OCA:LowLife

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LowLife
x=64, y = 64, rule = B3/S13 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 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
Rulestring	13/3 B3/S13
Rule integer	5128
Character	Chaotic
Black/white reversal	B0123468/S01234678

LowLife is a Life-like cellular automaton where cells are born if they have 3 neighbors, and survive if they have 1 or 3 neighbors. In this rule, random patterns, such as soups, tend to stabilize much quicker than in Life. This rule was the subject of a paper by Jean-Claude Heudin.

LowLife is one of the most heavily-searched rules on Catagolue, with its C1 census amassing nearly 1.3 trillion objects as of March 2026.

Patterns

Still lifes

The block remains as a still life in this rule, and the duoplet and domino take the form of common still lifes. These three are by far the most common still lifes in this rule, but many more are known.

Spaceships

Spaceships of speeds c/2o, c/3o, c/4o, c/5o, c/6o, c/4d, and c/6d are known in this rule. There are three named spaceships, those being the sidewinder, creeper, and fighter. The sidewinder is the most common spaceship, and moves at a speed of c/4 diagonal.

x = 0, y = 0, rule = B3/S13 obo3bobo$obo3bobo6b2o$obo3bobo$bo5bo4b3o$bo5bo5bo2$bo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 18 WIDTH 500 HEIGHT 240 ]]

The fighter (left), creeper (center), and sidewinder (right). (click above to open LifeViewer)

x = 0, y = 0, rule = B3/S13 2o7b2o$o9bo16bobo$b2o5b2o15bobobobo15b2o$2b3ob3o16bo5bo38bo2bo$3b2ob2o 18b2ob2o15b2obo16bobob2o17bobo9bobo$3obobob3o12b3obobob3o13b2o2b3o17bo 18bo11bo$obobobobobo12bobobobobobo15b2o3bo12bo2bo16bobo13bobo$b3obob3o 14b3obob3o17bobo11bobob2o17b2o15b2o16bobo11bobo$48bobo2bo11bo19bo3bo 13bo3bo12bo3bo11bo3bo$5bo22bo19b2obo14b3o17b3o15b3o14b3o13b3o$4bobo20b obo20bo16bobo17bo17bo16bo15bo$3bo3bo18bo3bo16bo2bo16bo2bo13bo17bo16bo 15bo$4bobo20bobo17bo21bo13b2o2bo13b2o2bo12b2o2bo11b2o2bo$6b2o21b2o15b 2o20bo14bo2b2o13bo2b2o12bo2b2o11bo2b2o$46b5o17bo18bo17bo16bo15bo$7bo 22bo14bo4bo19bo13bo17bo16bo15bo$7bo22bo14bo2b2o20bo13bobo15bobo14bobo 13bobo$4b2o21b2o17bobo18b2o17bo17bo16bo15bo$4b3o20b3o37b3o$5b2obo19b2o bo36b2obo$8bo22bo14b4o21bo11b4o14b4o13b4o12b4o$4bo3b3o16bo3b3o13b2obo 16bo3b3o10b2obo14b2obo13b2obo12b2obo$2b2ob2o18b2ob2o14bo2bo17b2ob2o11b o2bo14bo2bo13bo2bo12bo2bo$2bo3bo18bo3bo15bo5b2o12bo3bo12bo5b2o10bo5b2o 9bo5b2o8bo5b2o$4bob2o19bob2o15bo4bo15bob2o12bo4bo12bo4bo11bo4bo10bo4bo $b5obo16b5obo13b2o4bo13b5obo10b2o4bo11b2o4bo10b2o4bo9b2o4bo$o2bo2bo16b o2bo2bo18bo2bo11bo2bo2bo15bo2bo14bo2bo13bo2bo12bo2bo$bo4bo17bo4bo16bo 4bo12bo4bo13bo4bo12bo4bo11bo4bo10bo4bo$2o2bo2b2o14b2o2bo2b2o13b2o2bo2b 2o9b2o2bo2b2o10b2o2bo2b2o9b2o2bo2b2o8b2o2bo2b2o7b2o2bo2b2o$2b3o2bo17b 3o2bo16b3o2bo12b3o2bo13b3o2bo12b3o2bo11b3o2bo10b3o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 4.7 WIDTH 700 HEIGHT 240 ]]

