OCA:Day & Night

Day & Night
x=0, y = 0, rule = B3678/S34678 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
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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:

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
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 = 376, y = 81, rule = B3678/S34678 b4ob2o12bo8bo15b3o10b3o14bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo16bo 5bo14b2o14b3o2b3o17b3o17b3o15b2o30b2o27b3o2b2o21bo$obo3b3o10b3o6b3o12b 3ob3o6b3ob3o9b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo14bobo 3bobo13b2o12bob2o4b2obo15b2obo15b3obo12b3obo27bob3o24bo3b5o21b3o$5ob4o 8b4o6b4o10b3o2b4ob2ob4o2b3o8b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o2b2o8b2o4bo bo4b2o13b3o14b3o3b3o26b14o12b3o2b2o17b2o12b5o28b4o24b3o2b3o22b4o$4b5o 12b2o4b2o14b2o2b3ob4ob3o2b2o9bob2o5b2obo9b10o12b2o3b2o10b3o2b5o2b3o13b obo33b2ob2ob2o9bo4b2o4bo12bobo4b2o16b2o12b5o28b2o26b5ob2o25b2o$b2o2bo 3bo7bo6b2o6bo9bob3o2bob4obo2b3obo9b2o7b2o11b8o14b2ob2o12bobob5obobo31b 2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o11b4o2b4o16bo11b5o27b3o2bo25bob2obob2o 21bob4o$18b4o6b4o10b3o5b6o5b3o8bobo7bobo11bob2obo15b5o55b2o7b2o9b8o11b obo2bobo11bo2bobo4b2o29bob3o25bob2o27bob5o2bo20bo3bob2o$20b2ob4ob2o12b o7bo4bo7bo7b2o11b2o11bo2bo34bo9bo31bob2o3b2obo10b6o13b2o2b2o12bo2b6o3b o26b2obo27bobobo28b2ob4obo16b2obo6b2o$20b10o10b2o2bo6b4o6bo2b2o30b2o2b 2o17bo41b3o15bobobobo10bob6obo10b8o11b3o3bobo28bob2o28bobobo27b6ob2o 18bobob2o2bob3o$21b8o14bobo5bo2bo5bobo31b3o4b3o57b3o15b2o3b2o12b6o13bo b2obo17bo2b2o28bobo27bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b2o11b2o16b 2o30b3obo2bob3o54bo2bo2bo15bobo15b4o15bo2bo21b2o27bobo27bobobo27bo2b3o bo22bobo2bo$17b3o2b6o2b3o9bo2b3o10b3o2bo28b5o4b5o52bob5obo32b4o32bo6bo bo56bobobo24b3ob3o2bo25bo2bo$17bo2bob6obo2bo12b2obo8bob2o31b5o4b5o52b 9o12b2obob2o13b4o14bo4bo12b3o4bo2b2o52b2obobo26b4obo29b2obo$17b4obob2o bob4o8b8o8b8o27bob10obo49b4ob5ob4o9b7o11b2ob2ob2o12b2o2b2o13bob2o2bo 56bobobo24b10o29b3o$15b3ob12ob3o7bob4o10b4obo30b10o51b2obob5obob2o10b 5o13bob2obo12bobo2bobo11b2ob3o3bo55bobo23bob8o$17b4o3b2o3b4o9b2ob4o8b 4ob2o30b10o52b2o4bo4b2o9b3o3b3o10bo6bo9b5o2b5o12bo4b3o52b2ob2o23b11o$ 17b16o11bo2bo10bo2bo35bo2bo61bo13b3o7b3o11b2o14b3o2b3o18bo2bo53bo25bob 