OCA:B3/S135

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B3/S135
x=64, y = 64, rule = B3/S135 ! #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 135/3
B3/S135
Rule integer 21512
Character Stable
Black/white reversal B012468/S01234678

B3/S135 is a Life-like cellular automaton in which alive cells stay alive in the next generation if they have an odd number of neighbours below and including 5 cells, similar to LowLife, and dead cells are born in the generation if they have 3 alive neighbours. Soups in this rule stabilise very quickly and yield sparse collections of small objects.

Patterns

Still lifes

Every still life in LowLife is a still life in B3/S135, but not vice versa. The set of still lifes in B3/S135 is thus a superset of the set of still lifes in LowLife. Because cells can only survive on an odd number of alive neighbors, all still lifes have an even population.

x = 5, y = 5, rule = B3/S135 2b2o$2b2o$2ob2o$2b2o$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The most common natural still life in B3/S135 that does not work in LowLife
(click above to open LifeViewer)
Catagolue: here

Spaceships

B3/S135 differs from LowLife in the greater variety of spaceships that appear readily from soup. The fighter and the creeper are shared between the rules, but several c/2 orthogonal spaceships that depend on the S5 transition can be found in this rule only:

x = 57, y = 8, rule = B3/S135 2bo10bo9bo8bo11bo10bo$b3o8b3o8bo7b3o9b3o9bo$bobo8bobo7bobo6bobo9bobo$o 3bo10bo6bobo8bo9bobo9bo$bobo11bo6bobo7bobo6bo5bo7bo$o3bo29bo8bobo8bobo $33bo20bobo$54bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
From left-to-right: The six most common natural spaceships in B3/S135. Out of these six patterns, four rely on the S5 transition.
(click above to open LifeViewer)

Larger elementary spaceships have been found using spaceship search programs, bringing the number of known velocities in the rule to 8:

x = 171, y = 130, rule = B3/S135 b3o15b3o23b3o12bo9bo2b3o2bo9bo54b3o20b3o$b3o14b5o20bobobobo10bo8b2o2b 3o2b2o7b3o49b3ob4o20bo$2ob2o14bobo20b2o2bo2b2o8bobo8bo7bo59b5obob2o16b 6o$2ob2o11bo3bo3bo16bo9bo7bobo79bobob2o16bob2o2b2o$o3bo10b2obobobob2o 14b3o7b3o6bobo8bobobobobo8bobo49bo2b2obo17bo2bo$15b3ob3ob3o15bo2bo3bo 2bo18bo2b3o2bo8bobo44b4o3bobo19bob2o$14b2o2b2ob2o2b2o14b2obo3bob2o20bo 3bo10bobo43bo7b3o17bobo3bo$15b2ob2ob2ob2o14bo2b2o3b2o2bo19b2ob2o56bo3b 2o23b2o$16bob2ob2obo17bo7bo22bobo58bo7bo15b3o3bo$13bo13bo46bo62b5ob2o 16b3o$13b2o11b2o14bo2bobo2bo20b2obob2o55b2o2bo6bo11b3o2b2o$13bo3bo5bo 3bo16b5o24bobo55bo2bo2bo5bo14bo2bo$11bo6bo3bo6bo12b3o3b3o20b2o3b2o55bo bo7b2o10bo5bo$12b4o9b4o12bo9bo19bobobobo54bo3bo5bob2o8b2obo2bo$11bo2b 2o9b2o2bo13b3ob3o21bo2bo2bo53b2o3bo4bo3bo11b2o$12b2obo9bob2o14b2o3b2o 20bob2ob2obo52bob3o21bo$42b2o5b2o21b2ob2o53bo7b4o$14bobo7bobo15b2o5b2o 20bo5bo52bo2b2o2bob2o$15b3o5b3o18bo3bo21b3obob3o54b2obobobo$14bo2bo5bo 2bo13b2obo5bob2o20bobo53b2o2b2o5bo$15bobo5bobo18bo3bo21bo2bobo2bo50bo 2b3obo2bo$14b2obo5bob2o13bo5bo5bo77bob2o6bo$14bo11bo19bo84bob4o$15b2o 7b2o106bo3bo2b2o$13b3obo5bob3o17bobo82bobobobo2bo$11b2o4bo5bo4b2o15bob o84bo4bo$14bobo7bobo104bobobobobo$13bo2bo7bo2bo102bo3b2o$13bobo9bobo 101bobobobo$13bo2bo7bo2bo101b3o2bo$16bo7bo106bo$12b2obobo5bobob2o98bob 2obobobo$14bo11bo99bobo3bo3b2o$15bo9bo101bo8b2o$16bo7bo105bobobob2o$ 126bobob2ob3o$15b2o7b2o102bo6bo$16bo7bo101b2o5bobo$16bo7bo100b3o$14bo 11bo98bo5b2ob2o$13b3o9b3o101bo$12b2o13b2o97b2o3bobo$11bo17bo96bobobo2b o$14bo11bo100bo4b2o$14bo11bo101bo2bo$20bo103bo3b4o$12bobo3bobobo3bobo 96b4o$18b2ob2o103bo4bobo$13b2obo7bob2o96b4obo$14b3obobobob3o96b4obo$ 15bo9bo96b2o2bobo$15bo2bo3bo2bo97b3o4bo$15b2obobobob2o93b3obo2bo2bo$ 14bob2o5b2obo92b2o4b4obo$17bo5bo99bo2b2o$16bo7bo92b2obob2obo2bobo$14bo 2bo5bo2bo90bo2b2o3bo5bo$15b4o3b4o95bob2o$17bobobobo102bo4bo$120b2obo2b o$18bo3bo95b2ob2o3bo$17b2o3b2o96bobo2bo$16b2obobob2o97bo4b2o$14b2o3bob o3b2o97bo2b2o$16bo7bo97bo2bo2bo$16b2obobob2o97b3o$125b2obo$17b2o3b2o 99bo4bo$14b3obobobob3o95bo2b2obo$13bobo3b3o3bobo98b4o$13bo6bo6bo92bo5b o2bo$15b2o7b2o94bobo2bobo$16bo2bobo2bo95bo5bo$13bo13bo90b2o2b3o$12bo6b 3o6bo86bo2bobo3bo$11bo2bo11bo2bo85bobobo2bo$19b3o99b2o$18b2ob2o96b4o$ 18bo3bo93bobo$118bo$16b3o3b3o88bob2o$16b2o5b2o87bo$16b2o5b2o86bo2b2o$ 17bo5bo85b2ob2o$16b2o5b2o84bo$15b2o7b2o83b3o3bo$15bo2bo3bo2bo82bo2b4o$ 18bo3bo85bo5bo$107bob3obo$106bo5bobo$106bo4bobo$105b2o3b2o$104bo3bo2bo $104bob2o$102b3o2bo3bo$102bobo4b2o$101b3o2bo$105b2o3bo$100b3obo3bob2o$ 99bobob4o$107bobo$99bobobo5bo$98b2o2bobobobo$101bo3b3o$100b2obobobo$ 103b2o2bo$100bo7bo$101bo4bo$106bo$102b4obo$101bob3obo$102b2o3bo$104bob 2o$101bo4bo$100bo4bo$98b3o2b3o$97b2o4bo2bo$96bo6bobo$96b2ob2o$103bo$ 104b2o$105bo$105bo2$103b3o$104b2o$102b3o$101bobo$102bo$101b2o! #C [[ ZOOM 2 ]] #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Known elementary spaceships: six orthogonal velocities (c/2, 2c/5, c/3, c/4, c/5, c/6), one oblique velocity (c/5 knightwise[1]), and one diagonal velocity (c/4) are known in this rule.
(click above to open LifeViewer)

