Flock
x=64, y = 64, rule = B3/S12
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LifeViewer -generated pseudorandom soup
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Rulestring
12/3 B3/S12
Rule integer
3080
Character
Chaotic
Black/white reversal
B0123458/S01234678
Flock is a Life-like cellular automaton in which cells survive from one generation to the next if they have 1 or 2 neighbours, and are born if they have 3 neighbours. Its rulestring is B3/S12. It differs very strongly from Conway's Game of Life and similar automata. It is the second most searched rule on Catagolue in terms of the total number of objects censused from asymmetric soups as of March 2026, behind Conway's Game of Life itself.
Patterns
Due to the missing S3 survival condition and addition of the S1 survival condition, almost no patterns from Life are compatible with Flock and vice versa. Random starting soups rapidly degenerate into dominoes and still duoplets . Tub , beehive , loaf and mango still work as expected, as do the infinite family of lakes (including small lake and its extended derivatives).
The rule, however, does share many features with rules such as 2×2 , HighFlock , EightFlock , Pedestrian Flock and Goat Flock .
There are small p2 oscillators which resemble the ship , long ship and very long ship when played, one of which looks like a bipole in one phase. This family of oscillators does not appear to be extendable.
Familiar fours
Despite the vastly different behaviour of patterns, some patterns can still settle naturally into familiar fours and related constellations. One, for example, is called flock , a constellation of four duoplets, which evolves from a 3 × 3 square of cells as in the traffic light sequence.
x = 1, y = 1, rule = B3/S12
3o$obo$3o!
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Flock predecessor(click above to open LifeViewer )
x = 5, y = 5, rule = B3/S12
bobo$o3bo2$o3bo$bobo!
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Flock (click above to open LifeViewer )
Another familiar four, in fact a pseudo still life , is known as radiator , composed of four dominoes.
x = 13, y = 6, rule = B3/S12
bo$bobo$11bo$o8b2obo$b2o5bo$7bo!
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Two radiator predecessors with different sequences(click above to open LifeViewer )
x = 5, y = 3, rule = B3/S12
2ob2o2$2ob2o!
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Radiator(click above to open LifeViewer )
Spaceships
Both orthogonal and diagonal spaceships exist in this rule. David Eppstein lists two orthogonal period-4 c/4 ships and a diagonal period-8 c/4 ship; additionally, Josh Ball found a c/5 orthogonal ship in 2016, LaundryPizza03 found a 2c/5 orthogonal ship in 2020, and DroneBetter found a c/6 diagonal ship in 2023.
speed
period
first known
discoverer
minimal known
discoverer
c/3
3
434P3H1V0
May13, 2024[ 1]
219P3H1V0
lordlouckster, 2024[ 2]
c/4
4
54P4H1V0
unknown
40P4H1V0
unknown
8
68P8H2V0
unknown
16P8H2V0
Lapin Acharné, 2024[ 3]
c/5
5
184P5H1V0
Josh Ball , 2016[ 4]
126P5H1V0
DroneBetter, 2023[ 5]
2c/5
5
242P5H2V0
LaundryPizza03 , 2020[ 6]
82P5H2V0
DroneBetter, 2023[ 5]
c/6
6
58P6H1V0
DroneBetter, 2024[ 7]
c/4d
4
206P4H1V1
DroneBetter, 2023[ 5]
121P4H1V1
DroneBetter, 2025
8
18P8H2V2
unknown
c/6d
4
57P6H1V1
DroneBetter, 2023[ 5]
Currently, the p8 c/4 diagonal spaceship is the only natural one, and has only occurred naturally four times.
