B34/S267

[Extrementhusiast]

I am currently writing an Essay on this rule (but it's under construction). Two oscillators act as in Life, one is also an oscillator in Life but it oscillates differently, and about 20 are not oscillators in Life. I again would like a census for this rule, because, like B3/S013, B34/S267 also stabilizes quickly.

[gameoflifeboy]

I decided to census this rule on Catagolue today. One of the things I found was a p68:

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x = 5, y = 7, rule = B34/S267
2bo$bo$2bobo$o3bo$2bobo$bo$2bo!

There are also 3 period 10 oscillators. One has C1→C2_1 symmetry, one has C2_4→D4_x4 symmetry, and one has D2_x→D4_x4 symmetry.

[Saka]

Some oscillators

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x = 30, y = 4, rule = B34/S267
10bo2bo5b2o5b3o$b2o8b2o8bo7bo$o2bo7b2o6bo7b2o$o2bo6bo2bo6b2o!

[danieldb]

A cool p2 that some of these rules have. I call it "toadgether":

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x = 4, y = 6, rule = B34/S267
b2o$o$3bo$b2o$b2o$bo!

[velcrorex]

c/5 orthogonal ship

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x = 15, y = 45, rule = B34/S267
3b2obobob2o$b2o4bo4b2o$b2o4bo4b2o$bo4b3o4bo$2bobob3obobo$2bo4bo
4bo$4bo5bo$5bo3bo$5b2ob2o2$6bobo$2bo9bo$o2bob5obo2bo$o2b2o5b2o2b
o$bo5bo5bo$bo11bo$4b7o$b2o2bo3bo2b2o$2bo2bo3bo2bo$bobobo3bobobo$
4b2o3b2o$4b3ob3o$3bo2bobo2bo$o2bob2ob2obo2bo$o2bo7bo2bo$b3obobob
ob3o$2bo2bo3bo2bo$5bobobo2$2b4o3b4o$2bob7obo$7bo$4bo5bo$3bo7bo$4b
obobobo2$6b3o$6b3o$6bobo$4bo5bo$3b2o5b2o$4bob3obo$5bo3bo$5bo3bo$
7bo!

[gameoflifeboy]

A cool p2 that some of these rules have.

It can be extended:

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x = 4, y = 18, rule = B34/S267
b2o$3bo$o$b2o$b2o$3bo$o$b2o$b2o$3bo$o$b2o$b2o$3bo$o$b2o$b2o$2bo!

There are also other edge stabilizations:

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x = 17, y = 7, rule = B34/S267
o$2ob2obo3bo3bo$o3b2o2b2o2b2o2bo$bo2b2o2b2o2b2o2bo$b3o3bo3bo3bo$2b2o$
2bo!

[velcrorex]

c/6 orthogonal

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x = 15, y = 53, rule = B34/S267
4bo5bo$2bo2b5o2bo$bo3b5o3bo$bo2b7o2bo$2b4o3b4o$3bob5obo$2bo2bob
obo2bo$2o2bo2bo2bo2b2o$bobo7bobo$2bo9bo2$4b2o3b2o$3bo7bo$2bo9bo$
4b2o3b2o$bo2bob3obo2bo$b3o7b3o$3bo2bobo2bo$3bo2bobo2bo$3bo2b3o2b
o$3bo7bo$3b2o5b2o$4bo5bo$4bo5bo$b2obobobobob2o$b2o9b2o$b4o5b4o$2b
o2b5o2bo$5bobobo$3b9o$6b3o$5b5o2$2b2o7b2o$bo2bo5bo2bo$2b3o5b3o$2b
3o5b3o$3bo7bo$6bobo$3bo2bobo2bo$4b7o2$6bobo$4bob3obo$7bo$4bo5bo$
4bo5bo$6bobo$6bobo$b2o9b2o$b3obo3bob3o$bob2o5b2obo$b2o3b3o3b2o!

