User:TheWayOfTheCon/B35/S126

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Flockenstein
x=64, y = 64, rule = B35/S126 ! #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	126/35 B35/S126
Rule integer	35880
Character	Chaotic
Black/white reversal	B013458/S0124678

B35/S126, named Flockenstein, is a outer-totalistic rule where cells are born if they have 3 or 5 neighbors, and survive if they have 1, 2, or 6 neighbors. The rulestring resembles that 2x2's. This rule was probably first explored in the 1990s, with the first spaceship discovered in 1994, but not seriously investigated until newcomer Hunter made a topic about it. This rule has similar behavior to Life, but with overall shorter-lived chaos and less diversity in stable patterns like still lives and oscillators.

Goals

• Find 12 different spaceship speeds (currently 9)
• Reach 100 billion objects in C1 and D8_1 (currently 88 billion and 109 billion)
• Find a reflector (completed by Hunter)
• Find a glider collision that outputs a glider (or even better an over-unity reaction)
• Find a new oscillator above period 30 using apgsearch (completed by Hunter's p37)
• Catalog common evolutionary sequences (completed by TheWayOfTheCon)

The end goal for some of these is to use the technology to make a gun or rake.

How does it compare to LowLife?

LowLife is another rule I was interested in for a while, and made many discoveries in over the course of early to mid 2026. Seeing as I now have interest in this rule (and they are both B3xx/S1xx), I thought it would be nice to compare them.

• The behavior of B35/S126 is more active and spurty than LowLife
• LowLife seems to have more easy variety in still lifes and oscillators than B35/S126
• There seems to be a less intense king effect among dominoes and duoplets and their commonness in B35/S126 than LowLife. In the latter rule, those two still lifes (plus the block) make up over 99.9% of all still life occurrences, while in the former its more like 90.1%.
• B36/S126 has much more common elementary spaceships than LowLife, although the latter has more elementary spaceships than the former.

General behavior

As mentioned previously, chaotic patterns in this rule evolve similarly to Life, but are shorter-lived and less spurty. They also seem to be denser. I have not yet identified any common evolutionary sequences outside of a few predecessors.

Constellations

B35/S126 has a few common constellations. It has the Radiator pseudo still life and Flock constellation from Flock, as well as a slightly different, much more common version of flock where one side is spaced by two units instead of one. There is also a common arrangement of two parallel dominoes.

x = 24, y = 7, rule = B35/S126 bo$obo$10b3o8b2o$3o7bobo7bo2bo$10b3o8b2o$obo$bo! o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART WIDTH 800 HEIGHT 400 GPS 5 LOOP 25 ]]

Predecessors for Radiator, Flock, and "wide Flock". (click above to open LifeViewer)

Still lifes

The most common still lifes in the rule are the domino and duoplet, making up around 90% of all still life occurrences in the C1 census. The block does not exist due to a lack of S3.

x = 28, y = 4, rule = B35/S126 18b2o6bo$o8b2o6bo7bobo$bo9bo5bo9bo$2bo8bo6b2o6bo! o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 400 ]]

Several of the most common still lifes outside of the domino and duoplet. (click above to open LifeViewer)

Because of S1 and S2, arbitrarily long diagonal lines can be still lifes.

As of August 2026, the largest still life to have occurred naturally is Lake 2, and typically forms from this large diagonally symmetric predecessor.

x = 6, y = 6, rule = B35/S126 3b3o$b2ob2o$5bo$o3bo$bo2bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 500 HEIGHT 500 AUTOSTART GPS 3 LOOP 18 ]]

Lake 2's predecessor. (click above to open LifeViewer)

Oscillators

B35/S125 has only one common oscillator, a small period-12 which gets its own section in the article. The most common oscillators beside it tend to be boring. However, there are a handful of high-period oscillators across various symmetries in Catagolue, producing various usable sparks.

