OCA:Flock

Flock
x=0, y = 0, rule = B3/S12 ! #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	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 fourth most searched rule on Catagolue in terms of the total number of objects censused from asymmetric soups as of August 2022.

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Flock predecessor (click above to open LifeViewer)

x = 5, y = 5, rule = B3/S12 bobo$o3bo2$o3bo$bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Flock (click above to open LifeViewer)

Another familiar four is known as radiator, composed of four dominoes.

x = 13, y = 6, rule = B3/S12 bo$bobo$11bo$o8b2obo$b2o5bo$7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Two radiator predecessors with different sequences (click above to open LifeViewer)

x = 5, y = 3, rule = B3/S12 2ob2o2$2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

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/4	4	54P4H1V0	unknown	40P4H1V0	unknown
c/5	5	184P5H1V0	Josh Ball, 2016	126P5H1V0	DroneBetter, 2023
2c/5	5	242P5H2V0	LaundryPizza03, 2020	82P5H2V0	DroneBetter, 2023
c/6	6			58P6H1V0	DroneBetter, 2024
c/4d	4			206P4H1V1	DroneBetter, 2023
	8			18P8H2V2	unknown
c/6d	4			57P6H1V1	DroneBetter, 2023

Currently, the p8 c/4 diagonal spaceship is the only natural one, and has only occurred naturally once.

x = 38, y = 14, rule = B3/S12 b3o9b3o$o2bo9bo2bo9b3ob3o$25bo2bobo2bo$o2b2o7b2o2bo10b2ob2o$6bo3bo12bo2bo5bo2bo$2bo4bobo4bo7bo2bo7bo2bo$22bo3bo5bo3bo$5bo5bo$3bo2b2ob2o2bo7bo5bo3bo5bo$2bobo7bobo6bo5bo3bo5bo$b2ob2o5b2ob2o7bobo7bobo$4bo2bobo2bo11bo9bo$4b2obobob2o$4bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 4 TRACK 0 -1/4 ]]

Two orthogonal c/4 ships (Eppstein's 14679 and 14839) (click above to open LifeViewer)

x = 42, y = 50, rule = B3/S12 9bo4bo15bobo$8bo2b2o2bo13bo2bo$7b2o6b2o11b4o$6bobo6bobo6b2obo$8bobo2bobo$5bobobo4bobobo5b4o5bo$5b2o10b2o5b2o6b3o$4bo14bo$b2o4bo3b2o3bo4b2o3b2o3bo$3bo3b2obo2bob2o3bo7b2o3bo$3bo6bo2bo6bo12b2o$3b2o14b2o6bo5bo$2b2o2b2ob2o2b2ob2o2b2o8bobobo$8bobo2bobo17b2o$33b2o$7bo2b4o2bo15b2o2b2o$32bo2b4o$8bo6bo14bobo2bo$8b3o2b3o13bo4b2o$7b2o6b2o19bo$6bo2bo4bo2bo11bo6bobo$5bo4b4o4bo10b4ob3o2bo$4bo14bo10bo4b2o$9b2o2b2o22bobo$3bobo12bobo10bo2bo$6bo10bo14bobo$3bo4b2o4b2o4bo15bo$35b3o$bobo3bo8bo3bobo12bo3bo$4bob3o6b3obo15bo4bo$o4b3o8b3o4bo11bo$o2bo3bo8bo3bo2bo11bo3b2o$bobo4bo6bo4bobo12bo4bo$2b3o3bo6bo3b3o13bob2o$5bobo3b2o3bobo16bob3o$6bobo2b2o2bobo20b2o$7b2ob4ob2o20b3o2$10b4o$9b6o25bo$9bo4bo22b2obo$36b4o$34bobob2o$36bo2b3o$33bo2bo3bo$32bob2o$31bo$31bo$32bo$31bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 448 AUTOSTART GPS 5 TRACK 0 -1/5 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 392 AUTOSTART GPS 5 TRACK 0 -2/5 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 HEIGHT 336 AUTOSTART GPS 6 TRACK 0 -1/6 ]]

The only known c/6 (click above to open LifeViewer)

x = 52, y = 39, rule = B3/S12 23bo2b4o$22bo3bob2o$22bo3bo$19b2o3bob2o$18b3o3bo3bo$17b4o6b2o$25bo$17bo2bo4bo$15bo2bo2bo3bo$14bo3bo3bo2bo$14bo3bo3bo16bo$14bo4b2o3bo3bo8bo2bo$15b2o8bo3bo6bo$14bo2bo5bo2bo9bo3bo2bo$13b2o2bo3bo4b2ob2obo3bo2b3obo$13bo5bo5bo4b2obo3b3o3bo$6b4o19bobobo3bob2o2bobo$5bo4bo15bobo2b3o5bobo2bo$8bo23bobo3bo9bo$4bo23bo4b3ob2o7b2obo$3bo25b2o3b3obo3b4o2b2o$bo6bo21b2o3bo5bo3b2ob2o$o25bo2b4o7bo4bo2bo$o24bo3bobo17bobo$obo2bo19bo3b2o10bo2bo5b2o$o24bobo3b2obo8b2o$bo22bo7b2o10b2o$25b3o4bo3bo$26b2ob3o2bobo$26bo4bobo2bo$31b2o5b2o$27bo3bo3bob2o$30bo2b2ob2o$32b2ob3o$32b2o2bo$32bo$37bo$36bobo$37b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 336 AUTOSTART GPS 4 TRACK -1/4 -1/4 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 HEIGHT 336 AUTOSTART GPS 6 TRACK -1/6 -1/6 ]]

