Holstein (B35678/S4678)

[LaundryPizza03]

A self-complementary rule with no still lifes and mostly even-period oscillators. OCA:Holstein at wiki.

Collection of odd-period oscillators I found in February
Holstein odd-period oscillators

p3:

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#C 2023-02-10
x = 10, y = 14, rule = B35678/S4678
4b2o$3b4o$2b6o$2b6o$10o$2b2o2b2o$4b2o$4b2o$2b2o2b2o$10o$2b6o$2b6o$3b4o
$4b2o!

p5:

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#C 2023-02-10
x = 27, y = 9, rule = B35678/S4678
3b3o16b2o$3b5obo10b5o$2b6ob3o2b2ob8o$3b10o2b4ob7o$11obob11obo$3b10o2b
4ob7o$2b6ob3o2b2ob8o$3b5obo10b5o$3b3o16b2o!

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#C 2023-02-15
x = 19, y = 12, rule = B35678/S4678
8b3o$4bob7obo$2bo3b7o3bo$2b15o$19o$ob15obo$ob15obo$19o$2b15o$2bo3b7o3b
o$4bob7obo$8b3o!

p7:

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#C 2023-02-15
x = 18, y = 16, rule = B35678/S4678
8b2o$7b4o$3b12o$4b10o$2b14o$b16o$b16o$18o$18o$b16o$b16o$2b14o$4b10o$3b
12o$7b4o$8b2o!

p9:

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#C 2023-02-15
x = 21, y = 14, rule = B35678/S4678
7b7o$4bob4ob4obo$5b11o$2bob13obo$4b13o$2b17o$21o$21o$2b17o$4b13o$2bob
13obo$5b11o$4bob4ob4obo$7b7o!

p15:

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#C 2023-02-16
x = 41, y = 14, rule = B35678/S4678
10bo19bo$9bobo17bobo$6bob6o13b6obo$4bob10o9b10obo$2bobob29obobo$3b35o$
ob37obo$ob37obo$3b35o$2bobob12o5b12obobo$4bob10o9b10obo$6bob6o13b6obo$
9bobo17bobo$10bo19bo!

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#C 2023-02-17
x = 21, y = 21, rule = B35678/S4678
10b2ob3o$4b3ob6o3bo$2bo3b13o$b17o$2b16obo$ob16obo$ob18o$19o$b19o$20o$
21o$b20o$b19o$2b19o$b18obo$bob16obo$bob16o$3b17o$2b13o3bo$3bo3b6ob3o$
5b3ob2o!

p17:

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#C 2023-02-12
x = 10, y = 10, rule = B35678/S4678
2bo2bo$3b2o$2bob4obo$2b5obo$ob7o$b7obo$bob5o$ob4obo$5b2o$4bo2bo!

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#C 2023-02-16
x = 19, y = 19, rule = B35678/S4678
6bo5bo$5bob5obo$4b5ob5o$4b11o$2b15o$b17o$ob15obo$b17o$b17o$bob13obo$b
17o$b17o$ob15obo$b17o$2b15o$4b11o$4b5ob5o$5bob5obo$6bo5bo!

p21:

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#C 2023-02-15
x = 25, y = 25, rule = B35678/S4678
11b3o$7bob7obo$7bob7obo$6b13o$6b13o$5b15o$3b19o$b23o$3b19o$b23o$b23o$
25o$25o$25o$b23o$b23o$3b19o$b23o$3b19o$5b15o$6b13o$6b13o$7bob7obo$7bob
7obo$11b3o!

