OCA:Day & Night

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Day & Night
Day & Night rule
Rulestring 34678/3678
B3678/S34678
Rule integer 242120
Character Stable
Black/white reversal B3678/S34678
Strobing equivalent 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:

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
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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:

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
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External links