Flock
x=0, y = 0, 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 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$3o!
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Flock predecessor(click above to open LifeViewer )
x = 5, y = 5, rule = B3/S12
bobo$o3bo2$o3bo$bobo!
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Flock (click above to open LifeViewer )
Another familiar four 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$2ob2o!
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Radiator(click above to open LifeViewer )
Spaceships
Both orthogonal and diagonal spaceships exist in this rule. David Eppstein lists two orthogonal period-4 c/4 ships and a diagonal period-8 c/4 ship; additionally, Josh Ball found a c/5 orthogonal ship in 2016, LaundryPizza03 found a 2c/5 orthogonal ship in 2020, and DroneBetter found a c/6 diagonal ship in 2023.
Currently, the p8 c/4 diagonal spaceship is the only natural one, and has only occurred naturally once.[n 1]
x = 38, y = 14, rule = B3/S12
b3o9b3o$o2bo9bo2bo9b3ob3o$25bo2bobo2bo$o2b2o7b2o2bo10b2ob2o$6bo3bo12bo2bo5bo2bo$2bo4bobo4bo7bo2bo7bo2bo$22bo3bo5bo3bo$5bo5bo$3bo2b2ob2o2bo7bo5bo3bo5bo$2bobo7bobo6bo5bo3bo5bo$b2ob2o5b2ob2o7bobo7bobo$4bo2bobo2bo11bo9bo$4b2obobob2o$4bo7bo!
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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!
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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 = 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!
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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.[2]
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!
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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 = 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!
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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 2] and period-14[n 3] 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 4] (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
External links