x = 164, y = 55, rule = B3/S12
22b4o19b4o48b4o46b4o$20bo3bob2o15b2obo3bo44bo3bob2o42b2obo3bo$19b2obo
5b2o11b2o5bob2o42b2obo5b2o38b2o5bob2o$19bo5b2o2bo11bo2b2o5bo42bo5b2o2b
o38bo2b2o5bo$24bo2b4o9b4o2bo52bo2b4o36b4o2bo$13b2o3b2o3bo8bo5bo8bo3b2o
3b2o30b2o3b2o3bo8bo32bo8bo3b2o$11bo4b3o5bobo2bo3bo3bo3bo2bobo5b3o4bo26b
o4b3o5bobo2bo3bo30bo3bo2bobo4b2obo$11bo4bo3bo4b3obo4bobo4bob3o4bo3bo4b
o26bo4bo3bo4b3obo4bo28bo4bob3o8bobo$8b4ob2obobo2bo4b3o5bobo5b3o4bo2bo
bob2ob4o20b4ob2obobo2bo4bobo3bo3bo24bo3bo3bobo5bo6bo$18b2o8bo2bob2ob2o
bo2bo8b2o40b2o8b2o2bobob2o22b2obobo2b2o7b2o4bo$8bobo4b2o2bo11bo7bo11b
o2b2o4bobo20bobo4b2o2bo12b3o2bo22bo2b3o10bo2b2o$6bo3b2o2b2o5bo6bo13bo
6bo5b2o2b2o3bo16bo3b2o2b2o5bo8b3obobo24bobob3o5b4o7bo$6bo3b6o3b3o5bob
obo7bobobo5b3o3b6o3bo16bo3b6o3b3o5b2o2b2o4bo22bo4b2o5bo2bobo4bo2bo$3b
4o10bo2bo5bo17bo5bo2bo10b4o10b4o10bo2bo5bo11bo20bo9bo6b2o3b2o3bo$25b2o
17b2o54bo12b2o18b2o9bobo4bo2bo$2bo8bo2bo3bobo3b3o17b3o3bobo3bo2bo8bo8b
o8bo2bo3bobo6bo2b4o30b4obobobo5b2o2b5o$b3o21bo2b3o9b3o2bo21b3o6b3o19b
o17bo14bo12bob2obobo2b6ob3o$2o2bo23bo13bo23bo2b2o4b2o2bo17b2obo13bobo
14bobo8bobo17bo$bo2bobo21bo13bo21bobo2bo6bo2bobo15bo3bo14b3o10b3o12bo
4b3o7bo$bo5bo18bo2b2o9b2o2bo18bo5bo6bo5bo19bo13bo2bo8bo2bo8bobo5b5o2b
obo4bo$bobo3bo2bobo13b2o2bo9bo2b2o13bobo2bo3bobo6bobo3bo2bobo8bo43bo3b
2o3bob3o7b2o$bo8bo2bo13bo15bo13bo2bo8bo6bo8bo2bo6bo2b3obo12b5o8b5o9b5o
2bo2bo6b3o$7bob2o16b3o11b3o16b2obo18bob2o28b3ob2o8b2ob3o5b7o12bo2bo$5b
3o7bo10bobo13bobo10bo7b3o14b3o7bo4bobo17bo2bobo6bobo2bo5bo9bo2bo$4bo2b
ob2o3b2o9b2o4bo7bo4b2o9b2o3b2obo2bo12bo2bob2o3b2o29b2o4b2o10bobob2o3b
o10b5o$7bo7b3o6bo2b5o7b5o2bo6b3o7bo18bo7b3o23bo2b2o6b2o2bo5b3o4bo4bo8b
2ob3o$7b2o6bo2bo4bo6bo2bo3bo2bo6bo4bo2bo6b2o18b2o6bo2bo50bobo10bobo2b
o$6b2o16bobo3bo3bobo3bo3bobo16b2o16b2o53bo2bo3bo2b2o8b2o$14b5o6b3o2bo
9bo2b3o6b5o32b5o49b2o2bo9b2o2bo$13b3ob2o7bo5bobobobo5bo7b2ob3o30b3ob2o
41b3o14bo$14bo2bobo8bo13bo8bobo2bo32bo2bobo50bob2obob2o$19b2o6b2o13b2o
6b2o42b2o52b2o3bo$15bo2b2o31b2o2bo34bo2b2o53bobo2bo2bo$29b3o7b3o107b2o
2bo3bo$28b2o11b2o105bo4b2o2bo$27bo2b2o7b2o2bo107b3ob4o$26bo17bo102bo11b
o$27bobo2bo5bo2bobo101b2o6bo$28b3o2bo3bo2b3o100bo4b4o7bo$29b2obo5bob2o
100b2ob4o6b3o$142bo2bo12bo$143bo2bobobobo5b2o$140bo2bo2bobobo2bo4b3o$
139bo9b2o8bo$139bo2bo2b2o8bo$138b2o5b2o7b2o$144bobo5b3o$136bo6bobo5bo
2bo$135b2obo$135bo3bo3bobo5b5o$140bo10b2ob3o$134bo15bobo2bo$133bo2b3o
bo8b2o$150b2o2bo$133bobo!