A collection of similar c/3 orthogonal spaceships.. (click above to open LifeViewer)

x = 265, y = 54, rule = B3/S13 219bo18bo$218b3o16bobobo$2bo3bo3bo17bo3b2o9b2o3bo13bobo21b3o3b3o18b3o 2bo14bo12b3o3b3o17b2o13b2o13bo38bo$b3ob3ob3o15b3ob2ob2ob3ob2ob2ob3o13b o23bo5bo17b2o2bo2b2o13bo13bo5bo19b4o7b4o14bo18b2o19bo$3bo5bo19bo5b2ob ob2o5bo12b2o3b2o18b5ob5o16bo4bo14bobo11b3o3b3o22bo5bo49b3o3b2ob2o$3b2o 2bo4b3ob3o12bobo3bobo3bobo44bo20bo2bo2bo14bobo10bo3bobo3bo20bobo3bobo 17bo30b2ob2o4b2o$bo5bob2o2bob2o13b3obo2bobo2bob3o14bo3bo20bobo3bobo17b 5obo13bobo10bobobobobobo21bobobobo18bo30b2o2bo3bobo$bo4bo3b2o2bo14b2o 2bo9bo2b2o14bobo18b2o2bob3obo2b2o17bob2o82bobo28b4obobo2bo$o7bo8bo11b o5b2o3b2o5bo14bobo22b2o3b2o19bo3bo27b2obo3bob2o21bobobobo17bobo27bo2b o3bo$2b2o3b2o8b2o9b2o4b2o5b2o4b2o12bo3bo17b2o2b2o3b2o2b2o15b2ob2o28b2o 5b2o22b2o3b2o17bobo27bo2bob5o$19bo8bo7b2ob2o7bo13b3o22b2o3b2o21bo3b3o 54bo7bo48b2o4bo20b2o$bo2bo12b3o10b2o4b2ob2o4b2o16bo20bob3o3b3obo22bo24b o3bo3bo3bo18b2o7b2o48b2o22b3ob2o$o3bo11b2o18bo3bo20bo3bo19bob2o3b2obo 20b2obo25b2ob2ob2ob2o77bobo2bo19bo3b3o$2b2o11bo3bo41bo3bo21bobobobo21b 3o28b2o5b2o20bo9bo48b2o22bobo2bo$17bobo40b2obob2o20bo5bo21b2o32bobo21b o13bo67bo2bo2bobo$17b2o40bo7bo18bo2bobo2bo23bo25bobob2ob2obobo16bo13b o68bo$59bo3bo3bo18b3o3b3o23bo26bob3ob3obo18bo11bo66bo4bo$59bo3bo3bo76b ob2o5b2obo21bo3bo69b2o2bobo$58b3o5b3o17bo7bo22b2o26bo3bobo3bo18b2o2bo 3bo2b2o65b2o3b2o$57bo3bo3bo3bo15b3o5b3o19bobo54bo15bo70bo$58bo2b2ob2o 2bo16b5ob5o18bo3bo25bob2o5b2obo16b2o2b3ob3o2b2o60b3ob2ob2o$57b3obo3bo b3o45bobo26bo3bo3bo3bo91bo$57bo3bo3bo3bo17bo5bo22bo28bobo5bobo18bobo2b obo2bobo63b7o$58bobo5bobo18b2obob2o51b2o7b2o17b4o3bo3b4o$60b2o3b2o21b 2ob2o19b3obob3o25bo7bo20bob3ob3obo62bobo3bo$60b2o3b2o18b2o7b2o15bobob obobobo24bo7bo20b2obo3bob2o60bo3bob2o$57b2o9b2o15b2o7b2o15b3obobob3o24b 2o5b2o21bobobobobo62bo2bo$59bo7bo17b2o3bo3b2o18b2ob2o29b2ob2o23bobo3b obo55bo6bo$58b3o5b3o17b2o5b2o18b3ob3o29bobo28bo59bo3b4o$87bo5bo18b2o5b 2o28bobo22bob2o2bo2b2obo54bobob3o$86bo7bo16bo9bo25bo5bo19bob2o2bobo2b 2obo55b2o$87bo5bo17b2o7b2o23b2ob2ob2ob2o20b2o5b2o51bo3bo$88bo3bo55bo3b o23b2o5b2o51bo3b3ob2o$86bo7bo51bo7bo23b2ob2o52b2ob2o5b2o$86bo7bo52b2o 3b2o82bobo5b2o$147bo5bo76bob2o3bobo$175bobo5bobo43bo2b2o4b2obo$229bob o9b2o$173b2obob2ob2obob2o41bo11bo$227bo11b2o$225bo12bo$224bobobo$238b o$223b2o3bo6b2o2bo$225bo8bobo$222b2obobo7b3o$222b3ob2o5b2o$222bo7b2ob o$228bob2obo$225b2o$223bo4bo$223bo6b3o$227bo2bo$227b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 5 WIDTH 1423 HEIGHT 280 ]]

