Haven (B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak) and its close variants

[MDA]

Today I want to share a rule which is part of a long rulegolfing experiment. I named the rule Haven, as in XWSSHaven, because it supports the lightweight, middleweight, and heavyweight spaceships, as well as every single OWSS, though it doesn’t support the UWSS. Edit (June 17th, 2026, 11:24 AM): Haven now has its own LifeWiki page in my userspace. Feel free to edit it if you think it lacks anything important about Haven.

However, unlike XWSSHaven, it is a two-state rule and is much more dynamic. The lifespans of its 16x16 soups can be compared to those of Life’s. It actually has many interesting patterns. Below are some of them:

Still-Lives

This rule supports many still-lives similar to Life, but it also has some alien still-lives:

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x = 28, y = 8, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
24b2o$23bo2bo$12b2o8bo2bobo$11bo2bo6bob2o2bo$10bob2obo4bo2b2obo$b2obo
5bob2obo4bobo2bo$ob2obo5bo2bo6bo2bo$bob2o7b2o8b2o!

The three above are the only alien still-lives to have appeared in Catagolue’s C1 census for this rule.

Oscillators

Fully natural oscillator periods are 2, 4, 6, 8, 14, and 18. Other symmetries are also detailed in Catagolue.

Spaceships

There are known spaceships of speed c/2o, c/3o, c/4o, 2c/4o (obviously), c/5o, 2c/5o, 2c/6o, 3c/6o, 4c/8o, c/3d, c/4d, c/5d, and (2,1)c/5.

All except the c/5o, the 2c/5o, and the 2c/6o were found either naturally (2c/4o, 3c/6o, 4c/8o, and c/5d) or with ikpx2. The c/5o and the 2c/6o were found with qfind, and the 2c/5o was found by vilc using LLSSS.

Code: Select all

x = 299, y = 143, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
5b2o5bo21b2o16b3o19bo15b3o20bo17bo2bo20bo11bo18bo18b3o14bo12bo16bo12bo
21bobobo$4b2obo4b3o18b4o14bo20b5o13bo2bo17b4o15b6o17b2obo9bob2o15b3o
17bobo13b3o3bo2bo3b3o14bobo10bobo17b11o$3b3o4b4o17b2obo2bo12b2o4bo13b
2o2bo2b2o11bo19b2o2bo15bo4bo17bob3o7b3obo15bobo16b2ob2o12bobo10bobo14b
3o10b3o20b5o$2bo8b2o17bo3bobob2o11b4obo13bo2b3o2bo11bo20bo19bo2bo19bob
2o7b2obo16bobo16b2ob2o16b8o18b2o12b2o18bo3bo3bo$2b2obo5bo19b5obob2o10b
o4bo14bob3obo14bo59b2ob13ob2o11bo2b2obo14bobobobo11bo3b3o2b3o3bo15bo
12bo21b5o$b2ob2o24bo3bo15b3o3bo96b2obob2obob2obob2o10b2obo2bo2bo11bob
3ob3obo9bo3b2o4b2o3bo15bobo3b2o3bobo22bobo$bo2bo25bob3o2bobo14bo97b4ob
ob5obob4o10bobo5bo30b2o3b3o2b3o3b2o13b3o3b4o3b3o17bobob3obobo$2ob2o26b
ob5obo114b3o4bo4b3o33bob5obo9bob2o3bo2bo3b2obo13b16o17b3o5b3o$bo4bo2b
2o28bo112b2obo3bobobo3bob2o31b3o3b3o14bo6bo18bo2b2o6b2o2bo15b2o2b7o2b
2o$bobo3bo2bo21bo2b2o2b2o109b2ob2ob11ob2ob2o30bo5bo10bo3b3o4b3o3bo15b
3o6b3o16b4obobobobob4o$2bo3bo2bob3o18b2ob2o2bo111bobob2obo5bob2obobo
28bo2bo5bo2bo7b3obo8bob3o15b4ob2ob4o15b2o3bo2bobo2bo3b2o$3bo4b3obo27bo
111bo7b3o7bo29bobo2bobo2bobo40bobo6bobo18b4obobob4o$11bo3bo22bo114b2ob
o9bob2o30b3obo3bob3o41b4o2b4o20b2ob5ob2o$14b2o186b2o2bo2b2o41bo3bob2ob
o3bo19bo2b3o2bo$12bo2bo139b3o7b3o34b2obobob2o45b2o2b2o21b13o$12b2ob2o
2b2o132bobo4b3o4bobo34bo3bo44bobo6bobo19b2obobobob2o$13bob2ob3o131b3o
2bo7bo2b3o34bobo46bobo4bobo20b2o2bobo2b2o$13b4o3bo5bo125bo3b3o2bo2b3o
3bo32b3ob3o47b4o21bo4b2ob2o4bo$13b4o3bo132bo2b11o2bo34bobobo45b3o4b3o
19bobobo3bobobo$14bo6b2o2bo2bo130b5o40b5o43b2obo6bob2o19b3o3b3o$20bobo
2b2o128b2ob2o3b2ob2o36b5o42b4o8b4o20bo3bo$21b3obobo127bob2o5b2obo34bo
2b3o2bo39b4o10b4o17bo7bo$21b3o132bo9bo37b5o76b3o3b3o$22bo4bo127b3o7b3o
36b2ob2o43b3o8b3o17b2o9b2o$23b3o129b2o9b2o33b4o3b4o42bob6obo21bo2bobo
2bo$24b2o129bobob5obobo33bob7obo39bob2o2b4o2b2obo15bo2bob5obo2bo$24b3o
3bo126bo2b3o2bo36b2o2bo2b2o42bo3b4o3bo17b4ob5ob4o$31b2o127b3o38bo2b2ob
2o2bo71b3o3bo3b3o$27b2o2b2o123bo2b5o2bo36b3ob3o48b2o28b3o$28bob2o125bo
7bo38b2ob2o47b2o2b2o23b2o2bo2b2o$29bob2o123b3ob3ob3o36bobobobo44bo2bo
2bo2bo21bo7bo$30b3o123b2o7b2o36b2o3b2o45b2o4b2o22b2o2bo2b2o$30b3o123bo
9bo37b2ob2o44bo4b2o4bo21bob3obo$31bo125b2obobob2o38b5o46b8o23bob3obo$
155bo5bo5bo86b3o4b3o19b4obobob4o$157b2obobob2o38bo3bo46b3o2b3o22b4ob4o
$159bo3bo42bo48b2ob2ob2o22b4ob4o$157bo3bo3bo40bo45b3ob6ob3o23bo$155bo
2b2obob2o2bo38bo46b4ob2ob4o20bobobobobo$158b2o3b2o40b3o43bo2b2o6b2o2bo
20b5o$157b3o3b3o88b2o2b2o2b2o21b4ob4o$253b12o20bo2b3o2bo$257bo2bo23b3o
b3ob3o$254bobo4bobo22bob3obo$252bo3b2o2b2o3bo17bo2bo2bo2bo2bo$251b3ob
8ob3o17b5ob5o$253bobo6bobo17bo3bo2bo2bo3bo$253bo10bo17bo2bo7bo2bo$257b
4o20bo3b2o5b2o3bo$254bo2bo2bo2bo17bo2bob2o3b2obo2bo$256bo4bo19bobo2bo
5bo2bobo$256bo4bo26b3o$252bo4bo2bo4bo17b4ob3ob4o$251b3o2b2o2b2o2b3o18b
2o5b2o$253bobobo2bobobo20b3obob3o$253bo3bo2bo3bo21b2o3b2o$252b2obob4ob
ob2o20bob3obo$255b2ob2ob2o$250bo2b5o2b5o2bo20b3o$253bob3o2b3obo$252bob
4o2b4obo22b3o$254bobob2obobo$256bo4bo$253b2o2bo2bo2b2o19b2o3bo3b2o$
252bobo8bobo17b2o3bobo3b2o$253bo10bo21b2obob2o$252b2o10b2o16bo2bo7bo2b
o$252bob10obo16bobo2bobobo2bobo$251b16o14bo3bo3bo3bo3bo$253b12o17b2ob
9ob2o$256bo4bo23b2o2bo2b2o$255b2o4b2o22b9o$254bob2o2b2obo21b2ob3ob2o$
254bob6obo21bobobobobo$254b2ob4ob2o21bo2b3o2bo$254bob6obo24b3o$254bo8b
o22b3ob3o$254bo3b2o3bo22b7o$255bo6bo23b2o3b2o$257bo2bo25b3ob3o$286b3ob
3o$286bo5bo$286bo5bo$285b9o$285b2o5b2o$285bobobobobo$282bob5ob5obo$
283bob2ob3ob2obo$285b2o5b2o$287b5o$285b9o$284b11o$283bo2b7o2bo$286b7o$
284b2o3bo3b2o$287b5o$283b2o3b3o3b2o$284b4o3b4o$285bobobobobo$288bobo$
286bob3obo$284bo2bobobo2bo$286b3ob3o$285b2o2bo2b2o3$285bob5obo$283b2ob
7ob2o$282bo6bo6bo$282bobo2bobobo2bobo$282b2o5bo5b2o$282b2o3bo3bo3b2o$
281b2ob3o5b3ob2o$283bobob5obobo$283b4o2bo2b4o$281bo4bo2bo2bo4bo$284bo
9bo$282b2ob9ob2o$283b3ob2ob2ob3o$282b2o4b3o4b2o$282bo3b2o3b2o3bo$281b
2obob2obob2obob2o$287bobobo$287bo3bo$287bo3bo$288bobo$286bo5bo$288bobo
$287b2ob2o$287b5o$288bobo2$285bo3bo3bo$288b3o$286b2obob2o$285b3o3b3o$
283b3o2bobo2b3o$283bo2bo5bo2bo$283b3ob2ob2ob3o$282b3o9b3o$287bobobo$
287bo3bo$286bobobobo!