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Three orthogonal c/3 ships (left : May13's second gutter-symmetric[ 8] ,right : Keith Amling's asymmetric[ 9] ,centre : lordlouckster's smallest known which is effectively a weld of the others' edges[ 1] )(click above to open LifeViewer )
x = 52, y = 14, rule = B3/S12
b3o9b3o10b3ob3o10b3o$o2bo9bo2bo8bo2bobo2bo8bo2bo$27b2ob2o$o2b2o7b2o2b
o6bo2bo5bo2bo6bo2b2o$6bo3bo11bo2bo7bo2bo11bo$2bo4bobo4bo7bo3bo5bo3bo7b
o4bo$46bo$5bo5bo9bo5bo3bo5bo11bo$3bo2b2ob2o2bo7bo5bo3bo5bo9b2o2bo$2bo
bo7bobo8bobo7bobo15bo$b2ob2o5b2ob2o8bo9bo$4bo2bobo2bo$4b2obobob2o$4bo
7bo!
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Two orthogonal c/4 ships (Eppstein's 14679 and 14839) and the natural 2c/8(click above to open LifeViewer )
x = 45, y = 50, rule = B3/S12
9bo4bo18bobo$8bo2b2o2bo16bo2bo$7b2o6b2o14b4o$6bobo6bobo9b2obo$8bobo2b
obo$5bobobo4bobobo8b4o5bo$5b2o10b2o8b2o6b3o$4bo14bo$b2o4bo3b2o3bo4b2o
6b2o3bo$3bo3b2obo2bob2o3bo10b2o3bo$3bo6bo2bo6bo15b2o$3b2o14b2o9bo5bo$
2b2o2b2ob2o2b2ob2o2b2o11bobobo$8bobo2bobo20b2o$36b2o$7bo2b4o2bo18b2o2b
2o$35bo2b4o$8bo6bo17bobo2bo$8b3o2b3o16bo4b2o$7b2o6b2o22bo$6bo2bo4bo2b
o14bo6bobo$5bo4b4o4bo13b4ob3o2bo$4bo14bo13bo4b2o$9b2o2b2o25bobo$3bobo
12bobo13bo2bo$6bo10bo17bobo$3bo4b2o4b2o4bo18bo$38b3o$bobo3bo8bo3bobo15b
o3bo$4bob3o6b3obo18bo4bo$o4b3o8b3o4bo14bo$o2bo3bo8bo3bo2bo14bo3b2o$bo
bo4bo6bo4bobo15bo4bo$2b3o3bo6bo3b3o16bob2o$5bobo3b2o3bobo19bob3o$6bob
o2b2o2bobo23b2o$7b2ob4ob2o23b3o2$10b4o$9b6o28bo$9bo4bo25b2obo$39b4o$37b
obob2o$39bo2b3o$36bo2bo3bo$35bob2o$34bo$34bo$35bo$34bobo!
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The smallest known even-symmetric and asymmetric c/5's(click above to open LifeViewer ) Catagolue : here
x = 59, y = 40, rule = B3/S12
16b2o22bo11bo$14bo4bo17b3ob3o5b3ob3o$13b2o4b2o15bo4bo9bo4bo$13b2o4b2o19bo11bo$5b5o4bo4bo4b5o9bob4o5b4obo$4bo4b2o12b2o4bo6bo19bo$9bob3o6b3obo10bo3bobobo5bobobo3bo$5bo3bob3o6b3obo3bo10b3obo5bob3o$9b2o4bo2bo4b2o9bo4b3o9b3o4bo$9bo5bo2bo5bo9b2o5bo2bo3bo2bo5b2o$8bo16bo19bobo$5bo3bo3bobo2bobo3bo3bo14bobobobo$6b2o4bo8bo4b2o14bo2bobo2bo$10b2o10b2o$8b4o3bo2bo3b4o15bo9bo$8b4o2bo4bo2b4o15bob2o3b2obo$5bo2bo4b2o4b2o4bo2bo$5bo8bo4bo8bo$6bobo2bo2bo4bo2bo2bobo$7b2o4b8o4b2o$10bo3bo4bo3bo$11bo3bo2bo3bo2$7bo2b3o8b3o2bo$4bo2bo2b3o8b3o2bo2bo$2bo2bo4b2o10b2o4bo2bo$b2o28b2o$b2o6bo14bo6b2o$2bo2b2obo16bob2o2bo$bo4bobo16bobo4bo$bo6b3o12b3o6bo$9b2obo2b4o2bob2o$obo2bo5bob2ob2ob2obo5bo2bobo$bo8bo2bo6bo2bo8bo$8b2o2bo8bo2b2o$11b2o8b2o$11bo10bo$9bo2b2o6b2o2bo$8bo16bo$7b2o16b2o!
