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 35P4H1V1 35
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 5bo14b2o14b3o2b3o13bo18b3o11b3o15b2o30b2o27b3o2b2o21bo$obo3b3o10b3o6b 3o12b3ob3o6b3ob3o9b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo 14bobo3bobo13b2o12bob2o4b2obo9b4o17b2obo9b3obo12b3obo27bob3o24bo3b5o 21b3o$5ob4o8b4o6b4o10b3o2b4ob2ob4o2b3o8b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o 2b2o8b2o4bobo4b2o13b3o14b3o3b3o26b14o8b5o14b3o2b2o11b2o12b5o28b4o24b3o 2b3o22b4o$4b5o12b2o4b2o14b2o2b3ob4ob3o2b2o9bob2o5b2obo9b10o12b2o3b2o 10b3o2b5o2b3o13bobo33b2ob2ob2o9bo4b2o4bo9b5o13bobo4b2o10b2o12b5o28b2o 26b5ob2o25b2o$b2o2bo3bo7bo6b2o6bo9bob3o2bob4obo2b3obo9b2o7b2o11b8o14b 2ob2o12bobob5obobo31b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o9b4o13b4o2b4o10bo 11b5o27b3o2bo25bob2obob2o21bob4o$18b4o6b4o10b3o5b6o5b3o8bobo7bobo11bob 2obo15b5o55b2o7b2o9b8o11bobo2bobo10bobo13bo2bobo4b2o23bob3o25bob2o27bo b5o2bo20bo3bob2o$20b2ob4ob2o12bo7bo4bo7bo7b2o11b2o11bo2bo34bo9bo31bob 2o3b2obo10b6o13b2o2b2o12b2o2b2o9bo2b6o3bo20b2obo27bobobo28b2ob4obo16b 2obo6b2o$20b10o10b2o2bo6b4o6bo2b2o30b2o2b2o17bo41b3o15bobobobo10bob6ob o10b8o11bo3b2o9b3o3bobo22bob2o28bobobo27b6ob2o18bobob2o2bob3o$21b8o14b obo5bo2bo5bobo31b3o4b3o57b3o15b2o3b2o12b6o13bob2obo10bo2b2o17bo2b2o22b obo27bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b2o11b2o16b2o30b3obo2bob3o 54bo2bo2bo15bobo15b4o15bo2bo11bo2bo3b2o16b2o21bobo27bobobo27bo2b3obo 22bobo2bo$17b3o2b6o2b3o9bo2b3o10b3o2bo28b5o4b5o52bob5obo32b4o31bo3b4o 8bo6bobo50bobobo24b3ob3o2bo25bo2bo$17bo2bob6obo2bo12b2obo8bob2o31b5o4b 5o52b9o12b2obob2o13b4o14bo4bo13bobo2bo8b3o4bo2b2o46b2obobo26b4obo29b2o bo$17b4obob2obob4o8b8o8b8o27bob10obo49b4ob5ob4o9b7o11b2ob2ob2o12b2o2b 2o15bob2o9bob2o2bo50bobobo24b10o29b3o$15b3ob12ob3o7bob4o10b4obo30b10o 51b2obob5obob2o10b5o13bob2obo12bobo2bobo10b6obo8b2ob3o3bo49bobo23bob8o $17b4o3b2o3b4o9b2ob4o8b4ob2o30b10o52b2o4bo4b2o9b3o3b3o10bo6bo9b5o2b5o 10b5obo10bo4b3o46b2ob2o23b11o$17b16o11bo2bo10bo2bo35bo2bo61bo13b3o7b3o 11b2o14b3o2b3o11b9o13bo2bo47bo25bob10o$20bo3b2o3bo16bo12bo38b2o77b5ob 5o11b4o13b8o10bob5o16bobo46bo26bob9obo$23b4o21bo8bo39b4o78b7o14b2o11b 3o3b2o3b3o7b7o15bob2o45b2o26b11o$21b8o18b2o8b2o34b2o3b2o3b2o72b11o11bo 2bo11bo2bo4bo2bo7bob6o15bo2b4o38bo3bo25bo2b10o$21b8o19bo8bo35b3ob4ob3o 76b3o15b4o11b2obob2obob2o8b4o18bo5b2o36b4o28b2o2b6o$19bob8obo62b4ob2ob 4o75b5o15b2o12b3ob4ob3o6bob4obo18bob4o33b7o27bo2bo2b3ob2o$19bob8obo61b