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#C 2023-02-16
x = 53, y = 16, rule = B35678/S4678
5b2o39b2o$4b5o35b5o$2bob7o31b7obo$2b11o5b4o9b4o5b11o$2b13o2bo4b2ob3ob
2o4bo2b13o$2b49o$b51o$53o$53o$b51o$2b49o$2b13o2bo4b2ob3ob2o4bo2b13o$2b
11o5b4o9b4o5b11o$2bob7o31b7obo$4b5o35b5o$5b2o39b2o!

p25:

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#C 2023-02-16
x = 51, y = 14, rule = B35678/S4678
10bo13b3o13bo$9bobo2b10o3b10o2bobo$6bob35obo$4bob39obo$2bobob39obobo$
3b45o$ob47obo$ob47obo$3b45o$2bobob39obobo$4bob39obo$6bob35obo$9bobo2b
10o3b10o2bobo$10bo13b3o13bo!

p27:

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#C 2023-02-15
x = 16, y = 9, rule = B35678/S4678
3b10o$4b8o$2b12o$b14o$ob12obo$b14o$2b12o$4b8o$3b10o!

Spaceships

A user named Paintless dentisty just reduced the c/4o in Holstein:

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x = 19, y = 34, rule = B35678/S4678
7bo3bo$b6o5b6o$b4ob7ob4o$bo2bobob3obobo2bo$bobo2bo2bo2bo2bobo$bob2o9b2obo$2bo
2b2o2bo2b2o2bo$2bob2o7b2obo$4b11o$b4o2b2ob2o2b4o$bo3b9o3bo$2o3bobo3bobo3b2o$
2o3bobobobobo3b2o$obo4bo3bo4bobo$2bo6bo6bo$5bobobobobo$3b2o2bo3bo2b2o$2b2obo
2b3o2bob2o$4bob3ob3obo$6bo5bo$6bo5bo$6bo5bo$6bo5bo$5b4obo$5b4o$4b4o$8bo$5b3o$
3b2obobo$4b5obo$3b6o$4b5o$2bobob2o$6bobo!

[confocaloid]

Bounded universes, 16x16 torus

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#C p1376
x = 16, y = 16, rule = B35678/S4678:T16,16
bo4bobob4obo$b6obo6bo$b6obo6bo$8o$b6obo6bo$8o$8o$8o$ob4obobo4bo$o6bob
6o$o6bob6o$8b8o$o6bob6o$8b8o$8b8o$8b8o!

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#C p880
x = 16, y = 16, rule = B35678/S4678:T16,16
obo2bobobob2obo$o6bob6o$o6bob6o$8b8o$8b8o$o6bob6o$8b8o$8b8o$bob2obobob
o2bobo$b6obo6bo$b6obo6bo$8o$8o$b6obo6bo$8o$8o!

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#C p800
x = 16, y = 13, rule = B35678/S4678:T16,16
bo$4bo4bo5bo$8o$ob5ob4ob3o$9ob6o$16o$16o$16o$ob14o$4ob4ob5o$8b8o$bo5bo
4bo$9bo!

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#C p752
x = 16, y = 16, rule = B35678/S4678:T16,16
4b4o4b4o$bobobobobobobobo$4b4o4b4o$b3o3bob3o3bo$2obobo2b2obobo$2obobo
2b2obobo$4o4b4o$4o4b4o$4b4o4b4o$obobobobobobobo$4b4o4b4o$3obo3b3obo$ob
2o2bobob2o2bo$ob2o2bobob2o2bo$4o4b4o$4o4b4o!

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#C p488
x = 16, y = 16, rule = B35678/S4678:T16,16
4bo7bo$3ob2ob4ob2obo$3ob2ob4ob2obo$4o2b6o2b2o$b7ob7o$2bo4bo2bo4bo$2bo
4bo2bo4bo$2o6b2o$4bo7bo$3ob2ob4ob2obo$3ob2ob4ob2obo$4o2b6o2b2o$b7ob7o$
2bo4bo2bo4bo$2bo4bo2bo4bo$2o6b2o!

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#C p440
x = 16, y = 16, rule = B35678/S4678:T16,16
7o8bo$5obo6bobo$3ob2o5bo2b2o$obobo4bobob3o$o8b7o$o8b7o$o8b7o$o6bob6o$
7b8o$5bob6obo$3bo2b5ob2o$bobob4obobo$b8o$b8o$b8o$b6obo6bo!