Names:

c/2o - Starship

2c/4o - LWSS

3c/6o - Smoky

4c/8o

2c/5o - (reserved for vilc)

c/3o - Wheelchair

2c/6o - Battleship

c/4o - Pillow

c/5o - Cargoship

c/6o - (reserved for FWKnightship)

c/3d - LWDS (LightWeight Diagonal Ship)

c/4d - Giant Glider

c/5d - Telegraphship (alternatively telegraph)

(2,1)c/5 - Sir Hammerhead

Small orthogonal spaceships:

Code: Select all

x = 148, y = 74, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
4bo3bobobo14b3o30bobobo3bobobo17bo37bobobo12b3o$25b2o3b2o57b3o52bo2bo$
4bo3bo3bo11b2ob3ob2o31bo3bo3bo16bobo36bo3bo14bo$24bo3bo3bo56bobo55bo$
4bo3bobobo47bobobo3bo3bo13bo2b2obo35bobobo12bo$28bo55b2obo2bo2bo$4bo3b
o3bo47bo7bo3bo12bobo5bo34bo3bo2$4bo3bobobo47bobobo3bobobo55bobobo12$ob
obo3bobobo14b3o30bobobo3bobobo19bo31bo3bobobo12b3o$25b2o3b2o59bobo50bo
2bo$4bo3bo15b2ob3ob2o31bo7bo17bo3bo29bo3bo3bo14bo$24bo3bo3bo59bo50bo3b
o$obobo3bobobo47bobobo3bobobo16bo2bo2bo28bo3bo3bo14bo$28bo57b3o3bo3b2o
47bo$o11bo15b4o32bo7bo11b2o2b2obo3bob2o25bo3bo3bo$28bo2bo53bo2bo5bo$ob
obo3bobobo17bo29bobobo3bobobo12bo2bobo33bo3bobobo$87b2o$87b2o10$obobo
7bo24b3o20bobobo3bobobo19bo$25bo9b2o2bo51bobo$4bo7bo11b4o5b3o2bo25bo7b
o17bo3bo$24bo2b3ob3o58bo$obobo7bo14bobobobobo24bobobo7bo16bo2bo2bobo$
29bo3bo52b3o3bo3b3o$4bo7bo15bo5bo29bo7bo11b2o2b2obo3bobobo$85bo2bo5bo
4bo$obobo7bo47bobobo7bo12bo2bobo7bo$87b2o$87b2o10$obobo3bobobo11b3o13b
3o17bobobo3bobobo19bo$24bo2b2o9b2o2bo48b3o$4bo3bo16bo2b3o5b3o2bo22bo3b
o3bo18bobo$30b3ob3o54bobo$obobo3bobobo17bobobobobo21bobobo3bobobo13b2o
3b2obo$32bo3bo49bob2o2bo2bo$4bo7bo18bo5bo26bo3bo3bo12bobobo5bo$85bo$ob
obo3bobobo47bobobo3bobobo12bo$85b3o$84bob4o$86b2o2b2o$90bo$87bo!

There is also a collection with all c/3d ships with minimum populations between 19 and 29:

Code: Select all

x = 306, y = 91, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
4bo3bobobo13b3o81bobobo3bobobo13b3o17b3o17b3o17b3o17bo2bo$25bo109bo19b
o19bo4bo14bo19b5o$4bo3bo3bo11b2o4bo83bo3bo15b2o4bobo11b2o4bo13b2o4bo
13b2o4bo13bo2bobo$25b4obo104b4obob3o10b4obo14b4obobobo10b4obo13bo2bo$
4bo3bobobo12bo4bo79bobobo3bobobo12bo4bo14bo4bobobo10bo4bo2bo11bo4bobo
11bo2bo2b2o$24b3o3bo103b3o3bobobo9b3o3bo2bo10b3o3bo3b2o8b3o3bobobo16b
3o$4bo7bo15bo81bo11bo15bo19bobo3b2o12bo19bo3bo12b5obo$200bobo$4bo3bobo
bo97bobobo3bobobo12$obobo3bobobo13b3o17b3o61bobobo3bobobo13bo2bo16b3o
17bo2bo16bo2bo$25bo19bo4bo84b5o15bo19b5o15b5o$4bo3bo3bo11b2o4bo13b2o4b
o63bo3bo15bo2bobo14b2o4bo13bo2bobo14bo2bobo$25b4obo14b4obo83bo2bo17b4o
bo13bo2bo16bo2bo$obobo3bo3bo12bo4bo14bo4bo59bobobo3bobobo11bo2bo2bo14b
o4bo13bo2bo2bo13bo2bo2bo$24b3o3bo13b3o3bo103b3o3bobo$o7bo3bo15bobo17bo
61bo7bo3bo13b4ob5o12bo3bobo11b4ob4o11b4ob2o$143b2o16b2o20b2o17b3o$obob
o3bobobo97bobobo3bobobo39bobo18bo16bobo12$obobo7bo13b3o81bobobo3bobobo
13b3o17b3o17b3o17b3o17bo2bo16bo2bo16b3o$25bo4bo104bo19bo4bobo12bo4bo
14bo19b5o15b5o15bo$4bo7bo11b2o4bo83bo7bo11b2o4bobo11b2o4bobo11b2o4bo
13b2o4bobo11bo2bobo14bo2bobo14b2o4bo$25b4obo104b4obobo12b4obob2o11b4ob
obo12b4obobo11bo2bo16bo2bo17b4obo$obobo7bo12bo4bo79bobobo7bo12bo4bob2o
11bo4bo3bo10bo4bo2b2o10bo4bob2o10bo2bo2bo13bo2bo2bo14bo4bo$24b3o3bo
103b3o3bo3bo9b3o3bo3b2o8b3o3bo2b2o9b3o3bo53b3o3bo$o11bo15bobo79bo11bo
15bobo3b2o12bo19bobo2bo14bo4bo11b5ob5o9b5ob4o13bobob3o$204bo18b2o18b2o
17bo$obobo7bo97bobobo7bo80bobo37bo18bo2bo$264bo11$obobo3bobobo13b3o17b
3o61bobobo3bobobo13b3o17b3o17b3o17bo2bo$25bo19bo89bo4bo14bo4bo14bo19b
5o$4bo7bo11b2o4bo13b2o4bo63bo3bo3bo11b2o4bo13b2o4bobo11b2o4bobo11bo2bo
bo$25b4obo14b4obo84b4ob3o2b2o8b4obob2o11b4obobo11bo2bo$obobo3bobobo12b
o4bobo12bo4bo59bobobo3bobobo12bo4bo2b3o9bo4bo14bo4bob2o10bo2bo2bo$24b
3o3bob2o10b3o3bobobo79b3o3bo4bo8b3o3bo2bo10b3o3bo$o11bo15bo4bo14bo4bo
56bo7bo3bo15bo19bobo3bo13bo4bo12b4o$54bo108bobo18bo16bo$obobo3bobobo
97bobobo3bobobo60bobo13b3obo$185bo14b2ob2o11$obobo3bo3bo13b3o17b3o17b
3o17bo2bo20bobobo3bobobo13b3o17b3o17b3o17b3o17b3o17b3o17b3o17bo2bo16bo
2bo$25bo19bo4bo14bo19b5o45bo4bo14bo19bo4bobo12bo4bo14bo4bo14bo19bo4bo
14b5o15b5o$4bo3bo3bo11b2o4bo13b2o4bo13b2o4bo13bo2bobo24bo3bo3bo11b2o4b
o13b2o4bobo11b2o4bobo11b2o4bo13b2o4bobo11b2o4bo13b2o4bo13bo2bobo14bo2b
obo$25b4obo14b4obobobo10b4obo13bo2bo47b4obobo12b4obob3o10b4obob2o11b4o
bo14b4obob2o11b4obo14b4obobobo9bo2bo16bo2bo$obobo3bobobo12bo4bobobo10b
o4bo2bo11bo4bo13bo2bo2b2o18bobobo3bobobo12bo4bob3o10bo4bo14bo4bo14bo4b
o3bo10bo4bo14bo4bo14bo4bo2bo10bo2bo2bo13bo2bo2bo$24b3o3bo2bo10b3o3bo3b
o9b3o3bobobo16b3o40b3o3bob3o9b3o3bobob2o8b3o3bo2bo10b3o3bo2bo10b3o3bo
2bo10b3o3bo2b2o9b3o3bo3bo$o11bo15bobo3bo13bo19bo4bo12b4obo18bo11bo15bo
bobo15bo3bo15bobo3bo13bobobobobo11bobo3bo13bobobo15bo17b4ob5o10b4o$74b
2o86bo2bo17bobo20bo16bobo16b4o12b3o22b2o16bo$obobo7bo97bobobo3bobobo
81b2o19bo16bobo14bo26bo12b3obo$259bo26b2o12b2obobo$304bo!

Infinite Growth

In terms of linear growth, this rule has a c/3d wick/pole stretcher:

Code: Select all

x = 9, y = 10, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
2b4o$2bo2b3o$bo3bo$6o2$3b4o$4b3o$4b3obo$8bo$8bo!

The pole stretched by the spaceship can act as a rock in some cases.