10o$20bo3b2o3bo16bo12bo38b2o77b5ob5o11b4o13b8o18bobo52bo26bob9obo$23b 4o21bo8bo39b4o78b7o14b2o11b3o3b2o3b3o14bob2o51b2o26b11o$21b8o18b2o8b2o 34b2o3b2o3b2o72b11o11bo2bo11bo2bo4bo2bo15bo2b4o44bo3bo25bo2b10o$21b8o 19bo8bo35b3ob4ob3o76b3o15b4o11b2obob2obob2o15bo5b2o42b4o28b2o2b6o$19bo b8obo62b4ob2ob4o75b5o15b2o12b3ob4ob3o17bob4o39b7o27bo2bo2b3ob2o$19bob 8obo61bo3b6o3bo75b3o14b6o12bob4obo16b3o2bobo40b3o4bo26b5ob2obo$18b14o 63b3o2b3o95bob2obo12b8o15b4o44bob4o31b2obob2o$17b16o62bobo2bobo92b2o2b 4o2b2o8b10o15b2o2b2o42b5o30bobobo$19b12o64bo6bo91bo2b8o2bo8b8o15bo4bo 44b2o34b2obo$20b10o66bo4bo92b14o6b12o17bo45b2o$20b10o62bo3bo4bo3bo89b 12o7b2ob6ob2o16b2obo44bo$19bob8obo61b3obo4bob3o88bob10obo31b6o$22b6o 64b3o8b3o89b12o31bo2b4o$20bob6obo64bo8bo91bo3bo2bo3bo11b4o13b2ob2ob2ob o$21b8o62bo3bo6bo3bo110b6o12bo3bo4b3o$19bo2b6o2bo61b2obo6bob2o92b6o14b 4o15bo6bob2o$22b6o64b3obob2obob3o91b8o11b2o4b2o12b2o3bo4bo$20bob6obo 68b2o97bo2b2o2bo11bobo2bobo14b2ob4o2bo$22b2o2b2o65bobobo2bobobo92bo2b 2o2bo11b2ob2ob2o12bobo2bo2b2o$21bo6bo64b2o2bo2bo2b2o94bo2bo35b2obo2bob o$21b3o2b3o64b5o2b5o113bo2bo16bo2bo4b3o$19bo2bob2obo2bo64b3o2b3o115bo 2bo14bo2bobo4bobo$20bobo4bobo63bob8obo114b2o15b5o3b2o$17bob5o2b5obo59b o4b4o4bo132b2obobobob2o$17b5obo2bob5o59bobo2b4o2bobo133b2o2bobob2o$16b ob3o8b3obo58b5ob2ob5o132b2o6bo$17b2ob2o6b2ob2o62b2o4b2o135b4o2b5o$16bo 3bo8bo3bo59bo2bo4bo2bo135bo3b5o$16bobo12bobo59b3o6b3o133bob3ob3o$237bo b2o6bo$16b2ob2o8b2ob2o205b2o$17bo2b2o6b2o2bo203b2o3bo$16bo2b3o6b3o2bo 203bobo4b3o$18b5o4b5o206b4o3b2o$16b6o6b6o203bob2o$16b5o8b5o205b3o$16bo b4o6b4obo208b3o$18b2obo6bob2o206bob6o$17b2o12b2o206b2obob2o$17bo14bo 207bob2o$16b3obo8bob3o204b2o2b4o$16b3o12b3o204bo5b2o$15b6o8b6o205b3ob 2o$15b3obobo6bobob3o204bob3o$16b3ob2o6b2ob3o207b2ob2o$15b3o5bo2bo5b3o 206bob2o$15b3obo2b6o2bob3o210b2o$17bo2b10o2bo213bo$19b12o213bob2o$20b 10o216b2o$20bob6obo214b4o$20b10o210b6obo$23bo2bo210b2ob3ob2obo$21b8o 208b2ob3obo$21b2ob2ob2o209bob3obo$21bobo2bobo208bob4o$23bo2bo213bo$21b 3o2b3o208b2o2bo$20b2obo2bob2o209bo2b2o$19b2obo4bob2o209b4o$19bob3o2b3o bo208b2ob2o$19b2obo4bob2o207bo2bo$21b2o4b2o212bo$18bo12bo208b2o$19b2o 8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

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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