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#C p384
x = 16, y = 16, rule = B35678/S4678:T16,16
o4b3ob4o$3bo4b3ob4o$8b8o$7b8o$8b8o$8b8o$8b8o$6b8o$b4o3bo4b3o$3ob4o3bo$
8o$7o8bo$8o$8o$8o$6o8b2o!

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#C p368
x = 16, y = 16, rule = B35678/S4678:T16,16
b2o6b2o2$3b3o5b3o2$16o$2o3b5o3b3o$16o$5o2b6o2bo$b2o6b2o2$3b3o5b3o2$16o
$2o3b5o3b3o$16o$5o2b6o2bo!

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#C p240
x = 16, y = 16, rule = B35678/S4678:T16,16
obobobobobobobo$obobobobobobobo$obobobobobobobo$3obo3b3obo$3bob3o3bob
3o$bobobobobobobobo$3bob3o3bob3o$obobobobobobobo$obobobobobobobo$obobo
bobobobobo$obobobobobobobo$obobobobobobobo$obobobobobobobo$obobobobobo
bobo$obobobobobobobo$obobobobobobobo!

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#C p237
x = 16, y = 16, rule = B35678/S4678:T16,16
7ob7o$2ob4ob2ob4o$7ob7o$b4obo2b4obo$2b2obo4b2obo$3bo7bo$o2bo4bo2bo$3bo
7bo$3ob7ob4o$b2ob4ob2ob4o$3ob7ob4o$2o2bob4o2bob2o$o4bob2o4bobo$7bo7bo$
2bo4bo2bo4bo$7bo7bo!

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#C p236
x = 16, y = 15, rule = B35678/S4678:T16,16
16o$3o2b6o2b3o$4ob7ob3o$o2b6o2b5o$5b2o6b2o$o7bo$o6b2o6bo2$16o$3o2b6o2b
3o$4ob7ob3o$o2b6o2b5o$5b2o6b2o$o7bo$o6b2o6bo!

[DroneBetter]

A user named Paintless dentisty just reduced the c/4o in Holstein:

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x = 19, y = 34, rule = B35678/S4678
7bo3bo$b6o5b6o$b4ob7ob4o$bo2bobob3obobo2bo$bobo2bo2bo2bo2bobo$bob2o9b2obo$2bo
2b2o2bo2b2o2bo$2bob2o7b2obo$4b11o$b4o2b2ob2o2b4o$bo3b9o3bo$2o3bobo3bobo3b2o$
2o3bobobobobo3b2o$obo4bo3bo4bobo$2bo6bo6bo$5bobobobobo$3b2o2bo3bo2b2o$2b2obo
2b3o2bob2o$4bob3ob3obo$6bo5bo$6bo5bo$6bo5bo$6bo5bo$5b4obo$5b4o$4b4o$8bo$5b3o$
3b2obobo$4b5obo$3b6o$4b5o$2bobob2o$6bobo!

This is me (the name is a reference to The Simpsons). I didn't want to reply only to say this while turning up emptyhanded, so I had been searching for a c/6 spaceship in ikpx2, but at present it has adaptively widened from logical width 10 in 58.98 MiB (though this does not provide an exhaustive proof of nonexistence, as far as I know), and then reached 121.05 MiB in width 11 (still fruitlessly).

In other news, I don't think any infinite growth patterns are known (per the wiki page). Overnight ikpx2 searching for c/5 spaceships yielded two distinct wickstretcher mechanisms, the smallest of which has a wick three solid cells wide beneath the 2-cell fuzz on either side, while the larger has only two solid cells.

