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# | {{Glossary}} | ||
The '''block agar''' is an [[agar]] consisting of blocks arranged periodically in rows and columns, with distance of 1 cell between any two adjacent rows or columns. The average field density of the block agar is 4/9. | |||
Sometimes, more sparse arrangements of blocks are also described as block agars.{{refn|[[Lifeline Volume 3#Page 29]]}} | |||
== Reactions in the block agar == | |||
If an alive cell ("virus") is added to the block agar so that it touches the corners of four blocks, the agar self-repairs in two ticks. However, when a single cell is added so that it touches cells of two different blocks, it initiates an expanding disintegration of the agar.{{refn|Martin Gardner, ''[[Wheels, Life, and Other Mathematical Amusements]]'', The Game of Life, Part II}} | |||
[[Space clearer]]s for the block agar and for one quarter of the block agar were found by [[Hartmut Holzwart]];<ref name="post99952" /> these space clearers are reactions that expand through the infinite agar and leave empty space behind.<ref name="post160515" /> | |||
There are known p3 lightspeed "trimmers" on an array of blocks with zebra stripes boundary.<ref name="post104616" /> | |||
== Finite patches == | |||
Finite rectangular patches of the block agar (''n''-by-''m'' '''block arrays''') are [[pseudo still life]]s; the simplest example is the [[bi-block]], which is the {{times|1|2}} block array. | |||
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center" | |||
! x\y | |||
! 1 | |||
! 2 | |||
! 3 | |||
! ... | |||
|- | |||
! 1 | |||
! [[File:1×1 blocks.png]] | |||
! [[File:2×1 blocks.png]] | |||
! [[File:3×1 blocks.png]] | |||
! rowspan="3" | → | |||
|- | |||
! 2 | |||
! [[File:1×2 blocks.png]] | |||
! [[File:2×2 blocks.png]] | |||
! [[File:3×2 blocks.png]] | |||
|- | |||
! 3 | |||
! [[File:1×3 blocks.png]] | |||
! [[File:2×3 blocks.png]] | |||
! [[File:3×3 blocks.png]] | |||
|- | |||
! ... | |||
! colspan="3" | ↓ | |||
! ↘ | |||
|} | |||
=== Glider synthesis === | |||
In {{year|2005}}, Jason Summers found a way to extend any {{times|2|''n''}} block array.<ref name="lifenews_2005_04" /> | |||
On December 3, {{year|2015}}, [[Martin Grant]] found a method of constructing a {{times|3|''n''}} block array via [[glider synthesis]].<ref name="post25637" /> | |||
On May 6, {{year|2020}}, [[Goldtiger997]] found a method of constructing a {{times|4|''n''}} block array.<ref name="post96210" /> | |||
The [[problem]] of constructing an arbitrary ''m''-by-''n'' block array is still unsolved.<ref>https://conwaylife.com/forums/viewtopic.php?p=140125#p140125</ref><ref>https://conwaylife.com/forums/viewtopic.php?p=146722#p146722</ref> | |||
== References == | |||
<references> | |||
<ref name="lifenews_2005_04">{{cite web | |||
|url = https://web.archive.org/web/20160409092832/http://pentadecathlon.com/lifeNews/2005/04/block_array_constructions.html | |||
|title = Block Array Constructions | |||
|author = Heinrich Koenig | |||
|date = April 20, 2005 | |||
|work = Game of Life News | |||
}}</ref> | |||
<ref name="post25637">{{LinkForumThread | |||
|format = ref | |||
|p = 25637 | |||
|title = Re: Synthesising Oscillators | |||
|author = Martin Grant | |||
|date = December 3, 2015 | |||
}}</ref> | |||
<ref name="post96210">{{LinkForumThread | |||
|format = ref | |||
|p = 96210 | |||
|title = Re: Synthesising Oscillators | |||
|author = Goldtiger997 | |||
|date = May 6, 2020 | |||
}}</ref> | |||
<ref name="post99952">{{LinkForumThread | |||
|format = ref | |||
|p = 99952 | |||
|title = Re: Agar crawlers | |||
|author = Hartmut Holzwart | |||
|date = July 2, 2020 | |||
}}</ref> | |||
<ref name="post104616">{{LinkForumThread | |||
|format = ref | |||
|p = 104616 | |||
|title = Re: 'Skimmers' | |||
|author = wildmyron | |||
|date = September 21, 2020 | |||
}}</ref> | |||
<ref name="post160515">{{LinkForumThread | |||
|format = ref | |||
|p = 160515 | |||
|title = Re: Thread for basic questions | |||
|author = Dave Greene | |||
|date = April 15, 2023 | |||
}}</ref> | |||
</references> | |||
[[Category:Stable agars]] | |||
[[Category:Agars]] | |||
[[Category:Pseudo still lifes]] | |||
[[Category:Problems]] | |||
__NOTOC__ | |||
Revision as of 20:06, 18 April 2023
The block agar is an agar consisting of blocks arranged periodically in rows and columns, with distance of 1 cell between any two adjacent rows or columns. The average field density of the block agar is 4/9.
Sometimes, more sparse arrangements of blocks are also described as block agars.[1]
Reactions in the block agar
If an alive cell ("virus") is added to the block agar so that it touches the corners of four blocks, the agar self-repairs in two ticks. However, when a single cell is added so that it touches cells of two different blocks, it initiates an expanding disintegration of the agar.[2]
Space clearers for the block agar and for one quarter of the block agar were found by Hartmut Holzwart;[3] these space clearers are reactions that expand through the infinite agar and leave empty space behind.[4]
There are known p3 lightspeed "trimmers" on an array of blocks with zebra stripes boundary.[5]
Finite patches
Finite rectangular patches of the block agar (n-by-m block arrays) are pseudo still lifes; the simplest example is the bi-block, which is the 1 × 2 block array.
| x\y | 1 | 2 | 3 | ... |
|---|---|---|---|---|
| 1 | 
|
|
|
→ |
| 2 | 
|
|
| |
| 3 | 
|
|
| |
| ... | ↓ | ↘ | ||
Glider synthesis
In 2005, Jason Summers found a way to extend any 2 × n block array.[6]
On December 3, 2015, Martin Grant found a method of constructing a 3 × n block array via glider synthesis.[7]
On May 6, 2020, Goldtiger997 found a method of constructing a 4 × n block array.[8]
The problem of constructing an arbitrary m-by-n block array is still unsolved.[9][10]
References
- ↑ Lifeline Volume 3#Page 29
- ↑ Martin Gardner, Wheels, Life, and Other Mathematical Amusements, The Game of Life, Part II
- ↑ Hartmut Holzwart (July 2, 2020). Re: Agar crawlers (discussion thread) at the ConwayLife.com forums
- ↑ Dave Greene (April 15, 2023). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ wildmyron (September 21, 2020). Re: 'Skimmers' (discussion thread) at the ConwayLife.com forums
- ↑ Heinrich Koenig (April 20, 2005). "Block Array Constructions". Game of Life News.
- ↑ 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
- ↑ https://conwaylife.com/forums/viewtopic.php?p=140125#p140125
- ↑ https://conwaylife.com/forums/viewtopic.php?p=146722#p146722