x = 60, y = 0, rule = B35/S126 obo4bobobo12bobo4bo3bo12bobobo2bobobo2$2bo8bo14bo4bo3bo16bo6bo2$2bo4b obobo14bo4bobobo12bobobo2bobobo2$2bo8bo14bo8bo16bo2bo2$obobo2bobobo12b obobo6bo12bobobo2bobobo3$4bo2bo17bo$4bo2bo18bo22bo2bo3bobo$4bo2bo18bo 23bo2bo2b3o$b3o3bo40bob3o$27bo22bo2bo2b3o$9b4o15bo20bo2bo3bobo$b4o24b o$31b2o$6bo3b3o20bo$6bo2bo$6bo2bo$6bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 400 ]]

(UNFINISHED) a collection of known oscillators with strong, external sparks. (click above to open LifeViewer)

Period-12 T-tetromino oscillator

This is by far the most common oscillator in the rule. It is a small flipper with a relatively wide range of motion that also produces a moderately strong spark. Its smallest predecessor is the C-triplet. For simplicity, this will be called the 'T-oscillator' throughout the rest of the article.

x = 4, y = 3, rule = B35/S126 o$bobo$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 400 AUTOSTART GPS 4 ZOOM 64 ]]

The T-oscillator. (click above to open LifeViewer) Catagolue: here

x = 7, y = 5, rule = B35/S126 bo$2o$bo3bo$5b2o$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 400 AUTOSTART GPS 4 ZOOM 50 ]]

The T-oscillator can safely interact with a copy of itself. (click above to open LifeViewer) Catagolue: here

x = 18, y = 15, rule = B35/S126 b2o14bo$2o3b2o2b2o2b2o2bo$b2o3$15bo$15bo3$15bo$15bo3$15bo$15bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 700 HEIGHT 600 AUTOSTART PAUSE 1 GPS 12 ZOOM 28 T 23 PAUSE 0.5 LOOP 72 ]]

The T-oscillator can burn along dominoes. It can also make turns. (click above to open LifeViewer)

Hunter's p37

This is a high-period, sparky oscillator that was found semi-naturally via agpsearch by Hunter on July 30th, 2026.

x = 16, y = 14, rule = B35/S126 5b2o2b2o4$7b2o$o5bo2bo5bo$bo4bo2bo4bo4$6bo2bo$5bo4bo$5bo4bo$5b2o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 500 HEIGHT 600 ZOOM 23 GPS 15 AUTOSTART ]]

(click above to open LifeViewer)

Due to its powerful dot sparks, high period, and recessive motion after sparking, it has been used to construct the first spaceship reflectors.

Spaceships

B35/S126 has only one common spaceship; Glider 317. A few other spaceships have occurred semi-naturally.

Speed	First discovered (discoverer)	Smallest discovered (discoverer)	Minimum cells
c/3o	xq3_sm7iy18ih05z02688a65441zgk6h156a22ogz36e4y11480a	xq3_0h0fz131061e (Hunter)	16
c/4o
c/5o
c/6o	Smileship	Smileship	22
c/7o	Butterflyer (Hunter)	Butterflyer	24
2c/5o
2c/6o	Skidaddler (Robert Wainwright)	Skidaddler	6
c/4d	xq4_w45hb0is8u4z4o06p3nu0o69czw406x1 (Dean Hickerson)	xq4_w45hb0is8u4z4o06p3nu0o69czw406x1	49
c/5d