It also has puffers made of two interacting OWSSes, known by me to exist and found by FWKnightship:

Code: Select all

x = 332, y = 60, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
301b3o$10bo58b3o48bo179bo2bo$9b3o18b3o36bo2bo7bo38b3o57b3o56b3o62bo$8b
2obo18bo2bo35bo9b3o36b2obo57bo2bo55bo2bo57bo3bo$8b3o19bo38bo3bo4b2obo
36b3o58bo58bo60bo3bobo$8b3o19bo3bo32bobo3bo4b3o37b3o10bo47bo3bo54bo3bo
56bo3bo17b3o$8b3ob3o13bobo3bo34bo3bo4b3o37b3ob3o5b3o44bobo3bo11b3o38bo
bo3bo56bo3bo3bo12bo2bo$8b3ob3o15bo3bo30bo3bo3bo4b3ob3o33b3ob3o4b2obo
46bo3bo10bo2bo40bo3bo54bobo3bo3bo15bo$8b3ob3o11bo3bo3bo34bo3bo2bob3ob
3o33b3ob3o4b3o43bo3bo3bo13bo36bo3bo3bo56bo3bo3bo11bo3bo$4b3ob3ob3o11bo
3bo3bobo30bobo8b3ob3o29b3ob3ob3o4b3o43bo3bo3bobo7bo3bo36bo3bo3bobo50bo
3bo3bo3bo11bo3bobo$4b3ob3ob3o11bo3bo3bo36bo2b3ob3ob3o29b3ob3ob3o4b3ob
3o39bo3bo3bo9bo3bobo34bo3bo3bo13b3o36bo3bo3bo3bobo9bo3bo$4b3ob3ob3o11b
o3bo3bo3bo35b3ob3ob3o29b3ob3ob3o4b3ob3o39bo3bo3bo3bo5bo3bo36bo3bo3bo3b
o8bo2bo36bo3bo3bo3bo11bo3bo3bo$4b3ob3ob3ob3o5bobo3bo3bo3bo39b3ob3o29b
3ob3ob3o4b3ob3o37bobo3bo3bo3bo5bo3bo3bo30bobo3bo3bo3bo11bo36bo3bo3bo3b
o3bo5bobo3bo3bo$4b3ob3ob3ob3o7bo3bo3bo3bo39b3ob3ob3o25b3ob3ob3o4b3ob3o
39bo3bo3bo3bo3bobo3bo3bo32bo3bo3bo3bo7bo3bo34bobo3bo3bo3bo3bo7bo3bo3bo
$4b3ob3ob3ob3o3bo3bo3bo3bo3bo39b3ob3ob3o25b3ob3ob3o4b3ob3o35bo3bo3bo3b
o3bo5bo3bo3bo28bo3bo3bo3bo3bo7bo3bobo34bo3bo3bo3bo3bo3bo3bo3bo3bo$3ob
3ob3ob3ob3o3bo3bo3bo3bo3bobo35bob3ob3ob3o21b3ob3ob3ob3o4b3ob3o35bo3bo
3bo3bo3bo5bo3bo3bo28bo3bo3bo3bo3bobo5bo3bo36bo3bo3bo3bo3bo3bo3bo3bo3bo
bo$3ob3ob3ob3ob3o3bo3bo3bo3bo3bo37bo5b3o25b3ob3ob3ob3o4b3ob3ob3o31bo3b
o3bo3bo3bo5bo3bo3bobo26bo3bo3bo3bo3bo7bo3bo3bo30bobo3bo3bo3bo7bo3bo3bo
3bo$4b3ob3ob3ob3obobo3bo3bo3bo3bo37bo5bobo29b3ob3ob3o4b3ob3ob3o31bo3bo
3bo3bo3bo5bo3bo3bo28bo3bo3bo3bo3bo3bobobo3bo3bo36bo3bo3bobo5bo3bo3bo3b
o3bo$4b3ob3ob3o5b3o3bo3bo3bo3bobo73b3ob3ob3o4b3ob3ob3o35bo3bo3bo3bo5bo
3bo3bo3bo28bo3bo3bo3bobobo3bo3bo3bo34bobo3bo9bobo3bo3bo3bo3bo$8b3ob3o
5bo3bobo3bo3bo83b3ob3o4b3ob3ob3o33bobo3bo3bo5bo3bo3bo3bo3bo26bobo3bo3b
o7bo3bo3bo3bo40bobo5b2o2bo3bo3bo3bo3bo$8b3o19bo3bobo81b3o8b3ob3ob3o39b
o3bobo3bo3bo3bo3bo3bo32bo3bobo5bo3bo3bo3bobo36bo9bo3bo3bo3bo3bo3bo$10b
o17bobo89bo4b2o2b3ob3ob3o37bobo9bo3bo3bo3bo3bo30bobo11bo3bo3bo3bo48b3o
bo3bo3bo3bo$32bo96b3ob3ob3ob3o37bo7bo3bo3bo3bo38bo9bo3bo3bo3bo3bo52bo
3bo3bobo$20b3o53bo50bobo3b3ob3ob3o43bo5bo3bo3bobo44bobo3bo3bo3bo3bo50b
obo3bo$76bo54bob3ob3ob3o43b3obobo3bo49bo2bo3bo3bo3bo3bo56bobo$76bo49bo
2bo7b3ob3o43bo9bobo46bo3bo3bo3bo3bo3bo48bobo3bo$127bobo7b3o55bo50b3obo
3bo3bo3bo$20b3o103b3o10bo114bo3bo3bobo48b3o$127bo124bobo3bo$258bobo$
256bo$20b3o53bo$76bo168b2o$76bo167bobo$245bo$20b3o164bo$186b2o$187bo2$
76bo50bo$76bo50bo117b2o$76bo49b3o115bobo$245bo$313b3o4$76bo$76bo168b2o
$76bo167bobo$127bo117bo$126b3o4$76bo110bo$76bo108b3o57b2o$76bo110bo56b
obo$245bo$313b3o!

The only quadratic growth known is an infinitely expanding pattern with two OWSSes moving in opposite directions classified by Catagolue as "zz_REPLICATOR":

Code: Select all

x = 7, y = 4, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
bo3bo$o5bo$o5bo$7o!

The form shown above is the "cis-odd" form, which has both OWSSes on the same side and odd symmetry/length.

No breeders are currently known.

Variants and Rules

The only developed variant of Haven is Haven Minor (B3-ry4-ijkyz5eir6ain/S2-ac3-a4-aekrw5-ijqy6-ak), a variant of Haven with the UWSS and 2 TL-based high-period oscillators.

Rules:

1. The variant rule must not be explosive.

2. The variant rule must support Haven's LWSS, MWSS, HWSS, and OWSSes. In other words, it must be in the Havenspace (B3aijq4ant5ir6i/S2eik3ijnr <= rule <= B2i3-r4-i5-a67e8/S2-a3-a4-akrw5-ijqy6-ak), which has 36,028,797,018,963,968 (2^55) rules.

3. The variant rule must not be overly stable (like Flock, LowLife, or Morley). For a rule to be overly stable, its C1 soups in Catagolue must have an average lifespan of 40 generations or less. For reference, soups in Haven last an average of 168 generations, more than three times more than Life.

4. The variant rule must not contain infinitely-expanding one-sided OWSSes (infinitely-expanding two-sided OWSSes are practically omnipresent in Haven-like rules, but they are not very common in Haven).

You are also recommended to name the rule you pick, but you do not have to do so.

As long as a rule meets these four criteria, you may post it as a new subthread in this thread. Feel free to investigate such rules with the traditional search tools, but I must tell you that, on average, it takes apgsearch five minutes to process and upload ten thousand soups in Haven’s C1 census. Please be patient under such circumstances as there is nothing wrong with apgsearch. Otherwise, feel free to explore! If you're having trouble, pick one of the rules from this list and explore, name, and write about it as you please. Don't hesitate to suggest new rules for the list below, just as long as they meet the criteria above.

Unrecognized Havenrules:

- 4c Haven (B3-ry4acenqt5eir6-ek/S2-a3-a4cnq5aeknr6-ak) - 1TfH - MDA

- CheckerHaven (B3-ry4acnqt5eir6-ek/S2-a3-a4cnq5eknr6cin) - 4TfH - MDA

Recognized Havenrules:

- Haven Minor (B3-ry4-ijkyz5eir6ain/S2-ac3-a4-aekrw5-ijqy6-ak) - 11TfH - MDA

The Havenspace is fairly big, but it is quite hard to find quality rules in it. If you get stuck trying to find a new rule, I recommend starting at Haven and trying to add/remove transitions as necessary.

History

I started investigating this rule family around October 2025, when I decided, after reading the OWSS article on LifeWiki, to create rules which could support multiple kinds of OWSSes.

Then, around late November, I had the idea to mesh all of the resulting rules together, essentially creating a “Proto-Haven”. The resulting rule was B3-cenr4anrt5inr6i/S2eik34inrz5j.

However, the rule had a problem, seen with the simple pattern

Code: Select all

x = 5, y = 4, rule = B3-cenr4anrt5inr6i/S2eik34inrz5j
bobo$o2b2o$o$3o!

which grows infinitely and occurred rather frequently in my apgsearch sessions. I wanted to eliminate such patterns to make the rule maximally apgsearchable. Luckily, I found that adding S5a preserved most patterns, except for the small infinite growth.

I then developed another similar rule, which aimed to fix the original rule’s lack of long-lived chaotic behavior. The rule obtained was B3-cenr4anrt5ijnr6ai8/S2eik34inrz5aj6ein.

However, the rule had a few flaws, most notably its lack of support for the 10WSS, the 16WSS, and all (6N + 4 for N > 1)WSSes.