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The smallest known even- and odd-symmetric 2c/5's(click above to open LifeViewer )
x = 21, y = 15, rule = B3/S12
2bo3b3o3b3o3bo$bobobobo5bobobobo$o19bo$bo3bo3bobo3bo3bo$2bob2o3bobo3b2obo$6b
3o3b3o$6bobo3bobo$6bo7bo$7b2o3b2o2$7bobobobo2$10bo$8bobobo$9bobo!
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The only known c/6(click above to open LifeViewer )
x = 46, y = 36, rule = B3/S12
23bo$21bo2bo$20bo$20bo2bo$20bo3b2o$20b2o2bo2bo$19b2o3bo$24bo$14bobobo
2bo5bo$13bo3bo3bo$13bo4b2obo$13bo4b5ob2o$12bob2o3bo3bo3bo$13b2o6bo6bo
$16b5o4bob2o5bo$25b3o4bo2bo$6b4o16bo4b2o$5bo4bo15bobob3ob2o$8bo16bo3b
o2bobobo$4bo27bobo$3bo21b2obo5b3o$bo6bo19bo3bob2o$o27bo3b2o$o31bo$obo
2bo27bo$o31bobo$bo38b4o$32bobo4b5o$34bo3b3o2bobo$35bo$34b3o3b2obobo$35b
o2bo2bo$38bo2bo$36bo$36bo$39bo!
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c/4 diagonal ships, of periods 8 (Eppstein's 10618) and 4(click above to open LifeViewer )
x = 18, y = 17, rule = B3/S12
7b4o$9b2o2$5b3o$4bo2b3o5b2o$3bo3b3o4b2o$3b7o$3o5bob2obo$8bo2b4o$2o6bo4b3o$8b3o6bo$9bo7bo$12b5o$5bo3b3o2bo$5bo7b2o$10bob3o$5b2o5b2o!
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The only known c/6 diagonal(click above to open LifeViewer ) Catagolue : here
Linear growth
Linear growth is known in the form of 2c/5 domino puffers and c/4 diagonal linestretchers.[ 5]
x = 54, y = 37, rule = B3/S12
6bo11bo16bo11bo$3b3ob3o5b3ob3o10b3ob3o5b3ob3o$2bo4bo9bo4bo8bo4bo9bo4b
o$6bo11bo16bo11bo$4bob4o5b4obo12bob4o5b4obo$2bo19bo8bo19bo$bo3bobobo5b
obobo3bo6bo3bobobo5bobobo3bo$5b3obo5bob3o14b3obo5bob3o$o4b3o9b3o4bo4b
o4b3o9b3o4bo$2o5bo2bo3bo2bo5b2o4b2o5bo2bo3bo2bo5b2o$11bobo26bobo$9bob
obobo22bobobobo$8bo2bobo2bo20bo2bobo2bo2$7bo9bo18bo9bo$7bob2o3b2obo18b
ob2o3b2obo3$14bobo26bobo$16bo28bo$15bobo26bobo$16b2o27b2o2$16b2o27b2o
3$46b4o$44bo5bo$44bo$44b2o$42b2o$44bo2bobo$41bo4bo$48bo2$43bo$45b2o!
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A domino-pulling tagalong for the 2c/5 and additional tagalong with backward heavyweight sparks, that become stable dominoes(click above to open LifeViewer )
x = 43, y = 53, rule = B3/S12
28bo3bo$26bo2bobobo$25bo3bo2b2o$25bo$25bo2b3o$23b2o3bob3o$22bo8bo$21b
o8bo$21bo3bo4bo$18b3o3bo6b2o2bo$17bo9bo7bo$26bo6b2o3bo$16bo3b2o10b3o4b
o$17b2obo12bo6bo$20b2ob2o16bo$17bo3b2o2bo8bo7bo$16bobo2bo3bo2bo6bo$11b
o5b2o8b3o6bo$9bo2bo14b2o2bo5bo$8bo16b2o5bo$8bo2bo21bo$8bo3b2o20bo$8b2o
2bo2bo11bo$7b2o3bo15bo$12bo16bo$2bobobo2bo5bo14bo$bo3bo3bo21bo$bo4b2o
bo$bo4b5ob2o$ob2o3bo3bo3bo$b2o6bo6bo$4b5o4bob2o5bo$13b3o4bo2bo$14bo4b
2o$14bobob3ob2o$13bo3bo2bobobo$20bobo$13b2obo5b3o$16bo3bob2o$16bo3b2o
$20bo$21bo$20bobo$28b4o$20bobo4b5o$22bo3b3o2bobo$23bo$22b3o3b2obobobo
$23bo2bo2bo6bo$26bo2bo7bo$24bo13bo$24bo14bo$27bo!