Spaceships of several speeds, both orthogonal and diagonal. (click above to open LifeViewer)

Oscillators

Natural oscillators of periods 2, 3, 4, 6, 8, 10, and 20 are known. Patterns in LowLife which are common oscillators include the Z-tetromino and a flipping banana spark. Unlike in Life, the commonness of oscillators is more spread out. Most common oscillators in the rule are flippers.

x = 0, y = 0, rule = B3/S13 13bo6b3o15b2o7bo$b2o3b2o5bo5bo3bo5bob2o7bo4bo2bo$o6b2o21bo6bo6b2obo$12b obo23b3o5b2o$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 11 WIDTH 500 HEIGHT 500 AUTOSTART GPS 4 ]]

A collection of small, common oscillators. (click above to open LifeViewer)

Additionally, there is a period 5 that is not known to naturally occur.

x = 8, y = 17, rule = B3/S13 b2o2b2o2$3b2o$2bo2bo$2bo2bo$2bo2bo$2bo2bo2$2bo2bo$2bo2bo$o2b2o2bo2$b6o$2bo2bo $bo4bo$obo2bobo$o6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 25 WIDTH 500 HEIGHT 500 AUTOSTART GPS 4 ]]

The period 5 oscillator. (click above to open LifeViewer) Catagolue: here

Linear growth

Linear growth is known in this rule, with wickstretchers and puffers being known. The first was discovered by TheWayOfTheCon using ikpx2, the following period-14 c/2 orthogonal puffer:

x = 62, y = 23, rule = B3/S13 o$o6bo$2o2b2obo$bo6b2o$ob2o5bo41bo6bo$2o3bo9bobo23bo8bo6bo$obo11b2o16b o6b2obo5bo5bo5b2o$2obobo7bo10bo6b2o4bo4bob2obo4bobo5b2o$b3ob2o2bo3b2o 2bo2b2ob2o4b2ob2obobobo2b2obo$5bo5bo2bob2o4bob2o2b3o4b2o3bo3b2obo$bob 2o2b2ob3o6b2o6bo3bo16b3ob2o5b2o$2o22b2o2bo$bob2o2b2ob3o6b2o6bo3bo16b3o b2o5b2o$5bo5bo2bob2o4bob2o2b3o4b2o3bo3b2obo$b3ob2o2bo3b2o2bo2b2ob2o4b 2ob2obobobo2b2obo$2obobo7bo10bo6b2o4bo4bob2obo4bobo5b2o$obo11b2o16bo6b 2obo5bo5bo5b2o$2o3bo9bobo23bo8bo6bo$ob2o5bo41bo6bo$bo6b2o$2o2b2obo$o6b o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 WIDTH 800 HEIGHT 400 X -5 AUTOSTART TRACKLOOP 14 -1/2 0 GPS 6 ]]

(click above to open LifeViewer) Catagolue: here

A related p6 domino puffer was found in the same search:

