Difference between revisions of "OCA:Day & Night"
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{{Rule|name=Day & Night|imgname=Day&night|s=34678| | {{Rule | ||
'''Day & Night''' is a [[Life-like cellular automaton]] in which cells survive from one generation to the next if they have 3, 6, 7, or 8 neighbours, and are born if they have 3 | |name = Day & Night | ||
|imgname = Day&night | |||
|char = Stable | |||
|b = 3678 | |||
|s = 34678 | |||
|reversal = [[Day & Night|B3678/S34678]] | |||
|ruleinteger = 242120 | |||
|strobing = B01245/S0125 | |||
}} | |||
'''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 inverse of 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. | |||
===Oscillators=== | |||
Day & Night is home to many different periods of oscillators. Here are the smallest known examples of each period up to 16: | |||
{{EmbedViewer | |||
|rle = x = 183, y = 12, rule = B3678/S34678 | |||
2o5bo28b2o9b2o55bo77bo$2o5b2o5b4o7bo8b4o9b2o10bobo20b2o5b2o11bob3o9bo | |||
2bo9bobo7b2o9b3o28b2o$8bo6b2o7b3o7b6o6b5o7b6o6b5o6b3o5b3o10b5o9b3obo9b | |||
o8b2o10b2o28b2o$15b2o8bo10b4o7b4o7b6o7b3o7b2o7b2o6b2o2b4o10b5o8bo11bo | |||
9bo3bo7b2ob2o4b2o$15b2o18bob2o9bo9bo2b2o23bo11b9o8b5o8b2ob2o9b2o11b2o | |||
6b4o3b4o$14b4o19b2o22b3o21b3o11b4o2b2o7b5o12bo10b2o11b2o7b9o$60b3o9bo | |||
11b5o10b2o12b5o12bo32b4o3b4o$70b2o13b3o25bob3o11bobo31b2o4b2ob2o$72bo | |||
13bo27bo2bo$70bo10b2o7b2o$71b2o8b3o5b3o$70bo11b2o5b2o! | |||
|position = center}} | |||
===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. | |||
====Elementary==== | |||
{| class="wikitable" | |||
|- | |||
! Speed | |||
! Direction | |||
! Smallest known | |||
! Minimum # of [[cell]]s | |||
|- | |||
! [[c/2 orthogonal|c/2]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 29P2H1V0] | |||
| {{cells|29}} | |||
|- | |||
! [[3c/7 orthogonal|3c/7]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 584P7H3V0] | |||
| {{cells|584}} | |||
|- | |||
! [[2c/5 orthogonal|2c/5]] | |||
| orthogonal | |||
| [http://conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73994#p73994 164P5H2V0] | |||
| {{cells|164}} | |||
|- | |||
! [[c/3 orthogonal|c/3]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 41P3H1V0] | |||
| {{cells|41}} | |||
|- | |||
! [[2c/7 orthogonal|2c/7]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 290P7H2V0] | |||
| {{cells|290}} | |||
|- | |||
! [[c/4 orthogonal|c/4]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 32P4H1V0] | |||
| {{cells|32}} | |||
|- | |||
! [[c/5 orthogonal|c/5]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 40P5H1V0] | |||
| {{cells|40}} | |||
|- | |||
! [[c/6 orthogonal|c/6]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73901#p73899 63P6H1V0] | |||
| {{cells|63}} | |||
|- | |||
! [[c/7 orthogonal|c/7]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 104P7H1V0] | |||
| {{cells|104}} | |||
|- | |||
! [[c/8 orthogonal|c/8]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 190P8H1V0] | |||
| {{cells|190}} | |||
|- | |||
! [[c/9 orthogonal|c/9]] | |||
| orthogonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 212P9H1V0] | |||
| {{cells|212}} | |||
|- | |||
! colspan="5" | | |||
|- | |||
! [[(2,1)c/5|(2,1)c/5]] | |||
| oblique | |||
| [https://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=89850#p89850 343P5H2V1] | |||
| {{cells|343}} | |||
|- | |||
! [[(2,1)c/6|(2,1)c/6]] | |||
| oblique | |||
| [https://www.conwaylife.com/forums/viewtopic.php?p=90043#p90043 532P6H2V1] | |||
| {{cells|532}} | |||
|- | |||
! colspan="5" | | |||
|- | |||
! [[c/3 diagonal|c/3]] | |||
| diagonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 12P3H1V1(Butterfly)] | |||
| {{cells|12}} | |||
|- | |||
! [[c/4 diagonal|c/4]] | |||
| diagonal | |||
| [https://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=90512#p90512 29P4H1V1] | |||
| {{cells|29}} | |||
|- | |||
! [[c/5 diagonal|c/5]] | |||
| diagonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 83P5H1V1] | |||
| {{cells|83}} | |||
|- | |||
! [[c/6 diagonal|c/6]] | |||
| diagonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 184P6H1V1] | |||
| {{cells|184}} | |||
|- | |||
! [[c/7 diagonal|c/7]] | |||
| diagonal | |||
| [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 48P7H1V1] | |||
| {{cells|48}} | |||
|- | |||
|} | |||
A collection of these ships: | |||
{{EmbedViewer | |||
|rle = x = 385, y = 138, rule = B3678/S34678 | |||
b4ob2o12bo8bo15b3o10b3o14bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo16bo | |||
5bo14b2o14b3o2b3o13bo18b3o11b3o19b2o26b2o27b3o2b2o21bo$obo3b3o10b3o6b | |||
3o12b3ob3o6b3ob3o9b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo | |||
14bobo3bobo13b2o12bob2o4b2obo9b4o17b2obo9b3obo18bobo23bob3o24bo3b5o21b | |||
3o$5ob4o8b4o6b4o10b3o2b4ob2ob4o2b3o8b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o2b | |||
2o8b2o4bobo4b2o13b3o14b3o3b3o26b14o8b5o14b3o2b2o11b2o18b2obo23b4o24b3o | |||
2b3o22b4o$4b5o12b2o4b2o14b2o2b3ob4ob3o2b2o9bob2o5b2obo9b10o12b2o3b2o | |||
10b3o2b5o2b3o13bobo33b2ob2ob2o9bo4b2o4bo9b5o13bobo4b2o10b2o17b3ob2o22b | |||
2o26b5ob2o25b2o$b2o2bo3bo7bo6b2o6bo9bob3o2bob4obo2b3obo9b2o7b2o11b8o | |||
14b2ob2o12bobob5obobo31b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o9b4o13b4o2b4o | |||
10bo17bob2ob2o19b3o2bo25bob2obob2o21bob4o$18b4o6b4o10b3o5b6o5b3o8bobo | |||
7bobo11bob2obo15b5o55b2o7b2o9b8o11bobo2bobo10bobo13bo2bobo4b2o26bo2bo | |||
3bo19bob2o27bob5o2bo20bo3bob2o$20b2ob4ob2o12bo7bo4bo7bo7b2o11b2o11bo2b | |||
o34bo9bo31bob2o3b2obo10b6o13b2o2b2o12b2o2b2o9bo2b6o3bo24bo4bo21bobobo | |||
28b2ob4obo16b2obo6b2o$20b10o10b2o2bo6b4o6bo2b2o30b2o2b2o17bo41b3o15bob | |||
obobo10bob6obo10b8o11bo3b2o9b3o3bobo29bob2o21bobobo27b6ob2o18bobob2o2b | |||
ob3o$21b8o14bobo5bo2bo5bobo31b3o4b3o57b3o15b2o3b2o12b6o13bob2obo10bo2b | |||
2o17bo2b2o28bob2o20bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b2o11b2o16b2o | |||
30b3obo2bob3o54bo2bo2bo15bobo15b4o15bo2bo11bo2bo3b2o16b2o29bo21bobobo | |||
27bo2b3obo22bobo2bo$17b3o2b6o2b3o9bo2b3o10b3o2bo28b5o4b5o52bob5obo32b | |||
4o31bo3b4o8bo6bobo50bobobo24b3ob3o2bo25bo2bo$17bo2bob6obo2bo12b2obo8bo | |||
