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 9bo3bo7b2ob2o4b2o$15b2o18bob2o9bo9bo2b2o23bo36b5o8b2ob2o9b2o11b2o6b4o 3b4o$14b4o19b2o22b3o21b3o34b5o12bo10b2o11b2o7b9o$60b3o9bo11b5o12bo2b4o 2bo10b5o12bo32b4o3b4o$70b2o13b3o10b3o3b4o3b3o7bob3o11bobo31b2o4b2ob2o$ 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 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
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 = 352, y = 81, rule = B3678/S34678 b4ob2o12bo8bo15b3o10b3o14bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo16bo 5bo14b2o14b3o2b3o13b3o15b2o30b2o27b3o2b2o21bo$obo3b3o10b3o6b3o12b3ob3o 6b3ob3o9b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo14bobo3bobo 13b2o12bob2o4b2obo10b3obo12b3obo27bob3o24bo3b5o21b3o$5ob4o8b4o6b4o10b 3o2b4ob2ob4o2b3o8b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o2b2o8b2o4bobo4b2o13b3o 14b3o3b3o26b14o12b2o12b5o28b4o24b3o2b3o22b4o$4b5o12b2o4b2o14b2o2b3ob4o b3o2b2o9bob2o5b2obo9b10o12b2o3b2o10b3o2b5o2b3o13bobo33b2ob2ob2o9bo4b2o 4bo13b2o12b5o28b2o26b5ob2o25b2o$b2o2bo3bo7bo6b2o6bo9bob3o2bob4obo2b3ob o9b2o7b2o11b8o14b2ob2o12bobob5obobo31b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o 13bo11b5o27b3o2bo25bob2obob2o21bob4o$18b4o6b4o10b3o5b6o5b3o8bobo7bobo 11bob2obo15b5o55b2o7b2o9b8o11bobo2bobo28bob3o25bob2o27bob5o2bo20bo3bob 2o$20b2ob4ob2o12bo7bo4bo7bo7b2o11b2o11bo2bo34bo9bo31bob2o3b2obo10b6o 13b2o2b2o27b2obo27bobobo28b2ob4obo16b2obo6b2o$20b10o10b2o2bo6b4o6bo2b 2o30b2o2b2o17bo41b3o15bobobobo10bob6obo10b8o24bob2o28bobobo27b6ob2o18b obob2o2bob3o$21b8o14bobo5bo2bo5bobo31b3o4b3o57b3o15b2o3b2o12b6o13bob2o bo26bobo27bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b2o11b2o16b2o30b3obo2b ob3o54bo2bo2bo15bobo15b4o15bo2bo26bobo27bobobo27bo2b3obo22bobo2bo$17b 3o2b6o2b3o9bo2b3o10b3o2bo28b5o4b5o52bob5obo32b4o74bobobo24b3ob3o2bo25b o2bo$17bo2bob6obo2bo12b2obo8bob2o31b5o4b5o52b9o12b2obob2o13b4o14bo4bo 52b2obobo26b4obo29b2obo$17b4obob2obob4o8b8o8b8o27bob10obo49b4ob5ob4o9b 7o11b2ob2ob2o12b2o2b2o52bobobo24b10o29b3o$15b3ob12ob3o7bob4o10b4obo30b 10o51b2obob5obob2o10b5o13bob2obo12bobo2bobo52bobo23bob8o$17b4o3b2o3b4o 9b2ob4o8b4ob2o30b10o52b2o4bo4b2o9b3o3b3o10bo6bo9b5o2b5o48b2ob2o23b11o$ 17b16o11bo2bo10bo2bo35bo2bo61bo13b3o7b3o11b2o14b3o2b3o51bo25bob10o$20b o3b2o3bo16bo12bo38b2o77b5ob5o11b4o13b8o49bo26bob9obo$23b4o21bo8bo39b4o 78b7o14b2o11b3o3b2o3b3o45b2o26b11o$21b8o18b2o8b2o34b2o3b2o3b2o72b11o 11bo2bo11bo2bo4bo2bo42bo3bo25bo2b10o$21b8o19bo8bo35b3ob4ob3o76b3o15b4o 11b2obob2obob2o41b4o28b2o2b6o$19bob8obo62b4ob2ob4o75b5o15b2o12b3ob4ob 3o38b7o27bo2bo2b3ob2o$19bob8obo61bo3b6o3bo75b3o14b6o12bob4obo40b3o4bo 26b5ob2obo$18b14o63b3o2b3o95bob2obo12b8o39bob4o31b2obob2o$17b16o62bobo 2bobo92b2o2b4o2b2o8b10o39b5o30bobobo$19b12o64bo6bo91bo2b8o2bo8b8o41b2o 34b2obo$20b10o66bo4bo92b14o6b12o39b2o$20b10o62bo3bo4bo3bo89b12o7b2ob6o b2o40bo$19bob8obo61b3obo4bob3o88bob10obo$22b6o64b3o8b3o89b12o$20bob6ob o64bo8bo91bo3bo2bo3bo11b4o$21b8o62bo3bo6bo3bo110b6o$19bo2b6o2bo61b2obo 6bob2o92b6o14b4o$22b6o64b3obob2obob3o91b8o11b2o4b2o$20bob6obo68b2o97bo 2b2o2bo11bobo2bobo$22b2o2b2o65bobobo2bobobo92bo2b2o2bo11b2ob2ob2o$21bo 6bo64b2o2bo2bo2b2o94bo2bo$21b3o2b3o64b5o2b5o113bo2bo$19bo2bob2obo2bo 64b3o2b3o115bo2bo$20bobo4bobo63bob8obo114b2o$17bob5o2b5obo59bo4b4o4bo$ 17b5obo2bob5o59bobo2b4o2bobo$16bob3o8b3obo58b5ob2ob5o$17b2ob2o6b2ob2o 62b2o4b2o$16bo3bo8bo3bo59bo2bo4bo2bo$16bobo12bobo59b3o6b3o2$16b2ob2o8b 2ob2o$17bo2b2o6b2o2bo$16bo2b3o6b3o2bo$18b5o4b5o$16b6o6b6o$16b5o8b5o$ 16bob4o6b4obo$18b2obo6bob2o$17b2o12b2o$17bo14bo$16b3obo8bob3o$16b3o12b 3o$15b6o8b6o$15b3obobo6bobob3o$16b3ob2o6b2ob3o$15b3o5bo2bo5b3o$15b3obo 2b6o2bob3o$17bo2b10o2bo$19b12o$20b10o$20bob6obo$20b10o$23bo2bo$21b8o$ 21b2ob2ob2o$21bobo2bobo$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