As such, I developed a slight reluctance to continue working on the rule.

That changed, however, in March 2026, when I opened one of my old OWSS files. Out of curiosity, I decided to see how the rule would behave if S3a were removed. The result was an almost-perfectly viable 2-state XWSS Haven.

I kept on tinkering with the rulestring, adding and removing transitions as I felt necessary, and after a few days of work, around March 21st, this rule popped out. It lacked flaws frequently seen in older versions of Haven, such as:

- Fast stabilization of random soups

- Frequent quadratic growth

- The existence of growing puffers with OWSS engines

- Being explosive

Contributors

- MDA

- vilc

- FWKnightship

- B468S02357

- ThePlayzr

Goals

- Find a 2c/5o spaceship (Found by vilc using LLSSS)

- Find c/6o (found by FWKnightship using qfind) and c/6d spaceships

- Find a (2,1)c/6 spaceship

- Find a breeder

- Apgsearch 5LWSS in Haven (done by FWKnightship), enumerate all 2-LWSS (done by me) and 2-c/5d collisions, and develop LWSS syntheses (3 developed by me)

- Find a natural oblique spaceship, RRO, gun, or puffer (like SilverLife's (6,1)c/91)

- Find an eater for the c/5d spaceship (found by me) or the xWSSes (excluding OWSSes)

- Prove or disprove the existence of UWSSes in the Havenspace (see Variants and Rules, Rule 2)

- Develop conduit and catalyst systems for this rule

- Prove Haven Turing-complete and build a computer in Haven

[vilc]

2c/5o spaceship (found with LLSSS).

Code: Select all

x = 23, y = 41, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
5bo11bo$3b2obo9bob2o$3bob3o7b3obo$4bob2o7b2obo$2b2ob13ob2o$3b2obob2obo
b2obob2o$2b4obob5obob4o$4b3o4bo4b3o$2b2obo3bobobo3bob2o$2ob2ob11ob2ob
2o$bobob2obo5bob2obobo$2bo7b3o7bo$3b2obo9bob2o2$5b3o7b3o$3bobo4b3o4bob
o$2b3o2bo7bo2b3o$2bo3b3o2bo2b3o3bo$3bo2b11o2bo$9b5o$5b2ob2o3b2ob2o$5bo
b2o5b2obo$6bo9bo$5b3o7b3o$5b2o9b2o$5bobob5obobo$7bo2b3o2bo$10b3o$6bo2b
5o2bo$7bo7bo$6b3ob3ob3o$6b2o7b2o$6bo9bo$7b2obobob2o$5bo5bo5bo$7b2obobo
b2o$9bo3bo$7bo3bo3bo$5bo2b2obob2o2bo$8b2o3b2o$7b3o3b3o!

[MDA]

Thank you!

This particular speed had been giving qfind and ikpx2 some trouble, so it's nice to see such a spaceship completed!

I will be updating the goals shortly. (Done)

[FWKnightship]

Some c/2 puffers with different period:

Code: Select all

x = 332, y = 60, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
301b3o$10bo58b3o48bo179bo2bo$9b3o18b3o36bo2bo7bo38b3o57b3o56b3o62bo$8b
2obo18bo2bo35bo9b3o36b2obo57bo2bo55bo2bo57bo3bo$8b3o19bo38bo3bo4b2obo
36b3o58bo58bo60bo3bobo$8b3o19bo3bo32bobo3bo4b3o37b3o10bo47bo3bo54bo3bo
56bo3bo17b3o$8b3ob3o13bobo3bo34bo3bo4b3o37b3ob3o5b3o44bobo3bo11b3o38bo
bo3bo56bo3bo3bo12bo2bo$8b3ob3o15bo3bo30bo3bo3bo4b3ob3o33b3ob3o4b2obo
46bo3bo10bo2bo40bo3bo54bobo3bo3bo15bo$8b3ob3o11bo3bo3bo34bo3bo2bob3ob
3o33b3ob3o4b3o43bo3bo3bo13bo36bo3bo3bo56bo3bo3bo11bo3bo$4b3ob3ob3o11bo
3bo3bobo30bobo8b3ob3o29b3ob3ob3o4b3o43bo3bo3bobo7bo3bo36bo3bo3bobo50bo
3bo3bo3bo11bo3bobo$4b3ob3ob3o11bo3bo3bo36bo2b3ob3ob3o29b3ob3ob3o4b3ob
3o39bo3bo3bo9bo3bobo34bo3bo3bo13b3o36bo3bo3bo3bobo9bo3bo$4b3ob3ob3o11b
o3bo3bo3bo35b3ob3ob3o29b3ob3ob3o4b3ob3o39bo3bo3bo3bo5bo3bo36bo3bo3bo3b
o8bo2bo36bo3bo3bo3bo11bo3bo3bo$4b3ob3ob3ob3o5bobo3bo3bo3bo39b3ob3o29b
3ob3ob3o4b3ob3o37bobo3bo3bo3bo5bo3bo3bo30bobo3bo3bo3bo11bo36bo3bo3bo3b
o3bo5bobo3bo3bo$4b3ob3ob3ob3o7bo3bo3bo3bo39b3ob3ob3o25b3ob3ob3o4b3ob3o
39bo3bo3bo3bo3bobo3bo3bo32bo3bo3bo3bo7bo3bo34bobo3bo3bo3bo3bo7bo3bo3bo
$4b3ob3ob3ob3o3bo3bo3bo3bo3bo39b3ob3ob3o25b3ob3ob3o4b3ob3o35bo3bo3bo3b
o3bo5bo3bo3bo28bo3bo3bo3bo3bo7bo3bobo34bo3bo3bo3bo3bo3bo3bo3bo3bo$3ob
3ob3ob3ob3o3bo3bo3bo3bo3bobo35bob3ob3ob3o21b3ob3ob3ob3o4b3ob3o35bo3bo
3bo3bo3bo5bo3bo3bo28bo3bo3bo3bo3bobo5bo3bo36bo3bo3bo3bo3bo3bo3bo3bo3bo
bo$3ob3ob3ob3ob3o3bo3bo3bo3bo3bo37bo5b3o25b3ob3ob3ob3o4b3ob3ob3o31bo3b
o3bo3bo3bo5bo3bo3bobo26bo3bo3bo3bo3bo7bo3bo3bo30bobo3bo3bo3bo7bo3bo3bo
3bo$4b3ob3ob3ob3obobo3bo3bo3bo3bo37bo5bobo29b3ob3ob3o4b3ob3ob3o31bo3bo
3bo3bo3bo5bo3bo3bo28bo3bo3bo3bo3bo3bobobo3bo3bo36bo3bo3bobo5bo3bo3bo3b
o3bo$4b3ob3ob3o5b3o3bo3bo3bo3bobo73b3ob3ob3o4b3ob3ob3o35bo3bo3bo3bo5bo
3bo3bo3bo28bo3bo3bo3bobobo3bo3bo3bo34bobo3bo9bobo3bo3bo3bo3bo$8b3ob3o
5bo3bobo3bo3bo83b3ob3o4b3ob3ob3o33bobo3bo3bo5bo3bo3bo3bo3bo26bobo3bo3b
o7bo3bo3bo3bo40bobo5b2o2bo3bo3bo3bo3bo$8b3o19bo3bobo81b3o8b3ob3ob3o39b
o3bobo3bo3bo3bo3bo3bo32bo3bobo5bo3bo3bo3bobo36bo9bo3bo3bo3bo3bo3bo$10b
o17bobo89bo4b2o2b3ob3ob3o37bobo9bo3bo3bo3bo3bo30bobo11bo3bo3bo3bo48b3o
bo3bo3bo3bo$32bo96b3ob3ob3ob3o37bo7bo3bo3bo3bo38bo9bo3bo3bo3bo3bo52bo
3bo3bobo$20b3o53bo50bobo3b3ob3ob3o43bo5bo3bo3bobo44bobo3bo3bo3bo3bo50b
obo3bo$76bo54bob3ob3ob3o43b3obobo3bo49bo2bo3bo3bo3bo3bo56bobo$76bo49bo
2bo7b3ob3o43bo9bobo46bo3bo3bo3bo3bo3bo48bobo3bo$127bobo7b3o55bo50b3obo
3bo3bo3bo$20b3o103b3o10bo114bo3bo3bobo48b3o$127bo124bobo3bo$258bobo$
256bo$20b3o53bo$76bo168b2o$76bo167bobo$245bo$20b3o164bo$186b2o$187bo2$
76bo50bo$76bo50bo117b2o$76bo49b3o115bobo$245bo$313b3o4$76bo$76bo168b2o
$76bo167bobo$127bo117bo$126b3o4$76bo110bo$76bo108b3o57b2o$76bo110bo56b
obo$245bo$313b3o!

Also, There is already a rule named Haven.

