OCA:Seeds
- This article is about the rule B2/S. For a constellation that can be triggered to form a target object, see Seed.
| Seeds | |
| View static image | |
| View animated image | |
| 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).
| In order: duoplet, shiplet, radar, lever, and anchor (click above to open LifeViewer) |
| Period-5 oscillator (Keith Amling, August 2023)[2] (click above to open LifeViewer) 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 c/2 and c/5 orthogonal spaceships and c/3 and c/4 diagonal spaceships.
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
- ↑ Peter Naszvadi (October 30, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
- ↑ 2.0 2.1 Keith Amling (August 12, 2023). Re: Seeds (discussion thread) at the ConwayLife.com forums
External links
- A collection of patterns for the Seeds rule (archived from the original); collected by Jason Summers, includes patterns found by Stephen Wright, Mirek Wójtowicz, Noam Elkies, Mark Niemiec, Peter Naszvadi, and David Eppstein.
- Seeds (discussion thread) at the ConwayLife.com forums
- Seeds at David Eppstein's Glider Database
- Seeds at Adam P. Goucher's Catagolue
- MCell built-in Life rules: Seeds (2) at Mirek Wójtowicz's Cellebration page
- Seeds at Wikipedia