinkers, almost four times as common as transparent beehives, and more than twenty times as common as anything else.
All strict still lifes with a population of 23 or fewer cells, all oscillators with 16 or fewer cells, and all spaceships with 35 or fewer cells are known to be glider-constructible. A glider synthesis of this object can be found in the infobox to the right.
See also
References
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ Martin Grant (December 3, 2015). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (May 6, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
External links
- Block at the Life Lexicon
- Blockic at the Life Lexicon
- The 2 four-bit still-lifes at Mark D. Niemiec's Life Page
- The fantastic combinations of John Conway's new solitaire game "life" by Martin Gardner
- Blockic splitters (discussion thread) at the ConwayLife.com forums
- Blockic Seeds (discussion thread) at the ConwayLife.com forums
- Patterns
- Patterns with Catagolue frequency class 0
- Natural periodic objects
- Periodic objects with minimum population 4
- Patterns with 4 cells
- Patterns found by John Conway
- Patterns found in 1969
- Patterns that can be constructed with 2 gliders
- Still lifes
- Strict still lifes
- Strict still lifes with 4 cells
- Eaters
- Patterns with complete square symmetry