x = 82, y = 23, rule = B3/S13 bo$2o5b2o$b2o2b3o$4b2o3bo$bob2o4bo$2o2bo10bobo$o2bobo9bobo14bo40bo$bo 2bo2bo6bobo7bo6bo31bo7b2obo5b2o$b2o3b2o5b5o3bobo5bo3bo27b2obo4bo4bob2o bo$2bo3bob3obo3bo2b2o4bo3bo3bob2o24b3o3bobobo2b2obo$bob2o3b2o2bo7b2o2b o2bo3b2o3bo15b2o2b4o5bob2o3bo3b2obo$b2o22b4o21b3o2b3o2bob2o16b2o$bob2o 3b2o2bo7b2o2bo2bo3b2o3bo2b2o12b2o$2bo3bob3obo3bo2b2o4bo3bo3bob2o4bo5b 2obobobo$b2o3b2o5b5o3bobo5bo3bo4b2o3bobo3b2o4b3o2bob2o16b2o$bo2bo2bo6b obo7bo6bo10b2obobo8b4o5bob2o3bo3b2obo$o2bobo9bobo14bo9bo8b2o8b3o3bobo bo2b2obo$2o2bo10bobo24bo18b2obo4bo4bob2obo$bob2o4bo53bo7b2obo5b2o$4b2o 3bo63bo$b2o2b3o$2o5b2o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 9 WIDTH 800 HEIGHT 400 ]]

(click above to open LifeViewer) Catagolue: here

There are also c/3 wickstretchers that stretch a p2 wick:

x = 60, y = 12, rule = B3/S13 8bo$9bo$bo3bobo2bo4bo$bo3b2obo4bo3bo10b2o$b2obo2bo5bo2bob2o2bo4b2o3b2o 2bo$3bo4b5o8bo3b4o2bo2b2obo$b3o2bo4bo5b3o2bo2b2o8bobo3bo8bo2bobobo$2o 3b2obo20b3o7bobo2b2ob2ob3obobob2o$o2bo36bo3b2o2b2o$b2obobo34b2ob2obo2b 3obobob2o$2bo39b2o6bo2bobobo$43bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 WIDTH 800 HEIGHT 400 X -5 GPS 6 AUTOSTART TRACKLOOP 3 -1/3 0 ]]

A double wickstretcher by I6_I6 and reduced by TheWayOfTheCon, based on his partial (click above to open LifeViewer)

x = 83, y = 13, rule = B3/S13 19b2o3b2o$14bobo4bo8bo4b2o3b2o4bo8bo2bobobobo$16bobo2bob2ob2o2b3o2b3o b2o4bo8bo3b2obob2o4b2o$2b2o8bobobo4bob3o3bobobo3bo3bo2b2obo2bo3bo3bo3b o2b2obobo3b2obobobo$b6o3b2o5b3o3bo10bob2ob2o4bo5bobo12b3o3bobobobobob o$2o6bobob2o3b2o10bo4bo5b2o2b4ob3obo2bo7bo7bo$o7b2o4b2o12b2o4bo7bo10b o2bo7b3o$2o6bobob2o3b2o10bo4bo5b2o2b4ob3obo2bo7bo7bo$b6o3b2o5b3o3bo10b ob2ob2o4bo5bobo12b3o3bobobobobobo$2b2o8bobobo4bob3o3bobobo3bo3bo2b2ob o2bo3bo3bo3bo2b2obobo3b2obobobo$16bobo2bob2ob2o2b3o2b3ob2o4bo8bo3b2ob ob2o4b2o$14bobo4bo8bo4b2o3b2o4bo8bo2bobobobo$19b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 11 WIDTH 1000 HEIGHT 400 X -5 GPS 6 AUTOSTART TRACKLOOP 3 -1/3 0 ]]

A double wickstretcher with different spacing, by I6_I6 (click above to open LifeViewer)

x = 13, y = 19, rule = B3/S13 4b3obo$2b2o5b2o$b2ob2o5bo$2o$2b2o8bo$2bobo6b2o$3bo6bo$10bo$10bo$4bo6b o$3b6obo$5bo3bo$5bo$4bo$5bo$4bo$5bo$4bo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 21 WIDTH 500 HEIGHT 400 Y -2 GPS 6 AUTOSTART TRACKLOOP 3 0 -1/3 ]]

A 34-cell single wickstretcher by R2INT, the smallest linear growth in this rule (click above to open LifeViewer)

As well as a c/5 double wickstretcher for the same wick:

x = 40, y = 17, rule = B3/S13 o16bo$2o10b2o4bo2bo6bo$bo12bobobob2o5bo$bo7bobo4bo4b3o4bo5bobob2o$bob o4b2o10b2ob3ob4o2bobobo$2bobob2o10bo3bo4bob2o$3bo3bo7b2obo3b4o5bo$4bo bo11bobobo5bo2bo$21bo2bob2o$4bobo11bobobo5bo2bo$3bo3bo7b2obo3b4o5bo$2b obob2o10bo3bo4bob2o$bobo4b2o10b2ob3ob4o2bobobo$bo7bobo4bo4b3o4bo5bobo b2o$bo12bobobob2o5bo$2o10b2o4bo2bo6bo$o16bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 10 ]]