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c/4 diagonal linestretchers (note that the smaller right one's internal p8 mechanism is p4 in Pedestrian Flock )(click above to open LifeViewer )
Oscillators
Many oscillators occur naturally in this rule. There are many extremely common p2 and p4 oscillators. p3 oscillators are somewhat rare but have been observed.
Oscillators with higher periods have been known to occur naturally. One of the most common of these is the Tetris shuttle , consisting of a tetromino (which is a beehive grandparent in normal Life) being hassled by two dominoes. There is also a p9 which is a bit less common, along with one occurrence of a p7.
x = 50, y = 5, rule = B3/S12
15b2o20b2o$7bo7bobo8bo6b2o3bo4b2obo$2o5bobo16bo6bo2b2o7b2o2bo$o7bo8bo
bo4bobobo5bo2bo6bobo2bo$b2o6b2o7b2o4bo2b2o6b2o10bo!
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Small period-2 oscillators(click above to open LifeViewer )
x = 48, y = 6, rule = B3/S12
31bo4bo7bo$15b2o6b2o6bo4bo6bo$obo5b2o7bo4bo2bo7b2o6bobo3bo$o8b2o6bo5b
3o7b2o6bobo3bo$bo8bo4bo15bo4bo6bo$2b2o4b2o5b2o8b2o4bo4bo7bo!
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Small period-4 oscillators(click above to open LifeViewer )
x = 19, y = 9, rule = B3/S12
2bo9b2o2bo$2bo14bo$2obo2bo3bo3bo3bo$2bo2bo4bo4b2obo$12bo3b2o$3bo2bo6bo
$2bo2bob2obo2b2o$6bo4bo2bo$6bo5b2o!
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Seminatural period-5 oscillators, a D4_x1 one (Catagolue : here ) and D2_x one (Catagolue : here )(click above to open LifeViewer )
x = 6, y = 8, rule = B3/S12
obo$o$o2bo$b3o2$4b2o$2bob2o$4bo!
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The only natural nontrivial period-6 oscillator(click above to open LifeViewer ) Catagolue : here
x = 9, y = 8, rule = B3/S12
2b2o$o2bo$3bo$obo4bo$bo4bobo$5bo$5bo2bo$5b2o!
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Period-7 oscillator(click above to open LifeViewer ) Catagolue : here
x = 20, y = 6, rule = B3/S12
4bo2bo$2bo2bobo8bo$5bo7bobo3bo$5bobo5bobo3bo$2o5bo$3obo!
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Period-9[ n 1] and period-14[ n 2] oscillators(click above to open LifeViewer )
x = 14, y = 14, rule = B3/S12
6bo$5bo$5bo$6bo$6b2o$b2o3bo$o2b3o3bo$4bo3b3o2bo$7bo3b2o$6b2o$7bo$8bo$8bo$7bo!
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Strictly volatile p22 found by Josh Ball on 2016-01-31[ n 3] (click above to open LifeViewer ) Catagolue : here
x = 9, y = 9, rule = B3/S12
b3ob3o$4bo$2o2bo2b2o$b7o2$b7o$2o2bo2b2o$4bo$b3ob3o!
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The only known volatility-1 p4(click above to open LifeViewer ) Catagolue : here
Notes
See also
References
↑ 1.0 1.1 May13 (May 14, 2024). Re: B3/S12 (Flock) , in which the first c/3 spaceship was found using LSSS
↑ lordlouckster (August 8, 2024). Re: B3/S12 (Flock) , in which the current smallest known c/3 was found
↑ LaundryPizza03 (March 25, 2024). Re:B3/S12 (Flock) , noting Lapin Acharné's 2c/8 (which was later proven to be of minimal width by Darren Li )
↑ velcrorex (February 1, 2016). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
↑ 5.0 5.1 5.2 5.3 5.4 DroneBetter (December 27, 2023). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
↑ LaundryPizza03 (May 18, 2020). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
↑ DroneBetter (January 14, 2024). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
↑ May13 (May 14, 2024). Re: B3/S12 (Flock) , in which a width-71 gutter spaceship (from 79) was found, which also reduces from 434 to 428 cells
↑ amling (May 18, 2024). Re: amling questionable searches/ideas firehose , in which LLSSS was used (in even symmetry) to find a width-38 asymmetrical c/3 spaceship after disproving their existence at width-37
↑ muzik (February 18, 2016). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
External links