Oscillators

Like LowLife, oscillators in this rule are typically low-period and easy to come by from soup. There are also less common seminatural oscillators of varying periods:

x = 48, y = 108, rule = B3/S135 2bobo8b2o11bo$2bobo8bo11bo$2b3o7bo11bobo$4bo7b4o7bobo2bo$4bo23b2o$26b 2o$27bo11$2b3o9bo11b2o15b2o$2bo10bobo10bo15bo$2b3o6b2ob2o10bobo13b2o$ 4bo5bobo3bo8bobo2bo5bo2bo2b3o$2b3o6bo3bobo6bo3b3o5bob2o$12b2ob2o6bobo bo9b3o$12bobo9bobo17b3o$13bo11bo18b2obo$39b3o2bo2bo$40b2o$41bo$39b2o6$ 2b3o6b2o15bo$2bobo5b2o2bobo9b2ob2o$2b3o7b5o13bo$2bobo11bo10bo5bo$2b3o 19b2o2bo2bobo$24bo5bo3bo$23bo3bo5bo$24bobo2bo2b2o$24bo5bo$27bo$27b2ob 2o$29bo6$ob3o9b2o$obobo8bo2bo$obobo6b8o$obobo5bo8bo$ob3o5bo8bo$11b8o$ 13bo2bo$14b2o6$ob3o$o3bo6bo$ob3o5b2o$obo9bo$ob3o7bob2o$13bo$18bo$16b2o bo$19bo$20b2o$20bo6$ob3o10b2o$o3bo10b2o$ob3o8bo4bo$o3bo9bo2bo$ob3o8bo 4bo$10bobo6bobo$10bobo6bobo$13bo4bo$14bo2bo$13bo4bo$15b2o$15b2o6$ob3o 5b2ob2o3bo$obobo6b3o3b2o$ob3o12bo$obobo12b2o$ob3o5bo7bo$10b2o$11bo$10b 2o3b3o$10bo3b2ob2o! #C [[ ZOOM 2.75 ]] #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Interesting seminatural oscillators (two period-4, three period-5, two period-8, one period-10, one period-12, one period-13, one period-18).[2]
(click above to open LifeViewer)

References

  1. ↑ LuveelVoom (3 November 2025). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
  2. ↑ hibiscus (22 September 2026). Re: hibiscus' Home Here Had Heretofore Hidden (discussion thread) at the ConwayLife.com forums