Block agar: Difference between revisions
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== Reactions in the block agar == | == 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}} | 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}}{{refn|[[Lifeline Volume 9#Page 6]]}} | ||
[[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" /> | [[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" /> | ||
Revision as of 20:24, 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][3]
Space clearers for the block agar and for one quarter of the block agar were found by Hartmut Holzwart;[4] these space clearers are reactions that expand through the infinite agar and leave empty space behind.[5]
There are known p3 lightspeed "trimmers" on an array of blocks with zebra stripes boundary.[6]
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.[7]
On December 3, 2015, Martin Grant found a method of constructing a 3 × n block array via glider synthesis.[8]
On May 6, 2020, Goldtiger997 found a method of constructing a 4 × n block array.[9]
The problem of constructing an arbitrary m-by-n block array is still unsolved.[10][11]
References
- ↑ Lifeline Volume 3#Page 29
- ↑ Martin Gardner, Wheels, Life, and Other Mathematical Amusements, The Game of Life, Part II
- ↑ Lifeline Volume 9#Page 6
- ↑ 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