b2o31b5o4b5o52b9o12b2obob2o13b4o14bo4bo13bobo2bo8b3o4bo2b2o46b2obobo | |||
26b4obo29b2obo$17b4obob2obob4o8b8o8b8o27bob10obo49b4ob5ob4o9b7o11b2ob | |||
2ob2o12b2o2b2o15bob2o9bob2o2bo50bobobo24b10o29b3o$15b3ob12ob3o7bob4o | |||
10b4obo30b10o51b2obob5obob2o10b5o13bob2obo12bobo2bobo10b6obo8b2ob3o3bo | |||
49bobo23bob8o$17b4o3b2o3b4o9b2ob4o8b4ob2o30b10o52b2o4bo4b2o9b3o3b3o10b | |||
o6bo9b5o2b5o10b5obo10bo4b3o46b2ob2o23b11o$17b16o11bo2bo10bo2bo35bo2bo | |||
61bo13b3o7b3o11b2o14b3o2b3o11b9o13bo2bo47bo25bob10o$20bo3b2o3bo16bo12b | |||
o38b2o77b5ob5o11b4o13b8o10bob5o16bobo46bo26bob9obo$23b4o21bo8bo39b4o | |||
78b7o14b2o11b3o3b2o3b3o7b7o15bob2o45b2o26b11o$21b8o18b2o8b2o34b2o3b2o | |||
3b2o72b11o11bo2bo11bo2bo4bo2bo7bob6o15bo2b4o38bo3bo25bo2b10o$21b8o19bo | |||
8bo35b3ob4ob3o76b3o15b4o11b2obob2obob2o8b4o18bo5b2o36b4o28b2o2b6o$19bo | |||
b8obo62b4ob2ob4o75b5o15b2o12b3ob4ob3o6bob4obo18bob4o33b7o27bo2bo2b3ob | |||
2o$19bob8obo61bo3b6o3bo75b3o14b6o12bob4obo10b5ob3o12b3o2bobo34b3o4bo | |||
26b5ob2obo$18b14o63b3o2b3o95bob2obo12b8o11b8o11b4o38bob4o31b2obob2o$ | |||
17b16o62bobo2bobo92b2o2b4o2b2o8b10o9b3obob2obo11b2o2b2o36b5o30bobobo$ | |||
19b12o64bo6bo91bo2b8o2bo8b8o12bo5bo11bo4bo38b2o34b2obo$20b10o66bo4bo | |||
92b14o6b12o11b2o19bo39b2o$20b10o62bo3bo4bo3bo89b12o7b2ob6ob2o12b2obo | |||
15b2obo38bo$19bob8obo61b3obo4bob3o88bob10obo29b3o14b6o$22b6o64b3o8b3o | |||
89b12o30b3o13bo2b4o$20bob6obo64bo8bo91bo3bo2bo3bo11b4o16b3o9b2ob2ob2ob | |||
o$21b8o62bo3bo6bo3bo110b6o14bob3o8bo3bo4b3o$19bo2b6o2bo61b2obo6bob2o | |||
92b6o14b4o30bo6bob2o$22b6o64b3obob2obob3o91b8o11b2o4b2o13bo2bo10b2o3bo | |||
4bo$20bob6obo68b2o97bo2b2o2bo11bobo2bobo14bobo12b2ob4o2bo$22b2o2b2o65b | |||
obobo2bobobo92bo2b2o2bo11b2ob2ob2o14bob2o9bobo2bo2b2o$21bo6bo64b2o2bo | |||
2bo2b2o94bo2bo36bo13b2obo2bobo$21b3o2b3o64b5o2b5o113bo2bo15b2o3bo10bo | |||
2bo4b3o$19bo2bob2obo2bo64b3o2b3o115bo2bo15b2o12bo2bobo4bobo$20bobo4bob | |||
o63bob8obo114b2o15b2o2b2o9b5o3b2o$17bob5o2b5obo59bo4b4o4bo132b2o13b2ob | |||
obobob2o$17b5obo2bob5o59bobo2b4o2bobo134bo13b2o2bobob2o$16bob3o8b3obo | |||
58b5ob2ob5o131bo15b2o6bo$17b2ob2o6b2ob2o62b2o4b2o133b2obob2o10b4o2b5o$ | |||
16bo3bo8bo3bo59bo2bo4bo2bo132bo3b2o12bo3b5o$16bobo12bobo59b3o6b3o136bo | |||
11bob3ob3o$238b2o12bob2o6bo$16b2ob2o8b2ob2o204b2o14b2o$17bo2b2o6b2o2bo | |||
205bo12b2o3bo$16bo2b3o6b3o2bo202b4o12bobo4b3o$18b5o4b5o204b4obo11b4o3b | |||
2o$16b6o6b6o201bob5o10bob2o$16b5o8b5o202b6o12b3o$16bob4o6b4obo200b6o | |||
17b3o$18b2obo6bob2o202b5obo12bob6o$17b2o12b2o200b4o17b2obob2o$17bo14bo | |||
200b7o15bob2o$16b3obo8bob3o199b5o15b2o2b4o$16b3o12b3o199b6o14bo5b2o$ | |||
15b6o8b6o200b7o13b3ob2o$15b3obobo6bobob3o201b6o12bob3o$16b3ob2o6b2ob3o | |||
203b4o15b2ob2o$15b3o5bo2bo5b3o203bobo15bob2o$15b3obo2b6o2bob3o202b3o | |||
20b2o$17bo2b10o2bo202b4o22bo$19b12o204b5o19bob2o$20b10o204b6o21b2o$20b | |||
ob6obo208b2o19b4o$20b10o206bo18b6obo$23bo2bo208b3o14b2ob3ob2obo$21b8o | |||
209b2o12b2ob3obo$21b2ob2ob2o206b3obo13bob3obo$21bobo2bobo206b2ob3o11bo | |||
b4o$23bo2bo207bo2b3o15bo$21b3o2b3o206b4o13b2o2bo$20b2obo2bob2o203bo2b | |||
