OCA:Day & Night
| Day & Night | |
| View static image | |
| Rulestring | 34678/3678 B3678/S34678 |
|---|---|
| Rule integer | 242120 |
| Character | Chaotic |
| Black/white reversal | B3678/S34678 |
| Strobing dual | B01245/S0125 |
| Checkerboard dual | B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8 |
Day & Night is a Life-like cellular automaton in which cells survive from one generation to the next if they have 3, 4, 6, 7, or 8 neighbours, and are born if they have 3, 6, 7, or 8 neighbours.
Day & Night is the most well-known self-complementary rule; that is, if all grid cells have their on/off state exchanged, the history of the pattern is the same as the history of the original.
Nathan Thompson explored the rule starting in April 1997, and David Bell discussed the rule in detail the following November.
The rule is rich in spaceships, puffers, and oscillators.
On August 14, 2020, Peter Naszvadi constructed a Rule 110 unit cell in Day & Night, proving the rule Turing-complete.[1]
Oscillators
Day & Night is home to many different periods of oscillators. Here are the smallest known examples of each period up to 16:
| (click above to open LifeViewer) |
Spaceships
Many periods of c/2 spaceships are known, but different reduced speeds are common as well. The S8 transition allows many of the spaceships in Day & Night to be stable.
Rocket
The rocket was the first spaceship found in Day & Night, and it appears spontaneously from many reactions which have symmetry around a line. This spaceship is probably the reason that this particular Life rule was chosen for Day & Night. It is unexpectedly large and has the amazingly large period of 40.
| Rocket (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
The rocket is easily generated from tiny predecessors.
| Rocket predecessor (click above to open LifeViewer) |
Elementary
Unsimplified speeds are yet to be tabulated here.
Green means a spaceship has been proven to have minimal population via LLSSS.
| Speed | Period | Direction | Smallest known | Minimum # of cells |
|---|---|---|---|---|
| c/2 | 2 | orthogonal | 29P2H1V0 | 29 |
| 4 | orthogonal | 18P4H2V0 | 18 | |
| 3c/7 | 7 | orthogonal | 316P7H3V0 | 316 |
| 2c/5 | 5 | orthogonal | 164P5H2V0 | 164 |
| c/3 | 3 | orthogonal | 35P3H1V0 | 35 |
| 2c/7 | 7 | orthogonal | 160P7H2V0 | 160 |
| c/4 | 4 | orthogonal | 32P4H1V0 | 32 |
| c/5 | 5 | orthogonal | 40P5H1V0 | 40 |
| c/6 | 6 | orthogonal | 63P6H1V0 | 63 |
| c/7 | 7 | orthogonal | 104P7H1V0 | 104 |
| c/8 | 8 | orthogonal | 190P8H1V0 | 190 |
| c/9 | 9 | orthogonal | 212P9H1V0 | 212 |
| (2,1)c/5 | 5 | oblique | 343P5H2V1 | 343 |
| (2,1)c/6 | 6 | oblique | 288P6H2V1 | 288 |
| c/3 | 3 | diagonal | 12P3H1V1(Butterfly) | 12 |
| c/4 | 4 | diagonal | 24P4H1V1 | 24 |
| c/5 | 5 | diagonal | 46P5H1V1 | 46 |
| c/6 | 6 | diagonal | 76P6H1V1 | 76 |
| c/7 | 7 | diagonal | 48P7H1V1 | 48 |
| c/8[2] | 8 | diagonal | 176P8H1V1 | 176 |
| A collection of these ships (click above to open LifeViewer) |
In February 2020, AforAmpere found the first knightships in D&N, of speeds (2,1)c/5[3] and (2,1)c/6[4] respectively. On October 26, 2020, Adam P. Goucher found a second, larger (2,1)c/5 knightship using ikpx2,[5] and quickly found multiple tagalongs[6][7] (including a period-10 tagalong[8]) and a wickstretcher[9] based on it. The same day, Goucher found a smaller and thinner (2,1)c/6 spaceship.[10]
On October 27, Goucher found a "growing knightship" - a pattern in which the front end moves at (2,1)c/5 while the back end moves at (2,1)c/6.[11]
These knightships were collectively voted OCA Discovery of the Year for 2020 on the ConwayLife.com forums.[12]
References
- ↑ Peter Naszvadi (August 14, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
- ↑ LuveelVoom (May 31, 2025). Message in #naturalistic on the Conwaylife Lounge Discord server, which found the first c/8d (but laughably far from the minimal... yes indeed)
- ↑ AforAmpere (February 19, 2020). Re: Day & Night (B3678/S34678) (discussion thread) at the ConwayLife.com forums
- ↑ AforAmpere (February 22, 2020). Re: Day & Night (B3678/S34678) (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ Adam P. Goucher (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ Adam P. Goucher (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ wwei23 (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ Adam P. Goucher (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ Adam P. Goucher (October 26, 2020). Message in #naturalistic on the Conwaylife Lounge Discord server
- ↑ Adam P. Goucher (October 27, 2020). Re: Day & Night (B3678/S34678) (discussion thread) at the ConwayLife.com forums
- ↑ Peter Naszvadi (May 2, 2021). Re: OCA DOTY 2020 Voting (discussion thread) at the ConwayLife.com forums
External links
- David I. Bell (1997). "Day & Night - An Interesting Variant of Life". See also Bell's Day & Night pattern archive.
- Pete Carlton. "Pete's Game of Life Page: B3678 S34678".
- Day & Night (B3678/S34678) (discussion thread) at the ConwayLife.com forums
- Day & Night at Wikipedia
- Day & Night at Adam P. Goucher's Catagolue
- Day & Night at David Eppstein's Glider Database
- MCell built-in Life rules: Day & Night at Mirek Wójtowicz's Cellebration page
- The Rocket (glider 19979)