x = 142, y = 54, rule = B35/S126 11bo17b4o8b4o7b2o14bo9b6o4b2ob3o3b3ob2o21b3o$10b3o39bobo12b2obo19bobo 5bobo22bo3bo$b6o2b2ob2o2b6o7bobo6b3o3bo5bo4bo11bo21bo11bo23bobo$3bo2b 2o7b2o2bo17b4o8b2o3bo13bo8bo2b2o2bo7bobobobo17b2o3b3o3bo$8bo2bo2bo24b o9b4o3bo12bo8b2o2b2o5bobo7bobo16b4o2bobo$5bo2bob3obo2bo19b3o10b4obo13b o8bo4bo33b3obo2bo$8b2obob2o25bo9b2o15bobo45b3o4b3o8b2o$6b4obob4o22b2o 8bo14b2o2bo11b2o30bob4o5bo8bo2b3o$6bob2o3b2obo22b2o22b4o12b4o30b2obo5b 2o9bo4bo$7bob5obo24b2o9bo14bo4bo38bo11b2o9bo5bo$6bo2bo3bo2bo26bo5bob2o 17bo39b3o7b3obo9b2o4bo$6b3o2bo2b3o26bo7b2o13bo44b2obo4b3o2bo15bo$8bob obobo25bob3o4b3o12b2o3bobo38bo9b2o15bo2bo$5bobob2ob2obobo21b2o8b2obo11b 3obo39bo3bo3bo2b2o16bo3bo$4bo5bobo5bo22bobo5bob3o10bo5bo37bo10bo18b2o bo$2bo4bo7bo4bo21bo9b3o13b4o35b2o5bob2o2bo19bo$bo3bo3bo3bo3bo3bo20b2o 9b3o13b3o33bo10b2o$bo4bo4bo4bo4bo17b3o8b2o2bo52bo7bob2o$b2o5bo5bo5b2o 16bo2bo7bobo15bobo37bo$2b3o3bo5bo3b3o21bo69b3o$2b2o15b2o20bo67b2obo$b o4bo9bo4bo17b2o$ob2o3bo7bo3b2obo19b2o67bo$o2bo2bo9bo2bo2bo17bobo$2b2o 15b2o$3bo15bo$o3bo13bo3bo17b5o$3bobo11bobo$obob2o11b2obobo18bobo$2bob 2o11b2obo21bo$bo3bo11bo3bo2$3b7o3b7o$2bo7bobo7bo$4bo13bo$3bo15bo$5b2o 3bobo3b2o$10bobo$7b2o5b2o$6bob2o3b2obo$7bo7bo$6bobo5bobo$8b3ob3o$6bo9b o$9b2ob2o$7b3o3b3o$9bo3bo$4b4obo3bob4o$6bo2bo3bo2bo$3bo15bo$4b2o11b2o $4bo13bo$3b3o11b3o$3b2obo9bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1500 HEIGHT 900 ]]

All known spaceship speeds. The c/6, c/7, and c/5d have all occurred semi-naturally. (click above to open LifeViewer)

Glider 317

Glider 317, as named by David Eppstein and, also known as Skedaddler, is the most common and only common spaceship in B35/S125. It is a glide-symmetric 2c/6 orthogonal spaceship. On its backend it produces a weak obo! spark.

x = 3, y = 4, rule = B35/S126 2bo$obo$2bo$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 700 HEIGHT 500 ZOOM 64 AUTOSTART GPS 3 TRACK 1/3 0 ]]

Glider 317 (click above to open LifeViewer) Catagolue: here

Reactions

Despite the spaceship not being super common, there are several extremely easy ways to make it by manipulating stable objects with sparks or colliding stable objects with each other. If there's any way of making a gun or rake, these will probably be it.

x = 13, y = 4, rule = B35/S126 bo6bobobo$3o7bobo$obo8bo$4bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 400 ZOOM 40 AUTOSTART PAUSE 1 GPS 3 LOOP 10 ]]

Adding dot sparks to the T-oscillator in certain phases. (click above to open LifeViewer)

x = 6, y = 5, rule = B35/S126 o$2bo$o2bo$4bo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 500 HEIGHT 400 ZOOM 50 AUTOSTART PAUSE 1 GPS 3 LOOP 10 ]]