[B468S02357]

Code: Select all

x = 169, y = 145, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak:T169,148
169o4$169o4$169o4$169o4$169o2$10bo147bo2$11o147b11o2$12bo143bo2$13o143b
13o2$14bo139bo2$15o139b15o2$16bo135bo2$17o135b17o2$18bo131bo2$19o131b
19o2$20bo127bo2$21o127b21o2$22bo123bo2$23o123b23o2$24bo119bo2$25o119b
25o2$26bo115bo2$27o115b27o2$28bo111bo2$29o111b29o2$30bo53bo53bo2$31o51b
o3bo51b31o2$32bo49b5o49bo$82b5o$32o50b5o50b32o2$31bo48b9o48bo$81b7o$32o
48b9o48b32o2$33bo46b9o46bo$80b9o$34o45b11o45b34o2$35bo41b15o41bo$78b13o
$36o42b13o42b36o2$37bo38b17o38bo$77b15o$38o38b17o38b38o2$39bo36b17o36b
o$76b17o$40o35b19o35b40o2$41bo31b23o31bo$74b21o$42o32b21o32b42o2$43bo
28b25o28bo$73b23o$44o28b25o28b44o2$45bo26b25o26bo$72b25o$46o25b27o25b
46o2$47bo21b31o21bo$70b29o$48o22b29o22b48o2$49bo18b33o18bo$69b31o$50o
18b33o18b50o2$51bo16b33o16bo$68b33o$52o15b35o15b52o2$53bo11b39o11bo$66b
37o$54o12b37o12b54o2$55bo8b41o8bo$65b39o$56o8b41o8b56o2$57bo6b41o6bo$
64b41o$58o4b45o4b58o2$59bo3b43o3bo$64b41o$59obo3b41o3bob59o2$60b49o$61b
47o$169o4$169o4$169o4$169o4$169o!

Cool agarship i found

[MDA]

Some c/2 puffers with different period:

Code: Select all

…

These were the puffers I had mentioned in my first post. Thank you for finding some!

Also, There is already a rule named Haven.

I honestly didn’t know, but, in order to avoid confusion, outside of this thread, let’s avoid calling this rule Haven and call it MDA’s Haven to differentiate it from Moosey’s Haven (B2ce3any4ait5ey6i7e8/S2-n3-cikq4aert5eiy6ci8).

Thank you for contributing to this rule in Catagolue!

As for the agarship found by B468S02357, there is a much smaller one:

Code: Select all

x = 100, y = 97, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak:T100,100
100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o
3$49b2o$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$100o4$
100o4$100o4$100o!

This one is likely to be the smallest agarship possible.

Edit (June 11th, 2026, 3:48 PM): I found a poleeater for the c/3d polestretcher using ikpx2:

Code: Select all

x = 69, y = 68, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
3b2o$2b5o$b3o$2obo$b5o$b6o2$3bo3bo2$5bobobo2$9bobo2$11bobo2$13bobo2$
15bobo2$17bobo2$19bobo2$21bobo2$23bobo2$25bobo2$27bobo2$29bobo2$31bobo
2$33bobo2$35bobo2$37bobo2$39bobo2$41bobo2$43bobo2$45bobo2$47bobo2$49bo
bo2$51bobo2$53bobo3bo$58bob2o$55bob4o$58b3obo$57bobo2bo$57b2obobo$57bo
2b2obo$59b7o$63b4o$62bobo3bo$62bobo3bo$63bo3b2o$64bo3bo!

[FWKnightship]

My LLSSS search for c/6d ended with no results after 59992 seconds, command:

Code: Select all

./rlife llsss-recentering-wao --rule 'B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak' --left-edge gse --wao-left-edge-errors --pre-reify-autochoke 15GB c6d-f2b '@bg' 10 |  tee output4.txt

Final partial:

Code: Select all

x = 97, y = 98, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
7bo$5bo$b2ob2o2b2o$bo3b3ob2o$b5o2b3o$2bo5b2o$bo3b2obo$3o2b3o4bo$bo4b4o
3b2o$bo2b2ob2obo2b3o$bo2bo2b2ob2obobo$b3obobobo2b3o2b3o$3b5obo2b2o3b3o
$3b3o4bo2bob2ob2o$6b3obob4o2b2o$6bobo2b3o2bo3bo$8bo2b2ob2o5b2o$7b2o2b
2ob4obo2bo$8bob2o5b2o3b5o$9bo4bobo3b2o2b3o$14bob2o2b3ob3o$14bobobo2bo
2b2o$11bo3b3o2bo3bobo$15bo4bo2b2ob2o$13b7o3bo2bo$19b2obobo3b3o$19bobo
3b2obob2o$19bobo2b2ob2o$23b2o3bobo$24b5o3bo$23bo2bo2bo2b2o$23bo8b3o$
24bob4obob2obo$31b2o3b3o$28b3o2bo2b4o$30b2obo2bo4bo$29b2o3bob3o$31b4ob
o2b2obo$32b2o8b2o$32bob3obo2b2ob2o$34bob2o2b2ob2o$34b2ob2o2bo3b2ob3o$
35bob3ob3obo6bo$35bo3b9o3b2o$40bob2obob2o2bo$36b4obob2obo3bo$37b4o2b2o
3bob3o$37b3o3b2o6b4ob2o$41b3o5bo2b2o2b2o$40bob2o8b4ob2o$41b2obo11bobo$
41bo4bo10b2o$42b4obo8bobo3bo$41bo5b2o4bob3o$42b2o3b2o2b6obobo3bo$44bo
2b5obo3b3o4bo$44b2o3b3o5b2obo2b2o$46b2obobo4b2ob3obo3b2o$48b2o4bo7b3ob
2obo$53b3obo3bo2bo3bo$48b4o2bob3o6b2o$49b7o2bo4bo5bo2bo$49b5obo2b3ob2o
3b3o5bo$53b2obo3b2o6b3obobobo$57bo3b3obo2bo3bo4bo$54bo2bo2b6o2bo2b2o2b
o$57bob6o2b2obob3o2b2o$54bo6bo2b2o2bob2o$54bo2bo4b2obobo3b3obobo$56bo
3bob2obo2bo3b2o2bob3o3b2o$55b2ob3obo4b2obo2bo7bo2bo$59bo4bob4o3b2o2bob
obo2b3o$62b2o3bo3b3o2bobo3bob2o2b2o$62b2o3bo2b4o2b3o3bo2b4o2bo$62b3o3b
2ob2ob5obobobobo3bo$62b2o2bobob3o2b2o2b4o3b3obobo$62b2ob4obo2bo4bob2o
2bo2bob2o$61bo6bobo4bob2o2b3ob2o2b3o$64b5o4b2obob3o3b3o4b4o$62bo3b3o2b
3o3b4o2bob2o2b2obo2b2o$65bo4b3obob6ob3o3bob2o2bo$69bo3bo3b3ob4o2b3obo$
66b2o6bo2bo2bo5bob3obo$69bo2bo5b2o4b4o2b3o$68b2o2bo3bo2b3o3b2o3b2o$68b
2obo2b3obobobo6b2o$68bo2b4obob5o2bo2b2o$68b2o3bob3o4b2o3b2o$69bo4bobob
o2b4o2bo$72b4obo2bob2obo$71bo3b3o2bobobo$71b2o2b2ob6o$72bo3b6o$73bo4b
2o$74b5obo$75bo3bo$76bo$77bo!

I decide to try again with a larger mid-step value.

Also, here is a simple script that repeatedly run apgluxe, wait for it ends, if it is not end after a given time, kill it, then run it again.

apg_runner.txt

(2.88 KiB) Downloaded 8 times

(It seems that upload .py files are not allowed)

I think it is useful for apgsearching rules that sometimes explodes like this one.

How to use: put it in the folder where apgluxe exists, then run:

Code: Select all

python3 apg_runner.py -n 5000 -t 200 -k $APGKEY # replace $APGKEY with your own key.

I tried to place my python script in a code tag, but I always receive 403 error when I try to preview or submit my post (I even lost all the texts I typed and can't recover it), so I uploaded it as an attached file.

[MDA]

My LLSSS search for c/6d ended with no results after 59992 seconds, command:

Code: Select all

…

Final partial:

Code: Select all

…

That’s quite a big partial, FWKnightship! It may be possible to find a c/6d spaceship by extending it using ikpx2 if its rows aren’t too big. I’m also excited to know how this next search will progress.

Also, here is a simple script that repeatedly run apgluxe, wait for it ends, if it is not end after a given time, kill it, then run it again.

[…]

That’s also quite a good solution. Apgluxe can often get stuck on zz_REPLICATORs overnight, so in those cases killing the search and restarting it is the best way to go. I’d be interested to know if you have followed my recommendation about apgsearching 5LWSS_stdin? It may require some work, since the LWSS in Life is:

Code: Select all

x = 5, y = 4, rule = B3/S23
bo2bo$o$o3bo$4o!

But the LWSS in Haven is:

Code: Select all

x = 5, y = 4, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
bo$o3bo$o$4o!

But I’m still confident that modifying the 5LWSS code and apgsearching its output is possible, so I’d like to see someone try!

Edit (June 14th, 2026, 10:43 AM): I just realized that this thread now has more posts than the thread about Moosey′s Haven.

Edit (June 14th, 2026, 11:53 AM): Thank you for apgsearching 5LWSS_stdin, FWKnightship!

Edit (June 15th, 2026, 7:00 AM): Thanks to your great work, we now have a 3-LWSS synthesis for the cis-odd expanding OWSS:

Code: Select all

x = 50, y = 25, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
3bo$o3bo$4bo$b4o2$46bo$45bo3bo$45bo$45b4o12$24b3o$23bo2bo$26bo$26bo$
24bo!

And a 6-LWSS synthesis for this 14-bit still-life (5 LWSSes, with an extra one for cleanup):

Code: Select all

x = 246, y = 19, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
242bo$241bo3bo$241bo$241b4o4$22bo$19bo3bo$23bo$20b4o23bo$44bo3bo45b2o$
48bo44b2ob2o$29b2o14b4o45b3o$29b3o63b2o$b4o23b2ob2o$4bo25b2o$o3bo$3bo!