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.

x = 51, y = 37, rule = B3/S12 6bo11bo13bo11bo$3b3ob3o5b3ob3o7b3ob3o5b3ob3o$2bo4bo9bo4bo5bo4bo9bo4bo$6bo11bo13bo11bo$4bob4o5b4obo9bob4o5b4obo$2bo19bo5bo19bo$bo3bobobo5bobobo3bo3bo3bobobo5bobobo3bo$5b3obo5bob3o11b3obo5bob3o$o4b3o9b3o4bobo4b3o9b3o4bo$2o5bo2bo3bo2bo5b2ob2o5bo2bo3bo2bo5b2o$11bobo23bobo$9bobobobo19bobobobo$8bo2bobo2bo17bo2bobo2bo2$7bo9bo15bo9bo$7bob2o3b2obo15bob2o3b2obo3$14bobo23bobo$16bo25bo$15bobo23bobo$16b2o24b2o2$16b2o24b2o3$43b4o$41bo5bo$41bo$41b2o$39b2o$41bo2bobo$38bo4bo$45bo2$40bo$42b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 392 AUTOSTART GPS 5 TRACK 0 -2/5 ]]

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 = 78, y = 63, rule = B3/S12 11bo2bobo37b2ob3o$10b4o2bo35b2o5bo$9b3o39bo$13bo41bobo$5b6o3b2o34bo2bobo$4bo4b3o3bo33bo5b2o2bo$9b2obo35bo2bo4b2obo$7b2o3bo34bo2bo5bo$3b3o3b3o33bo3bobobo5bo$2b2o6b2o32bo15b3o$b4o6bo32bo2bo3bobo8b2o$4b2o2b2o2b2o11b3o15bo15b4o2bo$2bo2bob4o2b4o7b3o16bo2b3o11bo5bo$bo2b2ob3o6bo6b2obo3bo17b3o16bo$o5bo7b2o3bo7bo2bo12bo2bo2bo10bo$o2bo2bo5bobobobobo3b2o2b2o13bo17bo$13b3obo2bo4bo3bo13b2o3b2obo2bo7bo$14bo3bo7bobo2b3o18bob2obo$19bobo11b3o16bobo3bo$15bo6bob2o10bo15b3o4bo$16bo4bo7b2obo3bo16bo$17b2o3bo3bo2bo2bo2bo$14bo4bo8bobobo2bo18bo$13b4o5bo5b4o6b2o15bo$12b3o2bobo9b2o4bobo18bo$21bo$11bo2bo4b2o10b2o6b2o$12bo10bo16b2o$14b3obo3bo17bo2bo$14bo2bo3b2o17bo2b3o$14b4o2b3o2bobo5b4o4bo4bo$15bo2bobo4bo6b4ob2obo4b3o$17bo2bo2bo3bo3b2o3bo6bob3o$20bo2bo10bobo6bo2bo$19bo3bo6bo3bobobo6bo$19bo10bo3b2o$24bo9b5o6bo$21bobo7bo2bo4bo4b2o$26bo3b3o7b2o3b2o$24b2o3bo10b2o$28b2o8b2o$32bo8b2ob2o$28bo15b2o$31bob2o6b4o$29b6ob3o8bobobo$36b2o6bo4bo$45b2o4bo$45b2o$51b3o$44bo10bo3bo$45b2o4bo6b2o$53bobob3o$56bo5b4o$55bo4b4ob2o$60b2o3bo3b3o2bobo$55bo2bo12b3o2bo$64b3o3bo$73b2o$73bo2$75bo$76bo$77bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 700 HEIGHT 560 AUTOSTART GPS 4 TRACK -1/4 -1/4 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]]

Small period-2 oscillators (click above to open LifeViewer)

x = 48, y = 6, rule = B3/S12 31bo4bo7bo$15b2o6b2o6bo4bo6bo$obo5b2o7bo4bo2bo7b2o6bobo3bo$o8b2o6bo5b 3o7b2o6bobo3bo$bo8bo4bo15bo4bo6bo$2b2o4b2o5b2o8b2o4bo4bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 4 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 5 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 6 ]]

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 7 ]]

Period-7 oscillator (click above to open LifeViewer) Catagolue: here

x = 20, y = 6, rule = B3/S12 4bo2bo$2bo2bobo8bo$5bo7bobo3bo$5bobo5bobo3bo$2o5bo$3obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 9 ]]

Period-9 and period-14 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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 22 ]]

Strictly volatile p22 found by Josh Ball on 2016-01-31 (click above to open LifeViewer) Catagolue: here

x = 9, y = 9, rule = B3/S12 b3ob3o$4bo$2o2bo2b2o$b7o2$b7o$2o2bo2b2o$4bo$b3ob3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 4 ]]

The only known volatility-1 p4 (click above to open LifeViewer) Catagolue: here

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See also

• rules named after Flock

• HighFlock (B36/S12)
• Pedestrian Flock (B38/S12)
• EightFlock (B3/S128)
• Goat Flock (B2in3/S123a)

External links

• Flock at Adam P. Goucher's Catagolue
• Flock at David Eppstein's Glider Database
• Flock (discussion thread) at the ConwayLife.com forums