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, 6, 7, or 8 neighbours, and are born if they have 3, 4, 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 = 191, y = 16, rule = B3678/S34678 2o5bo28b2o9b2o56b2o83bo$2o5b2o5b4o7bo8b4o9b2o10bobo20b2o5b2o14b2o17bo 2bo9bobo7b2o9b3o28b2o$8bo6b2o7b3o7b6o6b5o7b6o6b5o6b3o5b3o13b2o17b3obo 9bo8b2o10b2o28b2o$15b2o8bo10b4o7b4o7b6o7b3o7b2o7b2o12bo2bo16b5o8bo11bo 9bo3bo8bob2o4b2o$15b2o18bob2o9bo9bo2b2o23bo36b5o8b2ob2o9b2o11b2o5b5o3b 4o$14b4o19b2o22b3o21b3o34b5o12bo10b2o11b2o5b13o$60b3o9bo11b5o12bo2b4o 2bo10b5o12bo32b4o3b5o$70b2o13b3o10b3o3b4o3b3o7bob3o11bobo31b2o4b2obo$ 72bo13bo11b3o3b4o3b3o8bo2bo$70bo10b2o7b2o9bo2b4o2bo$71b2o8b3o5b3o$70bo 11b2o5b2o$104bo2bo$105b2o$105b2o$105b2o! #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 276P5H2V0 276
c/3 orthogonal 41P3H1V0 41
2c/7 orthogonal 290P7H2V0 290
c/4 orthogonal 32P4H1V0 32
c/5 orthogonal 40P5H1V0 40
c/6 orthogonal 122P6H1V0 122
c/7 orthogonal 104P7H1V0 104
c/8 orthogonal 190P8H1V0 190
c/9 orthogonal 212P9H1V0 212
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 = 342, y = 81, rule = B3678/S34678 b4ob2o12bo8bo17b2o2b2o2b2o16bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo12bo 11bo5bo14b2o14b3o2b3o13b3o15b2o30b2o27b3o2b2o21bo$obo3b3o10b3o6b3o14b 2obob4obob2o11b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o11bo2bo8bob o3bobo13b2o12bob2o4b2obo10b3obo12b3obo27bob3o24bo3b5o21b3o$5ob4o8b4o6b 4o12bobo2b2o2b2o2bobo10b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o2b2o8b2o4bobo4b 2o9b2o2b2o7b3o3b3o26b14o12b2o12b5o28b4o24b3o2b3o22b4o$4b5o12b2o4b2o16b o2b2ob2ob2o2bo11bob2o5b2obo9b10o12b2o3b2o10b3o2b5o2b3o12b2o27b2ob2ob2o 9bo4b2o4bo13b2o12b5o28b2o26b5ob2o25b2o$b2o2bo3bo7bo6b2o6bo14bo8bo14b2o 7b2o11b8o14b2ob2o12bobob5obobo12bobo8b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o 13bo11b5o27b3o2bo25bob2obob2o21bob4o$18b4o6b4o13b2obo6bob2o11bobo7bobo 11bob2obo15b5o35bo11b2o7b2o9b8o11bobo2bobo28bob3o25bob2o27bob5o2bo20bo 3bob2o$20b2ob4ob2o12b2obob2o6b2obob2o7b2o11b2o11bo2bo34bo9bo10b2o11bob 2o3b2obo10b6o13b2o2b2o27b2obo27bobobo28b2ob4obo16b2obo6b2o$20b10o11b2o bob2ob6ob2obob2o31b2o2b2o17bo34b2o15bobobobo10bob6obo10b8o24bob2o28bob obo27b6ob2o18bobob2o2bob3o$21b8o11bo3bo2bob2o2b2obo2bo3bo28b3o4b3o51bo 15b2o3b2o12b6o13bob2obo26bobo27bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b 2o9b3ob3ob6ob3ob3o28b3obo2bob3o51b2o15bobo15b4o15bo2bo26bobo27bobobo 27bo2b3obo22bobo2bo$17b3o2b6o2b3o8bo3b2ob8ob2o3bo27b5o4b5o50bobo32b4o 