And a 3-LWSS synthesis for the bi-blinker (with added component):

Code: Select all

x = 97, y = 36, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
2b2o92bo$2ob2o91bo$b3o90bobo$b2o91bo$94bo13$91b3o$90bo2bo$93bo$93bo$
91bo$33bo$32b3o$32bob2o$33b3o$33bo5$29b3o$29bo2bo$29bo$29bo$31bo!

[ThePlayzr]

And a 3-LWSS synthesis for the bi-blinker (with added component):

Code: Select all

x = 97, y = 36, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
2b2o92bo$2ob2o91bo$b3o90bobo$b2o91bo$94bo13$91b3o$90bo2bo$93bo$93bo$
91bo$33bo$32b3o$32bob2o$33b3o$33bo5$29b3o$29bo2bo$29bo$29bo$31bo!

Useless, but can be extended:

Code: Select all

x = 10, y = 52, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
9bo$9bo$7bobo$7bo$7bo13$4b3o$3bo2bo$6bo$6bo$4bo6$3b3o$2bo2bo$5bo$5bo$
3bo6$2b3o$bo2bo$4bo$4bo$2bo6$b3o$o2bo$3bo$3bo$bo!

Anyway, I made a SKOP collection, including a p3 found with RLS:

Code: Select all

x = 78, y = 45, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
25b2o$25bobo2b2o31b2o$26bo2bo2bo29bob2o5bo2bo$b2o10bo13b4o2bo5bo3bo19b
2o6bo2bo$obo10bo17b2o6bo2b2o27bo2bo$bo11bo13bobo9bobobo27bo2bo$26bob2o
b2o$27b2obo2bo$31b2o5$8b3o4b3o$7bobo6bobo$8b2o6b2o7b2o$bo8bo4bo10b2o$
b2o7bo4bo11bobo$bo6b2o6b2o11b3o$7bobo6bobo12bo26b2o2b2o2b4o2b2o2b2o$8b
3o4b3o41bo3bo8bo3bo$59bo3bo8bo3bo$58b2o2b2o2b4o2b2o2b2o5$29bo$27b5o$26b
o2bo2bo$26bobobobo8bo$25b3obob3o6b3o$26bobobobo8b3o$26bo2bo2bo9bo$27b
5o$29bo7$30b2o$27bobobo$30b2o!

The left is the full SKOP rows, and the right are high-period extras.
Unfinished, need to add LCMs.

[FWKnightship]

My LLSSS search for c/6d ended with no results after 59992 seconds, command:

Code: Select all

./rlife llsss-recentering-wao --rule 'B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak' --left-edge gse --wao-left-edge-errors --pre-reify-autochoke 15GB c6d-f2b '@bg' 10 |  tee output4.txt

I changed the mid-step to 13, still no results after 95085 seconds, final partial:

Code: Select all

x = 108, y = 110, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
7bo$5bo$b2ob2o2b2o$bo3b3ob2o$b5o2b3o$2bo5b2o$bo3b2obo$3o2b3o4bo$bo4b4o
3b2o$bo2b2ob2obo2b3o$bo2bo2b2ob2obobo$b3obobobo2b3o2b3o$3b5obo2b2o3b3o
$3b3o4bo2bob2ob2o$6b3obob4o2b2o$6bobo2b3o2bo3bo$8bo2b2ob2o5b2o$7b2o2b
2ob4obo2bo$8bob2o5b2o3b5o$9bo4bobo3b2o2b3o$14bob2o2b3ob3o$14bobobo2bo
2b2o$11bo3b3o2bo3bobo$15bo4bo2b2ob2o$13b7o3bo2bo$19b2obobo3b3o$19bobo
3b2obob2o$19bobo2b2ob2o$23b2o3bobo$24b5o3bo$23bo2bo2bo2b2o$23bo8b3o$
24bob4obob2obo$31b2o3b3o$28b3o2bo2b4o$30b2obo2bo4bo$29b2o3bob3o$31b4ob
o2b2obo$32b2o8b2o$32bob3obo2b2ob2o$34bob2o2b2ob2o$34b2ob2o2bo3b2ob3o$
35bob3ob3obo6bo$35bo3b9o3b2o$40bob2obob2o2bo$36b4obob2obo3bo$37b4o2b2o
3bob3o$37b3o3b2o6b4ob2o$41b3o5bo2b2o2b2o$40bob2o8b4ob2o$41b2obo11bobo$
41bo4bo10b2o$42b4obo8bobo3bo$41bo5b2o4bob3o$42b2o3b2o2b6obobo3bo$44bo
2b5obo3b3o4bo$44b2o3b3o5b2obo2b2o$46b2obobo4b2ob3obo3b2o$48b2o4bo7b3ob
2obo$53b3obo3bo2bo3bo$48b4o2bob3o6b2o$49b7o2bo4bo5bo2bo$49b5obo2b3ob2o
3b3o5bo$53b2obo3b2o6b3obobobo$57bo3b3obo2bo3bo4bo$54bo2bo2b6o2bo2b2o2b
o$57bob6o2b2obob3o2b2o$54bo6bo2b2o2bob2o$54bo2bo4b2obobo3b3obobo$56bo
3bob2obo2bo3b2o2bob3o3b2o$55b2ob3obo4b2obo2bo7bo2bo$59bo4bob4o3b2o2bob
obo2b3o$62b2o3bo3b3o2bobo3bob2o4b2o$62b2o3bo2b4o2b3o3bo4bo3b2o$62b3o3b
2ob2ob5obobobobobo$62b2o2bobob3o2b2o2b4o4b3ob2o$62b2ob4obo2bo4bob2o2b
2o3b2o2b2o$61bo6bobo4bob2o2b3o2bo2bo3bobo2b3o$64b5o4b2obob3o3bob2ob2o
2bobo3b2o$62bo3b3o2b3o3b4ob3ob3o3bob3ob2ob2o$65bo4b3obob5o2bo2b3o4bobo
bobo$69bo3bo3b7o3b2o3b3o4bobobo$66b2o6bo2bo3bo2bo3b2o3b3o5b4o$69bo2bo
5b5obob2ob2ob4ob3o3b4o$68b2o2bo4bo2bo3bo2b2obo6bob2o4bobo$68b2ob2o3bob
5obo3bo2bo5b3o2bo3bo$68bo2bob3obo2bo3b2o5b3o4bob2obob2o$68b2o2bo2bobo
4b2obo3bo4b2ob4o3bo$69bo3b6o3bobo3b2obob2o2bo2bob2o$72bo2bo7b2o4b2o3bo
2bo2b2o$71bo2b2ob3o2bob2o2b2o3b2ob5obo$71b2obob6o2b3o2bobo5b3obo$71bob
o2b2o3bo3b3ob3o2bob3obo$71bo2bo6b4obo2bobo3bobobo$72b3o3bo3b3obo3bobob
obo$74b2o2bo4bo3bo2b2o3bobo$74b2ob2o3bo5bo2bo2bobo$76b4o4b2o$75b3o3b3o
2b3o2bo$75b2ob2o3b2obo2b5o$77b2obo2b2o2bobobo$78b2o2b5ob2obo$78bo2bobo
3b2obo$78bo6b2o$78bobobob2ob2o$79b3ob2ob2o$79bo3b2obo$85bo$82bo$83bo!

I cannot continue the search now because there are currently no free machines on the cloud computing platform I uses.

Also, here is the python script I uses for search 5LWSS_stdin.

five_lwss.txt

(1.72 KiB) Downloaded 8 times

[MDA]

[…]

Useless, but can be extended:

Code: Select all

…

Anyway, I made a SKOP collection, including a p3 found with RLS:

Code: Select all

…

A p3 has also occured in Catagolue’s D8_1 census, but it isn’t minimal.

Edit (June 15th, 2026, 2:09 PM): I didn’t know we already had a P7 in Haven. Thank you for bringing it to my attention, ThePlayzr!

The left is the full SKOP rows, and the right are high-period extras.
Unfinished, need to add LCMs.

If you decide to polish up the SKOP table, I would like to hear your suggestions regarding the still-life font for the table.

I changed the mid-step to 13, still no results after 95085 seconds, final partial:

Code: Select all

…

I cannot continue the search now because there are currently no free machines on the cloud computing platform I uses [sic].

Since your 13-mid-step partial isn’t much longer than your previous one, I have a feeling that c/6d is going to be a tough nut to crack. Once your cloud computing platform has a free machine available for you to use, I’d recommend searching for c/6o, (2,1)c/6, or 2c/7d spaceships. Alternatively, you could redo those searches using ikpx2, if reasonable. I am also willing to hear what you have to say regarding the searches you want me to do.

Also, here is the python script I uses [sic] for search 5LWSS_stdin.

[…]

Thank you for uploading it! Now more people can contribute to the development of LWSS syntheses in Haven.

Edit (June 15th, 2026, 2:13 PM): Congratulations for finding the P7 brought to my attention by ThePlayzr!

Edit (June 15th, 2026, 4:13 PM): Accidentally-discovered OWSS flotilla with checkerboard agar:

Code: Select all

x = 74, y = 77, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
18b5o2$16bo7bo2$16b13o22b8o$51b8o$15bo14bo19b9o2$17b18o15bob13o$52b13o
$15bo20bo11bobob13o2$15b26o5bobobobob17o$54b18o$14bo27bobobobobobob16o
b2o$70b2o$15b32obobobobob12o$56b12o$13bo34bobobobob12o2$13b40obobob4o$
58b4o$11bo42bobob4o2$11b48o2$9bo50bo2$9b56o2$7bo58bo2$7b64o$72bo$5bo
67bo$73bo$5b69o2$3bo65bo2$3b65o2$bo61bo2$b61o2$o56bo2$2b54o2$2bo48bo2$
4b46o2$4bo40bo2$6b38o2$6bo32bo2$6b32o2$5bo27bo2$7b25o2$6bo20bo2$8b18o
2$8bo12bo2$10b10o2$10bo4bo2$12b2o!