A c/5 orthgonal double wickstretcher by TheWayOfTheCon (click above to open LifeViewer)

A growing spaceship has also been found, with a c/3 puffer's debris being eaten by a 5c/24 Creeper-based fuse.

x = 13, y = 81, rule = B3/S13 3b3o2bo$b2o2bo2b2o$2bo4bo$bo2bo2bo$2b5obo$5bob2o$3bo3bo$3b2ob2o$5bo3b 3o$9bo$6b2obo$5b3o$5b2o$8bo$8bo2$7b2o$5bobo$4bo3bo$5bobo$6bo2$5b3o4$3b 7o$2b2ob3ob2o$b2obo3bob2o$b2o7b2o$2bo7bo$3bo5bo$2bo7bo$b3o5b3o2$2bo7b o$2bo3bo3bo$2b3obob3o$5bobo2$3b2o3b2o2$2b3o3b3o$4bo3bo$4b2ob2o$5bobo$ 3bo5bo$4bo3bo2$2b2o5b2o$2b2o5b2o$b2o7b2o$o11bo$b2o7b2o$2bo7bo$3bo5bo$ bobo5bobo$6bo$3bobobobo2$3bo5bo$5b3o2$6bo$6bo3$6bo$6bo$5b3o4$6bo$6bo2$ 6bo$6bo$5bobo$5bobo$5bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 7 HEIGHT 700 ]]

The growing spaceship, found by I6_I6. (click above to open LifeViewer)

Other patterns

Eaters, hasslers and wicks are known to exist in this rule.

x = 72, y = 65, rule = B3/S13 9bo$9bo$16b2o4bo6b2o$23bo5b2o2$9bo$9bo5$6b2o2$9bo$9bo6b2o4b2o5b2o6b2o bo5b2ob2o$18bo4b2o6b2o6bo8bo$6b2o2$4bo$4bo$16b2obobobobobobobobobobob obobobo$6b2o10bobobobobobobobobobobobobobob2o8$4bo4bo$4bo4bo19bo16bo17b 3o$17bo8bo2bo4bo3bo5b2o21b2o$6b2o8bo2b2o5b2obo5b3o6b2o18b3o$17bo10b2o 16bo$9bo$9bo4$6b2o2$4bo$4bo59b3o$67b2ob2o$6b2o56b3o2$4bo4bo$4bo4bo2$6b 2o5$6b2o2$o3bo4bo$o3bo4bo2$18bo$17b2o$o3bo4bo6bobo$o3bo4bo8bo2$6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 6 WIDTH 500 HEIGHT 500 ]]

A stamp collection of the patterns found by Heudin. (click above to open LifeViewer)

x = 0, y = 0, rule = B3/S13 31b2o2$33b3o$34bo6$22b2o2$24b3o$25bo2$17b2o2$19b3o$20bo$13b2o2$15b3o$ 16bo6$bo$o$o$o$bo$9b3o$8bo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 11 WIDTH 500 HEIGHT 500 ]]

p4 Sidewinder eater (click above to open LifeViewer)

x = 29, y = 3, rule = B3/S13 o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 20 WIDTH 700 HEIGHT 400 GPS 10 ]]

Simple lightspeed fuse (click above to open LifeViewer)

x = 9, y = 35, rule = B3/S13 3bobo$3bobo$3bobo$4bo$4bo4$3bobo$3bobo$3bobo$4bo$4bo4$3bobo$3bobo$3bo bo$4bo$4bo4$3bobo$3bobo$3bobo$4bo$4bo3$2o5b2o$2o5b2o$4bo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Inverse ZOOM 11 WIDTH 500 HEIGHT 500 ]]

Stable creeper eater (click above to open LifeViewer)

Universality

On May 26th, 2026, I6_I6 created a rule 110 "unit stripe" for LowLife, proving it turing-complete.

External links

• B3/S13 "LowLife" (discussion thread) at the ConwayLife.com forums
• LowLife at Adam P. Goucher's Catagolue