74bobobo24b3ob3o2bo25bo2bo$17bo2bob6obo2bo9b3obob8obob3o28b5o4b5o50b2o 13b2obob2o13b4o14bo4bo52b2obobo26b4obo29b2obo$17b4obob2obob4o11bo2b10o 2bo30bob10obo51bo13b7o11b2ob2ob2o12b2o2b2o52bobobo24b10o29b3o$15b3ob 12ob3o10bob10obo33b10o53b2o13b5o13bob2obo12bobo2bobo52bobo23bob8o$17b 4o3b2o3b4o10b2o2b10o2b2o31b10o54b4o8b3o3b3o10bo6bo9b5o2b5o48b2ob2o23b 11o$17b16o10bo5b6o5bo34bo2bo57b2obo6b3o7b3o11b2o14b3o2b3o51bo25bob10o$ 20bo3b2o3bo14b2o2b8o2b2o36b2o60bo8b5ob5o11b4o13b8o49bo26bob9obo$23b4o 17bob2ob6ob2obo35b4o56b2obo10b7o14b2o11b3o3b2o3b3o45b2o26b11o$21b8o13b obo5b4o5bobo29b2o3b2o3b2o53b2o9b11o11bo2bo11bo2bo4bo2bo42bo3bo25bo2b 10o$21b8o14bob3o3b2o3b3obo30b3ob4ob3o51bobo14b3o15b4o11b2obob2obob2o 41b4o28b2o2b6o$19bob8obo11bobobobo2b2o2bobobobo29b4ob2ob4o50b3obo12b5o 15b2o12b3ob4ob3o38b7o27bo2bo2b3ob2o$19bob8obo10b2ob3obo6bob3ob2o27bo3b 6o3bo49b2ob3o12b3o14b6o12bob4obo40b3o4bo26b5ob2obo$18b14o9bob3obo8bob 3obo30b3o2b3o52bo2bo31bob2obo12b8o39bob4o31b2obob2o$17b16o12b3o8b3o34b obo2bobo55b2o27b2o2b4o2b2o8b10o39b5o30bobobo$19b12o17b3o2b3o37bo6bo52b obo28bo2b8o2bo8b8o41b2o34b2obo$20b10o18b2ob2ob2o38bo4bo54bo29b14o6b12o 39b2o$20b10o19b6o35bo3bo4bo3bo49bo31b12o7b2ob6ob2o40bo$19bob8obo16b2o 2b2o2b2o33b3obo4bob3o51bo28bob10obo$22b6o22bo2bo36b3o8b3o50bobo28b12o$ 20bob6obo62bo8bo52bob2o27bo3bo2bo3bo11b4o$21b8o60bo3bo6bo3bo47b3ob3o 48b6o$19bo2b6o2bo59b2obo6bob2o49b2o33b6o14b4o$22b6o62b3obob2obob3o51bo bo29b8o11b2o4b2o$20bob6obo66b2o57b3o29bo2b2o2bo11bobo2bobo$22b2o2b2o 63bobobo2bobobo53b2o29bo2b2o2bo11b2ob2ob2o$21bo6bo62b2o2bo2bo2b2o53b2o 31bo2bo$21b3o2b3o62b5o2b5o53bob2o48bo2bo$19bo2bob2obo2bo62b3o2b3o54b2o bo49bo2bo$20bobo4bobo61bob8obo51bob3o50b2o$17bob5o2b5obo57bo4b4o4bo48b 2ob5o$17b5obo2bob5o57bobo2b4o2bobo49bob5o$16bob3o8b3obo56b5ob2ob5o49bo 2b3o$17b2ob2o6b2ob2o60b2o4b2o56b3o$16bo3bo8bo3bo57bo2bo4bo2bo54bo$16bo bo12bobo57b3o6b3o55b2o$157b2o$16b2ob2o8b2ob2o120b2ob2o$17bo2b2o6b2o2bo 121b2o$16bo2b3o6b3o2bo$18b5o4b5o$16b6o6b6o$16b5o8b5o$16bob4o6b4obo$18b 2obo6bob2o$17b2o12b2o$17bo14bo$16b3obo8bob3o$16b3o12b3o$15b6o8b6o$15b 3obobo6bobob3o$16b3ob2o6b2ob3o$15b3o5bo2bo5b3o$15b3obo2b6o2bob3o$17bo 2b10o2bo$19b12o$20b10o$20bob6obo$20b10o$23bo2bo$21b8o$21b2ob2ob2o$21bo bo2bobo$23bo2bo$21b3o2b3o$20b2obo2bob2o$19b2obo4bob2o$19bob3o2b3obo$ 19b2obo4bob2o$21b2o4b2o$18bo12bo$19b2o8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
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External links