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
View static image
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, 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 ]]

(click above to open LifeViewer)

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	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 = 350, y = 81, rule = B3678/S34678 b4ob2o12bo8bo17b2o2b2o2b2o16bo5bo10b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo 16bo5bo14b2o14b3o2b3o13b3o15b2o30b2o27b3o2b2o21bo$obo3b3o10b3o6b3o14b 2obob4obob2o11b5o3b5o8b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo14bob o3bobo13b2o12bob2o4b2obo10b3obo12b3obo27bob3o24bo3b5o21b3o$5ob4o8b4o6b 4o12bobo2b2o2b2o2bobo10b4ob3ob4o8bo2b2o2b2o2bo9b2o2b3o2b2o8b2o4bobo4b 2o13b3o14b3o3b3o26b14o12b2o12b5o28b4o24b3o2b3o22b4o$4b5o12b2o4b2o16bo 2b2ob2ob2o2bo11bob2o5b2obo9b10o12b2o3b2o10b3o2b5o2b3o13bobo33b2ob2ob2o 9bo4b2o4bo13b2o12b5o28b2o26b5ob2o25b2o$b2o2bo3bo7bo6b2o6bo14bo8bo14b2o 7b2o11b8o14b2ob2o12bobob5obobo31b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o13bo 11b5o27b3o2bo25bob2obob2o21bob4o$18b4o6b4o13b2obo6bob2o11bobo7bobo11bo b2obo15b5o55b2o7b2o9b8o11bobo2bobo28bob3o25bob2o27bob5o2bo20bo3bob2o$ 20b2ob4ob2o12b2obob2o6b2obob2o7b2o11b2o11bo2bo34bo9bo31bob2o3b2obo10b 6o13b2o2b2o27b2obo27bobobo28b2ob4obo16b2obo6b2o$20b10o11b2obob2ob6ob2o bob2o31b2o2b2o17bo41b3o15bobobobo10bob6obo10b8o24bob2o28bobobo27b6ob2o 18bobob2o2bob3o$21b8o11bo3bo2bob2o2b2obo2bo3bo28b3o4b3o57b3o15b2o3b2o 12b6o13bob2obo26bobo27bobobo29bob2ob4o17b2o2b2obo$18b2o2b6o2b2o9b3ob3o b6ob3ob3o28b3obo2bob3o54bo2bo2bo15bobo15b4o15bo2bo26bobo27bobobo27bo2b 3obo22bobo2bo$17b3o2b6o2b3o8bo3b2ob8ob2o3bo27b5o4b5o52bob5obo32b4o74bo bobo24b3ob3o2bo25bo2bo$17bo2bob6obo2bo9b3obob8obob3o28b5o4b5o52b9o12b 2obob2o13b4o14bo4bo52b2obobo26b4obo29b2obo$17b4obob2obob4o11bo2b10o2bo 30bob10obo49b4ob5ob4o9b7o11b2ob2ob2o12b2o2b2o52bobobo24b10o29b3o$15b3o b12ob3o10bob10obo33b10o51b2obob5obob2o10b5o13bob2obo12bobo2bobo52bobo 23bob8o$17b4o3b2o3b4o10b2o2b10o2b2o31b10o52b2o4bo4b2o9b3o3b3o10bo6bo9b 5o2b5o48b2ob2o23b11o$17b16o10bo5b6o5bo34bo2bo61bo13b3o7b3o11b2o14b3o2b 3o51bo25bob10o$20bo3b2o3bo14b2o2b8o2b2o36b2o77b5ob5o11b4o13b8o49bo26bo b9obo$23b4o17bob2ob6ob2obo35b4o78b7o14b2o11b3o3b2o3b3o45b2o26b11o$21b 8o13bobo5b4o5bobo29b2o3b2o3b2o72b11o11bo2bo11bo2bo4bo2bo42bo3bo25bo2b 10o$21b8o14bob3o3b2o3b3obo30b3ob4ob3o76b3o15b4o11b2obob2obob2o41b4o28b 2o2b6o$19bob8obo11bobobobo2b2o2bobobobo29b4ob2ob4o75b5o15b2o12b3ob4ob 3o38b7o27bo2bo2b3ob2o$19bob8obo10b2ob3obo6bob3ob2o27bo3b6o3bo75b3o14b 6o12bob4obo40b3o4bo26b5ob2obo$18b14o9bob3obo8bob3obo30b3o2b3o95bob2obo 12b8o39bob4o31b2obob2o$17b16o12b3o8b3o34bobo2bobo92b2o2b4o2b2o8b10o39b 5o30bobobo$19b12o17b3o2b3o37bo6bo91bo2b8o2bo8b8o41b2o34b2obo$20b10o18b 2ob2ob2o38bo4bo92b14o6b12o39b2o$20b10o19b6o35bo3bo4bo3bo89b12o7b2ob6ob 2o40bo$19bob8obo16b2o2b2o2b2o33b3obo4bob3o88bob10obo$22b6o22bo2bo36b3o 8b3o89b12o$20bob6obo62bo8bo91bo3bo2bo3bo11b4o$21b8o60bo3bo6bo3bo110b6o $19bo2b6o2bo59b2obo6bob2o92b6o14b4o$22b6o62b3obob2obob3o91b8o11b2o4b2o $20bob6obo66b2o97bo2b2o2bo11bobo2bobo$22b2o2b2o63bobobo2bobobo92bo2b2o 2bo11b2ob2ob2o$21bo6bo62b2o2bo2bo2b2o94bo2bo$21b3o2b3o62b5o2b5o113bo2b o$19bo2bob2obo2bo62b3o2b3o115bo2bo$20bobo4bobo61bob8obo114b2o$17bob5o 2b5obo57bo4b4o4bo$17b5obo2bob5o57bobo2b4o2bobo$16bob3o8b3obo56b5ob2ob 5o$17b2ob2o6b2ob2o60b2o4b2o$16bo3bo8bo3bo57bo2bo4bo2bo$16bobo12bobo57b 3o6b3o2$16b2ob2o8b2ob2o$17bo2b2o6b2o2bo$16bo2b3o6b3o2bo$18b5o4b5o$16b 6o6b6o$16b5o8b5o$16bob4o6b4obo$18b2obo6bob2o$17b2o12b2o$17bo14bo$16b3o bo8bob3o$16b3o12b3o$15b6o8b6o$15b3obobo6bobob3o$16b3ob2o6b2ob3o$15b3o 5bo2bo5b3o$15b3obo2b6o2bob3o$17bo2b10o2bo$19b12o$20b10o$20bob6obo$20b 10o$23bo2bo$21b8o$21b2ob2ob2o$21bobo2bobo$23bo2bo$21b3o2b3o$20b2obo2bo b2o$19b2obo4bob2o$19bob3o2b3obo$19b2obo4bob2o$21b2o4b2o$18bo12bo$19b2o 8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

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