Edit (June 16th, 2026, 3:05 PM): All 2-LWSS collisions in Haven (87 in total):

Code: Select all

x = 589, y = 307, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-akHistory
160.30F250.30F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F
28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F
28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.
F$160.F28.F231.A18.F20.A7.F$160.F28.F151.A39.A38.A3.A15.F19.A3.A4.F$
160.F28.F71.A39.A38.A3.A35.A3.A35.A19.F19.A8.F$160.F20.A7.F31.A38.A3.
A35.A3.A35.A39.A39.4A16.F19.4A5.F$101.A39.A18.F19.A3.A4.F30.A3.A35.A
39.A39.4A36.4A56.F28.F$7.A13.A26.A12.A25.A12.A3.A23.A11.A3.A15.F6.A
12.A8.F18.A11.A26.A12.4A24.A11.4A23.A40.A38.A32.F7.A20.F$4.A3.A11.A3.
A20.A3.A10.A3.A19.A3.A11.A24.A3.A10.A19.F3.A3.A11.4A5.F15.A3.A10.4A
20.A3.A36.A3.A34.A3.A36.A3.A34.A3.A31.F4.A3.A19.F$8.A11.A28.A10.A27.A
11.4A25.A10.4A16.F7.A20.F19.A38.A40.A38.A40.A38.A31.F8.A19.F$5.4A11.
4A22.4A10.4A21.4A37.4A30.F4.4A20.F16.4A35.4A37.4A35.4A37.4A35.4A31.F
5.4A19.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$
160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.F28.F
250.F28.F$160.F28.F250.F28.F$160.F28.F250.F28.F$160.30F250.30F2$500.
4A$420.4A36.4A36.A$340.4A76.A39.A39.A3.A$260.4A36.4A36.A79.A3.A35.A3.
A36.A$180.4A36.4A36.A39.A39.A3.A76.A39.A$7.A40.A38.A12.4A24.A11.4A23.
A12.A27.A11.A26.A12.A3.A23.A11.A3.A22.A13.A65.A40.A38.A$4.A3.A11.4A
21.A3.A10.4A20.A3.A11.A24.A3.A10.A23.A3.A11.A3.A20.A3.A10.A3.A19.A3.A
12.A23.A3.A11.A22.A3.A75.A3.A36.A3.A34.A3.A$8.A11.A28.A10.A27.A11.A3.
A24.A10.A3.A23.A12.A27.A11.A26.A40.A38.A79.A40.A38.A$5.4A11.A3.A21.4A
10.A3.A20.4A12.A24.4A11.A23.4A37.4A35.4A37.4A35.4A76.4A37.4A35.4A$21.
A39.A3$380.4A$380.A$380.A3.A$368.A12.A$365.A3.A$369.A$366.4A2$501.2A$
421.2A77.2A.2A$341.2A77.2A.2A76.3A$261.2A77.2A.2A76.3A78.2A$181.2A77.
2A.2A76.3A78.2A$7.A79.A13.2A64.A12.2A.2A62.A13.3A63.A14.2A63.A79.A$4.
A3.A12.2A61.A3.A11.2A.2A59.A3.A12.3A60.A3.A13.2A60.A3.A75.A3.A75.A3.A
$8.A11.2A.2A63.A12.3A64.A13.2A64.A79.A79.A79.A$5.4A12.3A61.4A13.2A61.
4A76.4A76.4A76.4A76.4A$22.2A11$422.2A$342.2A77.3A$262.2A77.3A76.2A.2A
$182.2A77.3A76.2A.2A76.2A$102.2A77.3A76.2A.2A76.2A$7.A14.2A63.A13.3A
63.A12.2A.2A62.A13.2A64.A79.A$4.A3.A12.3A60.A3.A11.2A.2A59.A3.A12.2A
61.A3.A75.A3.A75.A3.A$8.A11.2A.2A63.A12.2A65.A79.A79.A79.A$5.4A12.2A
62.4A76.4A76.4A76.4A76.4A21$502.2A$501.3A$500.2A.2A$501.2A3$487.A$
484.A3.A$488.A$485.4A41$17.A59.A59.A59.A59.A59.A59.A59.A59.A59.A$19.A
26.A32.A26.A32.A26.A32.A59.A26.A32.A26.A32.A26.A32.A26.A32.A26.A32.A
26.A$19.A28.A30.A28.A30.A28.A30.A59.A28.A30.A28.A30.A28.A30.A28.A30.A
28.A30.A28.A$16.A2.A28.A27.A2.A28.A27.A2.A28.A27.A2.A56.A2.A28.A27.A
2.A28.A27.A2.A28.A27.A2.A28.A27.A2.A28.A27.A2.A28.A$17.3A25.A2.A28.3A
25.A2.A28.3A25.A2.A28.3A57.3A25.A2.A28.3A25.A2.A28.3A25.A2.A28.3A25.A
2.A28.3A25.A2.A28.3A25.A2.A$46.3A57.3A57.3A117.3A57.3A57.3A57.3A57.3A
57.3A2$543.A29.A$483.A29.A26.A3.A25.A3.A$423.A29.A26.A3.A25.A3.A29.A
29.A$363.A29.A26.A3.A25.A3.A29.A29.A26.4A26.4A$303.A29.A26.A3.A25.A3.
A29.A29.A26.4A26.4A$243.A29.A26.A3.A25.A3.A29.A29.A26.4A26.4A$183.A
56.A3.A25.A3.A29.A29.A26.4A26.4A$123.A29.A26.A3.A59.A29.A26.4A26.4A$
63.A29.A26.A3.A25.A3.A29.A56.4A26.4A$3.A29.A26.A3.A25.A3.A29.A29.A26.
4A$A3.A25.A3.A29.A29.A26.4A26.4A$4.A29.A26.4A26.4A$.4A26.4A$378.F10$
19.A59.A59.A59.A59.A59.A59.A59.A59.A59.A$17.A59.A59.A59.A59.A59.A59.A
59.A59.A59.A$17.A59.A59.A59.A59.A59.A59.A59.A59.A59.A$17.A2.A56.A2.A
56.A2.A56.A2.A56.A2.A56.A2.A56.A2.A56.A2.A56.A2.A56.A2.A$17.3A57.3A
57.3A57.3A57.3A57.3A57.3A57.3A57.3A57.3A3$543.A$483.A56.A3.A$423.A56.
A3.A59.A$363.A56.A3.A59.A56.4A$303.A56.A3.A59.A56.4A$243.A56.A3.A59.A
56.4A$183.A56.A3.A59.A56.4A$123.A56.A3.A59.A56.4A$63.A56.A3.A59.A56.
4A$3.A56.A3.A59.A56.4A$A3.A59.A56.4A$4.A56.4A$.4A12$18.A59.A59.A59.A
119.A59.A59.A59.A$18.3A57.3A57.3A57.3A117.3A57.3A57.3A57.3A$17.A.2A
56.A.2A56.A.2A56.A.2A116.A.2A56.A.2A56.A.2A56.A.2A$17.3A57.3A57.3A57.
3A117.3A57.3A57.3A57.3A$18.A59.A59.A59.A119.A59.A59.A59.A3$483.A$423.
A56.A3.A$363.A56.A3.A59.A$303.A56.A3.A59.A56.4A$300.A3.A59.A56.4A$
183.A120.A56.4A$123.A56.A3.A116.4A$63.A56.A3.A59.A$3.A56.A3.A59.A56.
4A$A3.A59.A56.4A$4.A56.4A$.4A2$258.A$258.3A$257.A.2A$257.3A$258.A6$
18.A59.A59.A59.A119.A59.A59.A59.A$16.3A57.3A57.3A57.3A44.A72.3A57.3A
57.3A57.3A$16.2A.A56.2A.A56.2A.A56.2A.A40.A3.A71.2A.A56.2A.A56.2A.A
56.2A.A$17.3A57.3A57.3A57.3A44.A72.3A57.3A57.3A57.3A$18.A59.A59.A59.A
42.4A73.A59.A59.A59.A3$483.A$423.A56.A3.A$363.A56.A3.A59.A$303.A56.A
3.A59.A56.4A$300.A3.A59.A56.4A$183.A120.A56.4A$123.A56.A3.A116.4A$63.
A56.A3.A59.A$3.A56.A3.A59.A56.4A$A3.A59.A56.4A$4.A56.4A$.4A2$258.A$
256.3A$256.2A.A$257.3A$258.A7$243.A$240.A3.A$244.A$241.4A16$226.A$
228.A$228.A$225.A2.A$226.3A8$213.A$210.A3.A$214.A$211.4A!

Edit (June 16th, 2026, 4:06 PM):

[…]

Code: Select all

…

The pole stretched by the [c/3d] spaceship can act as a rock in some cases.

[…]

c/5d eater:

Code: Select all

x = 13, y = 14, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
10bo$8b4o$9b4o$o9b2o$o10bo$obo2$2bobo2$4bobo2$6bobo$8bo$8bo!

It is agnostic to its own parity, thus making it suitable for future technology. On a side note, out of all known oscillators in this rule, I think the P116 is the most gosperizable. If anyone succeeds in making a gun with it, I’d like to see it!