Adding an obo! spark to a diagonal line of four. (click above to open LifeViewer)

x = 27, y = 8, rule = B35/S126 20b2o3b2o$2bobo17bobo$2bobo17bobo$2o3b2o2$2bobo17bobo$2bobo17b3o$3bo19b o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 900 HEIGHT 500 ZOOM 25 AUTOSTART PAUSE 1 GPS 20 T 11 PAUSE 1 T 43 PAUSE 1 LOOP 80 ]]

Colliding a T-oscillator with half-ponds in certain ways can produce two Glider 317's. (click above to open LifeViewer)

Syntheses

See also: B35/S126/Syntheses

Collisions between Glider 317s can be used to synthesize many objects, much like the gliders in Life. Catagolue has three symmetries for glider collisions: 3G_stdin, 5G_stdin, and 8G_stdin.

Infinite growth

Infinite growth is currently only known in the form of diagonal linestretchers. The first was a c/5 diagonal found by TheWayOfTheCon using Rlifesrc.

x = 32, y = 32, rule = B35/S126 23b2o$22bo3bo$24b4o2$22b2ob2o2bo$22b2obobob2o$20b2o4b2obo$29bobo$19bo 2bo3b2o3bo$16b3o4bo2b2o2bo$14bo10bo$14bo2b3o5bo$16b2o2bo2bo$10b2o8bob o$9bo3bo5b2obo$11b4o4bo2bo2$9b2ob2o2bo3b2o$9b2obobob2o$13b2obo$8bo7bo bo$7bo5b2o3bo$6bo6b2o2bo$5bo5bo$4bo5bo$3bo5bo$2bo5bo$bo5bo$o5bo$5bo$4b o$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 700 X 5 Y -5 AUTOSTART GPS 10 TRACK 1/5 -1/5 ZOOM 20 ]]

The c/5d diagonal linestretcher. This is actually 3 different spaceships very close to each other, including the bottom, actual line-stretching pattern. But this is what Rlifesrc spat out so I didn't notice at first. (click above to open LifeViewer)

Technology

Reflectors

One spaceship reflector is known in B35/S126. It was found by Hunter on July 31st, 2026 and utilizes a newly-discovered period-37 oscillator, and thus has a repeat time of 37.

x = 32, y = 60, rule = B35/S126 5bo4bo$5b2o2b2o$6bo2bo2$6b4o$o4bob2obo4bo$bo2bo2b2o2bo2bo$3bo8bo2$2bo b8obo$2bo2b6o2bo$5bo4bo15bo$4b8o13bo$5b6o$6b4o2$17b3o11bo$17bo2bo4b2o 4bo$18bo8bo$18bo8bo$17bo2bo4b2o4bo$17b3o11bo4$25bo$26bo6$9bo2bo$10b2o $9b2o10$10b2o$9b4o$9bob2o11$9b4o2$10bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 Y -15 ZOOM 15 GPS 30 AUTOSTART T 36 PAUSE 1 T 41 PAUSE 0.5 T 44 PAUSE 0.5 T 45 PAUSE 0.5 LOOP 150 ]]

The period-37 reflector for Glider 317. (click above to open LifeViewer)

Previously, there had been a period-13 "almost reflector". It utilizes two period-13 strong sparkers, and successfully reflects the glider. Unfortunately, there is not enough time or clearance for the glider to make it past the second copy, and the whole pattern is destroyed.

x = 26, y = 20, rule = B35/S126 13bobo2$12b4o4$4bo4bo$5bo$5bobo3bo5bo2bo$4bobo9b6o$o2bo5bo5bobob3o$b2o 5bo5b3o3bo$3bo5b2o4bo7b2o$2bo5bo2bo3b2o5b4o$5bobo6b4o5b2o$o3bobo8b2o7b o$6bo12bo3b3o$2bo4bo10b3obobo$18b6o$19bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 900 HEIGHT 600 AUTOSTART T 0 GPS 10 T 12 PAUSE 1 T 17 PAUSE 1 LOOP 45 ]]

The "almost reflector". (click above to open LifeViewer)