2o16bo2b2o$19b2obo4bob2o202b5o17b4o$19bob3o2b3obo202b4o17b2ob2o$19b2ob | |||
o4bob2o203bob2o15bo2bo$21b2o4b2o205b3o19bo$18bo12bo223b2o$19b2o8b2o | |||
202bo2b2o$235b2o2$237b2o$234bob3o$237b3o2$233b2ob2obo$233bo4b3o$236bob | |||
3o$233b2o3b2o$233b3ob3o$237bobo$235b4o$233bo3b3o$234bo$232b4o2b2o$234b | |||
obob3o$232bobo5b2o$237bo3bo$233bo2b3ob3o$235bo4bo$234bo3b2obo$237b2o$ | |||
236bob2obo$234b3ob2o$237b2o$234bobobobo$235b2ob4o$237b2obo$235b3obo2$ | |||
234b3o$236b2o$234b2ob3o$234bo4bo$236b3o$238bo$239b2o$237b2obo$237b2obo | |||
$237bo$234b6o$234b6o$233bob3o$234b7o$233bob5obo$233bob6o$233b9o$235b5o | |||
$233b6o$233bo2b4o$233bo2b3obo$234b6o$234b5o$234b5o$232b2o2bo$234b2o! | |||
|position = center}} | |||
==External links== | ==External links== | ||
* {{cite web | * {{cite web | ||
| author = David I. Bell | | author = David I. Bell | ||
Line 10: | Line 219: | ||
| title = Day & Night - An Interesting Variant of Life | | title = Day & Night - An Interesting Variant of Life | ||
| work = See also Bell's [http://www.tip.net.au/~dbell/archive/b3678s34678.tar.gz Day & Night pattern archive]}} | | work = See also Bell's [http://www.tip.net.au/~dbell/archive/b3678s34678.tar.gz Day & Night pattern archive]}} | ||
* {{cite web | * {{cite web | ||
| author = Pete Carlton | | author = Pete Carlton | ||
| url = http://www.ocf.berkeley.edu/~pcarlton/CA.html | | url = https://web.archive.org/web/20080617233100/http://www.ocf.berkeley.edu/~pcarlton/CA.html | ||
| title = Pete's Game of Life Page: B3678 S34678}} | | title = Pete's Game of Life Page: B3678 S34678}} | ||
{{LinkForumThread|f=11|t=702|title=Day & Night (B3678/S34678)}} | |||
{{LinkWikipedia|Day_and_Night_(cellular_automaton)}} | |||
{{LinkCatagolueRule|b3678s34678}} | |||
{{LinkEppsteinRule|b3678s34678}} |
Revision as of 21:07, 1 March 2020
Day & Night | |
View static image | |
Rulestring | 34678/3678 B3678/S34678 |
---|---|
Rule integer | 242120 |
Character | Stable |
Black/white reversal | B3678/S34678 |
Strobing dual | B01245/S0125 |
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 inverse of 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.
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.
Elementary
Speed | Direction | Smallest known | Minimum # of cells | |
---|---|---|---|---|
c/2 | orthogonal | 29P2H1V0 | 29 | |
3c/7 | orthogonal | 584P7H3V0 | 584 | |
2c/5 | orthogonal | 164P5H2V0 | 164 | |
c/3 | orthogonal | 41P3H1V0 | 41 | |
2c/7 | orthogonal | 290P7H2V0 | 290 | |
c/4 | orthogonal | 32P4H1V0 | 32 | |
c/5 | orthogonal | 40P5H1V0 | 40 | |
c/6 | orthogonal | 63P6H1V0 | 63 | |
c/7 | orthogonal | 104P7H1V0 | 104 | |
c/8 | orthogonal | 190P8H1V0 | 190 | |
c/9 | orthogonal | 212P9H1V0 | 212 | |
(2,1)c/5 | oblique | 343P5H2V1 | 343 | |
(2,1)c/6 | oblique | 532P6H2V1 | 532 | |
c/3 | diagonal | 12P3H1V1(Butterfly) | 12 | |
c/4 | diagonal | 29P4H1V1 | 29 | |
c/5 | diagonal | 83P5H1V1 | 83 | |
c/6 | diagonal | 184P6H1V1 | 184 | |
c/7 | diagonal | 48P7H1V1 | 48 |
A collection of these ships:
(click above to open LifeViewer) |
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