Difference between revisions of "OCA:Day & Night"
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! [[c/4 diagonal|c/4]] | ! [[c/4 diagonal|c/4]] | ||
| diagonal | | diagonal | ||
| [ | | [https://www.conwaylife.com/forums/viewtopic.php?f=11&t=702&p=90512#p90512 29P4H1V1] | ||
| {{cells| | | {{cells|29}} | ||
|- | |- | ||
! [[c/5 diagonal|c/5]] | ! [[c/5 diagonal|c/5]] | ||
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A collection of these ships: | A collection of these ships: | ||
{{EmbedViewer | {{EmbedViewer | ||
|rle = x = | |rle = x = 385, y = 138, rule = B3678/S34678 | ||
b4ob2o12bo8bo15b3o10b3o14bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo16bo | 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}} | |position = center}} | ||
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