Edit (June 17th, 2026, 9:34 AM): One per generation in Haven:

Code: Select all

x = 35, y = 11, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
16b2o10bo2bo$2b4o9b5o7b5o$2bo2b3o6b3o9bo2bobo$bo3bo7b2obo9bo2bo$6o8b5o
7bo2bo2bo$14b6o$3b4o21b5o$4b3o9bo3bo$4b3obo23bobo$8bo9bob3o11bo$8bo25b
o!

Edit (June 17th, 2026, 7:40 PM): I propose the c/5d be named “telegraphship” in reference to this larger spaceship

Code: Select all

x = 18, y = 18, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
2bo$2b3o$4o$b2o$bo2bo$5bo$6bo$7b2o$7b2o$9bo$10bo$11bo$12bo$13bo$14bo$
15b2o$15b2o$17bo!

which looks like a telegraph pulling a wire tagalong. This larger spaceship will get the name “wireship”.

Edit (June 18th, 2026, 6:21 PM): LLSSS found this minimal minpop-20 c/3o:

Code: Select all

x = 10, y = 7, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
6bo$5b3o$5bobo$5bobo$2bo2b2obo$2obo2bo2bo$bobo5bo!

Edit (June 18th, 2026, 8:52 PM): CheckerHaven now has a C1 census which revealed a C2/D2 p34:

Code: Select all

x = 6, y = 5, rule = B3-ry4acnqt5eir6-ek/S2-a3-a4cnq5eknr6cin
bo$ob2o$b4o$2b2obo$4bo!

And a period-doubling mechanism not present in Haven:

Code: Select all

x = 9, y = 5, rule = B3-ry4acnqt5eir6-ek/S2-a3-a4cnq5eknr6cin
bo$obo2bo2bo$bo3bo2bo$5bo2bo$5bo2bo!

Anyone interested in doing more research in this rule is welcome to do as much as they wish. CheckerHaven is also roughly 20 times more amenable to apgsearch than Haven.

[FWKnightship]

C/6o by qfind:

Code: Select all

x = 19, y = 143, rule = B3-ry4acenqt5eir6-ek/S2-a3-a4nq5aeknr6-ak
5b9o$5bo3bo3bo$4b2o3bo3b2o$9bo2$8bobo$5bo2bobo2bo$4b2o2b3o2b2o$bo5b2ob
2o5bo$o3bob2o3b2obo3bo$bobobob5obobobo$4bobo5bobo$3b3obo3bob3o$3b3obo
3bob3o$4bobo2bo2bobo$3bo2b7o2bo$3bo11bo$3bo3b2ob2o3bo$6bobobobo$4b5ob
5o3$5b2o5b2o$4bob2o3b2obo$3bob9obo$3bob2obobob2obo$2bo3bo2bo2bo3bo$2bo
3b7o3bo$4bobobobobobo$5bo2b3o2bo$4bobo5bobo$5b9o$5b3obob3o$4bob2o3b2ob
o$4b3o5b3o$9bo$8bobo$6b2obob2o$8bobo$7bo3bo$5bobo3bobo$4b3o5b3o$6b2o3b
2o$4bob2obob2obo$4bo4bo4bo$3b2o3b3o3b2o$3b2ob7ob2o$b2o2bo7bo2b2o$b2obo
2bo3bo2bob2o$3obo2bo3bo2bob3o$5bob5obo$2bob2o7b2obo$4bo9bo$9bo$6bo5bo$
5b2o2bo2b2o$8b3o$7bobobo$9bo$9bo$9bo$9bo2$3b2o4bo4b2o$4b11o$3b13o$3bob
o2bobo2bobo$b2ob2o7b2ob2o$bo3bobo3bobo3bo$2bobob2o3b2obobo$4bo4bo4bo$
4bob7obo$4bob7obo$4b2ob5ob2o$6b2obob2o$6bo5bo2$5bo2bobo2bo$5bo2b3o2bo$
5bo7bo$5bo7bo$5b2o5b2o$5bo2b3o2bo$8b3o$4bobob3obobo$4b2obobobob2o$3b2o
3b3o3b2o$3bo3b2ob2o3bo$4bobob3obobo2$4bo9bo$4b2o7b2o$4bo9bo$4bobo2bo2b
obo$5bobobobobo$3bobo2b3o2bobo$4b3o5b3o$3bo3bobobo3bo$4b4obob4o$9bo2$
7b5o$5bo3bo3bo$6b7o2$8b3o$4b2o7b2o$3b4o2bo2b4o$2bo2b3o3b3o2bo$b2o5b3o
5b2o$bo2bo9bo2bo$bo3b2o5b2o3bo$5bo2b3o2bo$5b9o$2b2o11b2o$3b2o9b2o$2b3o
b7ob3o$4bo9bo$2bob4o3b4obo$2bob2o7b2obo$bo3bobobobobo3bo$2bo5bobo5bo$
6b3ob3o$6b3ob3o$7b2ob2o$7bo3bo$9bo$7bo3bo$8bobo$9bo$7b5o2$8b3o$6b3ob3o
$5bobobobobo$4bo2bo3bo2bo$3bo11bo$2bo3bo2bo2bo3bo$2b6o3b6o$5b2o5b2o$3b
o11bo$6b2o3b2o$7bo3bo!

[MDA]

C/6o by qfind:

Code: Select all

…

Congratulations, FWKnightship! It seems you are very successful with these kinds of searches. The next step now is to try (2,1)c/6 or 2c/7d, but it would also be helpful to start researching Haven’s close variants. Two are currently mentioned on the LifeWiki page, one of which I investigated using qfind and found several speeds. However, I also think you should do the searches you think are necessary for Haven or its variants. I will be updating the article, the spaceship collection, and the goals for this rule.

Edit (June 24th, 2026, 11:31 AM): I think we should also focus on finding a p5 oscillator, given that we now have p1, p2, p3, p4, and p6 oscillators, but no p5s. I will probably run an osrc search today and post my results here.

Edit (June 24th, 2026, 3:28 PM): Currently running a P5 osrc search, changed LLS to osrc in previous edit.

Edit (June 25th, 2026, 7:15 AM): I found no P5 oscillators in my searches.

Edit (July 1st, 2026, 5:39 PM): CheckerHaven now has a 5LWSS census.

[MDA]

(Sorry for doubleposting, but it has been over a month since the last post was made.)

I rulegolfed this variant of Haven today to have the UWSS and be reasonably chaotic. Its level of activity is comparable to CheckerHaven, and has many interesting patterns nonexistent in Haven.

I am currently apgsearching this rule, and have found the following patterns:

There is a common evolutionary sequence in this rule, starting from the pre-traffic light:

Code: Select all

x = 3, y = 3, rule = B3-ry4-ijkyz5eir6ain/S2-ac3-a4-aekrw5-ijqy6-ak
bo$3o$bo!

This evolutionary sequence can be used to make oscillators of periods 19 and 132:

Code: Select all

x = 37, y = 26, rule = B3-ry4-ijkyz5eir6ain/S2-ac3-a4-aekrw5-ijqy6-ak
o3bobobo11bo3bobobo3bobobo2$o3bo3bo11bo7bo7bo2$o3bobobo11bo3bobobo3bob
obo2$o7bo11bo7bo3bo2$o3bobobo11bo3bobobo3bobobo11$4b3o18b3o$4bobo13b3o
2bobo$4b3o13bobo2b3o$20b3o$3o$obo$3o!

Other known periods include p7, p8, and p10.

There are known spaceships of speeds c/2o, 2c/4o, 2c/6o, c/5o, c/3d, and c/4d:

Code: Select all

x = 125, y = 50, rule = B3-ry4-ijkyz5eir6ain/S2-ac3-a4-aekrw5-ijqy6-ak
10bo29bo10bo19bo21bo23bo$9b4o26b2o9b3o17b3o20bo$8b2o27b2obo9bobo17bob
2o18b3o$6b2o2b4o23bob3o29bo20bobo19b2o3b2o$5bob2obo4bo17b6ob2o48b3ob3o
15b2ob5ob2o$5bobo2b3o19b5ob5o69b2o2b3o2b2o$4bo2b2o4bo2bo14b3o2bobobo
70b6ob6o$2b2o3b2ob3o2b2o13b4ob3obo3bo68bo4bo4bo$2b3o5b2obo2bo13b2o4b2o
3bo2bo67b4obob4o$bo3b2o3b3o3bo14b4o5b4o70b7o$ob2o3bo3b3ob2o14bo4bo5bob
o68bo2b3o2bo$7bob3o3bo18bo75bob3ob3ob3obo$3bo4b4o3bo16bobo75bobo3bobo
3bobo$4b4ob2o100b4o2bo2b4o$7b2ob2o100b2o2b3o2b2o$10bo2bo100bo5bo$7bo$
11bo102b3ob3o$9bo105bo3bo$114b2o3b2o2$114b2o3b2o$115b2ob2o$116bobo$
115b5o$114b7o$116bobo$114bo5bo$114b7o$113bob5obo$113b2obobob2o$113b2ob
obob2o$113b3obob3o$113b2o2bo2b2o$112b3o2bo2b3o$117bo$111b2o3b3o3b2o$
112b3o5b3o$111b3o7b3o2$112b2o7b2o2$113b2o5b2o$112bob2o3b2obo$111b5o3b
5o$113bo7bo$110b2obo2bobo2bob2o$110b2obo7bob2o$113b3o3b3o$113b2o5b2o!

The only known infinite growth patterns in this rule are the infinitely-expanding OWSSes; no linear-growth patterns are known.

Goals:

- Find c/3o and c/4o spaceships

- Find an oblique ship

- Find a puffer or other linear-growth pattern

Edit (July 21st, 2026, 2:04 PM): Changed post title from “Haven 2” to “Haven Minor”.