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x = 29, y = 98, rule = B35678/S4678
21b2o$21b2o$19b6o$18b8o$18b8o$17b2o6b2o$17b10o2$15b14o$16b2o8b2o$18bo6bo2$18b8o$20bo2bo$19b6o$20b4o$19b6o$21b2o$20b3obo$19bob2obo$22b2o$20b5o$21bo$21b5o$22bo$22bobo$21bo2$22b2o2$20bobo$20bobo$20b2obo$21bo$20b2ob2o$23bo$19b6o$21b2obo$20b5o$20b5o$21b3o$21b4o$19b2obo$20bob2o$22bo$21bob2o$21bob3o$22b3o$20b6o$22b3o$21b5o$22b3o$20b6o$23b2o$6b2o12b6o$6b2o15b2o$4b6o11b5o$3b8o11b3o$3b8o10b5o$2b2o6b2o11b2o$2b10o8b6o$23b2o$14o7b5o$b2o8b2o9b3o$3bo6bo9b6o$23b2o$3b8o10b5o$5bo2bo14b2o$4b6o11bob3o$5b4o14bobo$4b6o13bo$6b2o15b4o$5b3obo14b2o$4bob2obo12b4o$7b2o14bobo$5b5o11b3o2bo$6bo18bo$6b5o11b4o$7bo14bobo$7bobo13b3o$6bo16bo$24b5o$7b2o17bo$25b4o$5bobo17b2o$5bobo15b4o$5b2obo$6bo15b3obo$5b2ob2o$8bo14b5o$4b6o14b2o$6b2obo13b4o$5b5o13b3obo$5b4obo11bob3o$4bob4o13b4o$5b6o11b4o$4bob3o15bob2o$6bo2bo13bobo!

[DroneBetter]

I created a new section in my userspace page, User:DroneBetter/qfind results#B35678/S4678_(Holstein), in which I found minimal-width odd- and even-symmetric spaceships for c/3, c/5 (for which the width-15 odd is in fact 100 cells, as opposed to the known width-14 even's 110), 2c/6 and c/7 (new speed :-), and that there is no odd- or even-symmetric c/4 thinner than the known width-21 one (though I am away from my most powerful computer so have not found its length to be minimal), here is a collection for it