o3b6o3bo75b3o14b6o12bob4obo10b5ob3o12b3o2bobo34b3o4bo26b5ob2obo$18b14o 63b3o2b3o95bob2obo12b8o11b8o11b4o38bob4o31b2obob2o$17b16o62bobo2bobo 92b2o2b4o2b2o8b10o9b3obob2obo11b2o2b2o36b5o30bobobo$19b12o64bo6bo91bo 2b8o2bo8b8o12bo5bo11bo4bo38b2o34b2obo$20b10o66bo4bo92b14o6b12o11b2o19b o39b2o$20b10o62bo3bo4bo3bo89b12o7b2ob6ob2o12b2obo15b2obo38bo$19bob8obo 61b3obo4bob3o88bob10obo29b3o14b6o$22b6o64b3o8b3o89b12o30b3o13bo2b4o$ 20bob6obo64bo8bo91bo3bo2bo3bo11b4o16b3o9b2ob2ob2obo$21b8o62bo3bo6bo3bo 110b6o14bob3o8bo3bo4b3o$19bo2b6o2bo61b2obo6bob2o92b6o14b4o30bo6bob2o$ 22b6o64b3obob2obob3o91b8o11b2o4b2o13bo2bo10b2o3bo4bo$20bob6obo68b2o97b o2b2o2bo11bobo2bobo14bobo12b2ob4o2bo$22b2o2b2o65bobobo2bobobo92bo2b2o 2bo11b2ob2ob2o14bob2o9bobo2bo2b2o$21bo6bo64b2o2bo2bo2b2o94bo2bo36bo13b 2obo2bobo$21b3o2b3o64b5o2b5o113bo2bo15b2o3bo10bo2bo4b3o$19bo2bob2obo2b o64b3o2b3o115bo2bo15b2o12bo2bobo4bobo$20bobo4bobo63bob8obo114b2o15b2o 2b2o9b5o3b2o$17bob5o2b5obo59bo4b4o4bo132b2o13b2obobobob2o$17b5obo2bob 5o59bobo2b4o2bobo134bo13b2o2bobob2o$16bob3o8b3obo58b5ob2ob5o131bo15b2o 6bo$17b2ob2o6b2ob2o62b2o4b2o133b2obob2o10b4o2b5o$16bo3bo8bo3bo59bo2bo 4bo2bo132bo3b2o12bo3b5o$16bobo12bobo59b3o6b3o136bo11bob3ob3o$238b2o12b ob2o6bo$16b2ob2o8b2ob2o204b2o14b2o$17bo2b2o6b2o2bo205bo12b2o3bo$16bo2b 3o6b3o2bo202b4o12bobo4b3o$18b5o4b5o204b4obo11b4o3b2o$16b6o6b6o201bob5o 10bob2o$16b5o8b5o202b6o12b3o$16bob4o6b4obo200b6o17b3o$18b2obo6bob2o 202b5obo12bob6o$17b2o12b2o200b4o17b2obob2o$17bo14bo200b7o15bob2o$16b3o bo8bob3o199b5o15b2o2b4o$16b3o12b3o199b6o14bo5b2o$15b6o8b6o200b7o13b3ob 2o$15b3obobo6bobob3o201b6o12bob3o$16b3ob2o6b2ob3o203b4o15b2ob2o$15b3o 5bo2bo5b3o203bobo15bob2o$15b3obo2b6o2bob3o202b3o20b2o$17bo2b10o2bo202b 4o22bo$19b12o204b5o19bob2o$20b10o204b6o21b2o$20bob6obo208b2o19b4o$20b 10o206bo18b6obo$23bo2bo208b3o14b2ob3ob2obo$21b8o209b2o12b2ob3obo$21b2o b2ob2o206b3obo13bob3obo$21bobo2bobo206b2ob3o11bob4o$23bo2bo207bo2b3o 15bo$21b3o2b3o206b4o13b2o2bo$20b2obo2bob2o203bo2b2o16bo2b2o$19b2obo4bo b2o202b5o17b4o$19bob3o2b3obo202b4o17b2ob2o$19b2obo4bob2o203bob2o15bo2b o$21b2o4b2o205b3o19bo$18bo12bo223b2o$19b2o8b2o202bo2b2o$235b2o2$237b2o $234bob3o$237b3o2$233b2ob2obo$233bo4b3o$236bob3o$233b2o3b2o$233b3ob3o$ 237bobo$235b4o$233bo3b3o$234bo$232b4o2b2o$234bobob3o$232bobo5b2o$237bo 3bo$233bo2b3ob3o$235bo4bo$234bo3b2obo$237b2o$236bob2obo$234b3ob2o$237b 2o$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