OCA:Seeds

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This article is about the rule B2/S. For a constellation that can be triggered to form a target object, see Seed.
Seeds
x=64, y = 64, rule = B2/S ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
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Rulestring /2
B2/S
Rule integer 4
Character Explosive
Black/white reversal B012345678/S01234578

Seeds is a Life-like cellular automaton in which a new cell is born when it has exactly two live neighbours, and live cells never survive to the next generation. Even though all the living cells die in every generation (turning every pattern into a phoenix), most patterns are still exploding quadratically. The rule was initially investigated by Brian Silverman and named by Mirek Wójtowicz.

On October 30, 2020, Peter Naszvadi proved that Seeds is Turing-complete on an infinite, periodically-tiled grid by constructing a Rule 110 "unit stripe".[1] Interestingly, no patterns can be endemic to this rule as S8 and S7 cannot appear in periodic patterns (Due to them having 0/1 cell(s) adjacent to the Center cell).

Notable patterns

Oscillators

No still lifes can exist in this rule, due to the absence of survival conditions. Known oscillator periods include 2, 3, 4, 5,[2] 6, 8, 12, 15, 20, 24, and 40. The five smallest oscillators are duoplet (2 cells, p2), shiplet (3 cells, p2), radar (4 cells, p4), lever (4 cells, p4) and anchor (4 cells, p4).

x = 33, y = 5, rule = B2/S 22bo$6bo7bo8bo5bobo$bo6bo4bo14bo3bo$o6bo8bo4bo$15bo6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 300 ZOOM 16 GPS 2 THUMBSIZE 2 AUTOSTART ]]
In order: duoplet, shiplet, radar, lever, and anchor
(click above to open LifeViewer)
x = 34, y = 34, rule = B2/S 10bob2o6b2obo$9bo3bo6bo3bo$8bo6bo2bo6bo$6bob2o14b2obo$7b3o5bo2bo5b3o$ 5bo4bo12bo4bo$3bo5bob2obo4bob2obo5bo$4bo6b3o6b3o6bo$2b3o6bo10bo6b3o$b ob2obo5bo8bo5bob2obo$o4bo4bo12bo4bo4bo$6b3o16b3o$o5b2obo14bob2o5bo$2o 5bo18bo5b2o$6bo20bo$2bobo24bobo3$2bobo24bobo$6bo20bo$2o5bo18bo5b2o$o5b 2obo14bob2o5bo$6b3o16b3o$o4bo4bo12bo4bo4bo$bob2obo5bo8bo5bob2obo$2b3o 6bo10bo6b3o$4bo6b3o6b3o6bo$3bo5bob2obo4bob2obo5bo$5bo4bo12bo4bo$7b3o5b o2bo5b3o$6bob2o14b2obo$8bo6bo2bo6bo$9bo3bo6bo3bo$10bob2o6b2obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 ZOOM 12 GPS 2 THUMBSIZE 2 AUTOSTART ]]
Period-5 oscillator (Keith Amling, August 2023)[2]
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Catagolue: here


Spaceships

With B2, the Seeds rule allows spaceships to travel at the speed of light. The three smallest ones, known as photons, have a period of 1 and consist of only 4 cells each. Larger lightspeed spaceships with higher periods are also known.

There also exist 3c/5, c/2, c/4, and c/5 orthogonal spaceships and c/3 and c/4 diagonal spaceships.

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117bobo7bo$137bobo137bobo$138b2o31b2o71b2o31b2o$143bo2bo23bo75bo23bo2b o$142b2o24bo2bo73bo2bo24b2o$139bo7bob3o18bo75bo18b3obo7bo$138bo3b2o3b 3obo16b2o77b2o16bob3o3b2o3bo$140bo2bo4bo20b2o75b2o20bo4bo2bo$137bobo6b 2obobo19bo73bo19bobob2o6bobo$135b2o11b2o19bo2bo71bo2bo19b2o11b2o$137b o9bobo21bo73bo21bobo9bo$134bobo12bo21bobo69bobo21bo12bobo$150bo18bobo 73bobo18bo$153bo109bo$137bobo11b2o18bo73bo18b2o11bobo$136bo3bo12b3o12b obo75bobo12b3o12bo3bo$136bo3bo12bo15bo77bo15bo12bo3bo$136b2ob2o10b2o5b o8b3o77b3o8bo5b2o10b2ob2o$138bo14bo3bo101bo3bo14bo$138bo14b3o3b2o3bo87b o3b2o3b3o14bo$156bobo99bobo$164bo87bo$156bo6bo89bo6bo2$158bo99bo$158b o5bo87bo5bo$158bobo95bobo2$154b3o103b3o$157bo101bo2$155b2obo99bob2o$154b o107bo2$160bo95bo$151bob2o4bo97bo4b2obo$152b2obo4b2o93b2o4bob2o$150b3o 4bo3bo93bo3bo4b3o$157bo3bo93bo3bo$151b2obobobobo95bobobobob2o$153bo2b o103bo2bo$152bobo107bobo2$154b2o105b2o2$142b5o4bo6bo4b5o81b5o4bo6bo4b 5o$144bo20bo85bo20bo$139bo11bo6bo11bo75bo11bo6bo11bo$140bo3b2o2b2o10b 2o2b2o3bo77bo3b2o2b2o10b2o2b2o3bo$140bo28bo77bo28bo$140bo2b2o5bo8bo5b 2o2bo77bo2b2o5bo8bo5b2o2bo$142bo2bo3b2o8b2o3bo2bo81bo2bo3b2o8b2o3bo2b o$141bobo6b3o4b3o6bobo79bobo6b3o4b3o6bobo$145bo4bo8bo4bo87bo4bo8bo4bo $145bo3bo2bo4bo2bo3bo87bo3bo2bo4bo2bo3bo$143b3o3bo3bo2bo3bo3b3o83b3o3b o3bo2bo3bo3b3o$146b3ob2o2b2o2b2ob3o89b3ob2o2b2o2b2ob3o$144bo2bo2bo3b2o 3bo2bo2bo85bo2bo2bo3b2o3bo2bo2bo$145b3o5bo2bo5b3o87b3o5bo2bo5b3o$148b o12bo93bo12bo2$148bo12bo93bo12bo$149bobo6bobo95bobo6bobo$151bob4obo99b ob4obo4$151bo6bo99bo6bo2$154b2o105b2o2$150bo2bo2bo2bo97bo2bo2bo2bo$149b o10bo95bo10bo$151bo6bo99bo6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 900 WIDTH 1200 ZOOM 1.5 THUMBSIZE 2 ]]
Smallest known spaceships for each speeds.
(click above to open LifeViewer)
RLE: here Plaintext: here

Guns

Two period-4 photon guns (lasers) have been found, yet their photon stream is too dense to implement any signal logic.

Puffers, rakes and breeders

Quite a lot of progress has been made in producing engineered patterns consisting of lightspeed puffers and photon rakes. A rake puffer breeder is known.

References

  1. ↑ Peter Naszvadi (October 30, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
  2. ↑ 2.0 2.1 Keith Amling (August 12, 2023). Re: Seeds (discussion thread) at the ConwayLife.com forums
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