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x = 173, y = 69, rule = B35678/S4678
3b5o3b5o8b5o3b5o8b5o4b5o8b5o4b5o8b5o5b5o7b5ob5o8b4o10b9o10b4o$2b3ob3ob3ob3o6b3ob3ob3ob3o6b3ob3o2b3ob3o6b3ob3o2b3ob3o9b4obob4o11b2obob2o8b8o7b4o3b4o8b6o$4b3o2bo2b3o10b3o2bo2b3o10b2o3b2o3b2o10b2o3b2o3b2o7b4ob2obobob2ob4o4b13o5b8o7b11o8b6o$2b3o4bo4b3o6b3o4bo4b3o6b2ob3o4b3ob2o6b2ob3o4b3ob2o5bob2obobobobobob2obo6b9o8bo4bo8b4o3b4o6b3o4b3o$b2ob5ob5ob2o9bo5bo9b3o5b2o5b3o4b3o5b2o5b3o4bobo4b2ob2o4bobo3b3o3b3o3b3o3b10o5bob4ob4obo3b4obo2bob4o$3b2o3b3o3b2o8bo2b3ob3o2bo6b4obo6bob4o4b4obo6bob4o6bo3bo5bo3bo9b3ob3o8bo6bo6bobo7bobo5b3o4b3o$4o2b7o2b4o7bob2ob2obo8b2o4b2o2b2o4b2o4b2o4b2o2b2o4b2o5bob3o7b3obo5b3o3bo3b3o4b10o5b2ob2o3b2ob2o4b12o$2o3bobobobobo3b2o4b3ob7ob3o4b4obo8bob4o4b2obo8bob2o9b3o5b3o24b2o8b2o22b4o2b4o$3bo3b5o3bo12bobobo12bo4bo2bo4bo10bobo4bobo9bobo2b7o2bobo11bo8b2obob4obob2o3b3o7b3o3bob2obo2bob2obo$ob2obo2bobo2bob2obo2bobo3b7o3bobo5bo2b2o4b2o2bo8b4o6b4o10b11o10b3o3b3o6bo8bo7b3o3b3o8bobo2bobo$b3o11b3o9bobobobo14bo2b2o2bo11b5ob2ob5o7b3o5bo5b3o9b5o9bob4obo7b3obobob3o4b2ob2o4b2ob2o$3b3o3bo3b3o5b3o2bob5obo2b3o4bob2ob2o2b2ob2obo5b7o4b7o4b3obob3ob3obob3o6bo3bo3bo23b4ob4o7b2o6b2o$3obo2b2ob2o2bob3o4b2obobo3bobob2o7bobo3b2o3bobo7b3o10b3o4b2obo3bo5bo3bob2o5b9o7b8o6b13o3b5o4b5o$b5o3bo3b5o3bo3bobob3obobo3bo3b2o3bo2b2o2bo3b2o4b5o8b5o5bo4bo5bo4bo9bo3bo12b2o11b9o5b3obo4bob3o$3obo2bobobo2bob3o3bo3b2o5b2o3bo3b2obo3b6o3bob2o3b3o12b3o5bo4bo5bo4bo8bob3obo9b6o8b11o4bobo8bobo$2b3o3bobo3b3o4b2ob2ob7ob2ob2o4b2o3bob2obo3b2o5b6ob4ob6o7b2obo5bob2o11bobobo10b6o9b9o7bobo4bobo$6obo3bob6o3b3ob9ob3o11b4o12b5o6b5o7bob2o2bobo2b2obo11b3o10bob4obo8bob5obo5b2obo6bob2o$b5obo3bob5o5bobo2b5o2bobo10bobo2bobo11b14o9b2o2b5o2b2o10b7o8bob4obo10b2ob2o8b3obo2bob3o$ob5o5b5obo4bo2b9o2bo12b4o14bo10bo10bo3bobobo3bo12b3o26bo2bobo2bo4b16o$b4o2b5o2b4o6b2o3b3o3b2o31bobob4obobo14bo3bo16b3o9b2ob4ob2o20b5o6b5o$ob5o5b5obo9b5o37bo6bo14bobo3bobo42bobo5bobo4b3ob6ob3o$b5o2b3o2b5o5bo2bo2b3o2bo2bo35b2o13bo3bobo3bobo3bo24b6o22b2ob2o6b2ob2o$ob3o2bo3bo2b3obo6b11o53b6o3b6o38b4o5b4o8b4o$3ob2o7b2ob3o3b2ob11ob2o34b2o12b3ob2obo3bob2ob3o25b2o26bobo6bobo$2bo13bo7b13o50bo3bo9bo3bo37b4obob4o7b8o$22bo2b11o2bo50b5o5b5o40b3obob3o6bo3b4o3bo$26b3o3b3o56b3o5b3o40b13o4b5o2b5o$25bob3ob3obo55b5ob5o42b9o9bob2obo$26bo7bo56b3o5b3o40b13o5b10o$93b2o3b2o44b9o9bo4bo$90b4ob3ob4o41b9o8b8o$90b3o7b3o43b5o12bo2bo$92b4ob4o46b3o10b10o$94b2ob2o65b2o$94b5o62bobo2bobo$93b7o$95b3o62b2o2b2o2b2o$95b3o61b3obo2bob3o$95b3o62b10o$158bob10obo$96bo61bob10obo$94bobobo60b12o$94b5o61b10o$92bobobobobo60b8o$94bobobo61bobob2obobo$94b5o$94b5o62b8o$93bob3obo$94b5o61b10o$92bob5obo61b2o2b2o$92bob5obo59b2ob4ob2o$90b13o60bo2bo$90b13o$89b15o$89b15o$89b6obob6o$90b5obob5o$90bobo7bobo$90bob3o3b3obo$90bobo7bobo$90bob3o3b3obo2$93b7o$92b2obobob2o$94b2ob2o$92b3obob3o$94bobobo$92b3obob3o$94b2ob2o!

despite my c/7 I have not found a c/6, and suspect that in general, of speeds with odd displacements, those with odd period will be easier to find in this rule, since spaceships seem often to contain internal lateral zebra stripes (which strobe unlike Life, due to B6 and no S2), so even period would require working without them or phase-inverting them each period