[Saka]

Code: Select all

x = 79, y = 78, rule = B34/S267
29bo5bo30bob2o5b2obo$28bo7bo32b2o3b2o$12bo5bobo6b3ob3ob3o11bo16bo3bo3b
o3bo$11b2o4bobo6bobobo3bobobo9b3o15b2o3bobo3b2o$2bob2o6b2o2bob2o9bo2bo
2bo12b3o16b2o2b3o2b2o$b3obo9bobo2bo7bo7bo9b2o3b2o6b3o7b2o3b2o$16bo11bo
bo3bobo8b3o3b3o6b2o8bo3bo$17bo10bo7bo9b2o3b2o6b3o7b2o3b2o$29bo2bo2bo
12b3o16b2o2b3o2b2o$26bobobo3bobobo9b3o15b2o3bobo3b2o$27b3ob3ob3o11bo
16bo3bo3bo3bo$28bo7bo32b2o3b2o$29bo5bo30bob2o5b2obo6$3bo5bo$6bob2o3bo$
2b11o2bo$b3o3b2o2b2o$2b11o2bo$6bob2o3bo$3bo5bo5$13bo9b2o$13b2o7bobo2bo
$3b2o8bo8bobobobo$2bo2bo6b3o6bo2bobo2bo$bo2b2o3b2obobo3bo2bo2b3o$2b2o
3bo3b4obo2b2o3b4o2bo$5b3o3b2o6b6ob2o2bo$4bo6b2o6bo2bob3ob3o$5b3o3b2o6b
6ob2o2bo$2b2o3bo3b4obo2b2o3b4o2bo$bo2b2o3b2obobo3bo2bo2b3o$2bo2bo6b3o
6bo2bobo2bo$3b2o8bo8bobobobo$13b2o7bobo2bo$13bo9b2o6$2bo$b2o$3o2bo$b3o
$4b2o$2bobo2bo$4bobo3$2bo5bo$5bob2o3bo$b11o2bo$3o3b2o2b2o$b11o2bo$5bob
2o2bo2bo$2bo5bo$12bo2bo$12b3o$11b3o$11b3o$12b3o$12bo2bo$2bo5bo$5bob2o
2bo2bo$b11o2bo$3o3b2o2b2o$b11o2bo$5bob2o3bo$2bo5bo!

Also, why do an essay on this rule instead of Life or Highlife or Day and Night?

[Scorbie]

Also, why do an essay on this rule instead of Life or Highlife or Day and Night?

There are already good essays on well-known rules such as Life, HighLife, Day and Night, JustFriends, Morley, LFOD etc. I think you can find them on LifeWiki or by googling them. And of course, pretry much all posts on Koenig's Life News, David and Adam's Life blog, LifeLine etc. are good essays on their own.

[velcrorex]

c/7 orthogonal:

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x = 12, y = 32, rule = B34/S267
4b4o$2bo6bo$2bob4obo$b2o6b2o$2bobo2bobo$o3b4o3bo$2bo2b2o2bo$bo2b
4o2bo$b3o4b3o$2bo6bo$3b6o$4b4o$2b8o2$2b2o4b2o$4bo2bo$2b3o2b3o$2b
3o2b3o4$3b6o$3bo4bo$3bo4bo$3bob2obo$bo3b2o3bo$o2b2o2b2o2bo$ob3o2b
3obo$3bo4bo$bobo4bobo$b3o4b3o$2b8o!

[velcrorex]

p22 oscillator from gsearch.

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x = 6, y = 12, rule = B34/S267
b4o$b4o$6o$2b2o$bo2bo$bo2bo$bo2bo$bo2bo$2b2o$6o$b4o$b4o!

symmetric p5 from wls

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x = 18, y = 12, rule = B34/S267
3bo4b2o4bo$3b3o2b2o2b3o$3b2ob6ob2o$b5o6b5o$4bob6obo$2o14b2o$2o14b2o$4b
ob6obo$b5o6b5o$3b2ob6ob2o$3b3o2b2o2b3o$3bo4b2o4bo!

[wildmyron]

c/4 diagonal, glide reflective - from gfind

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x = 49, y = 49, rule = B34/S267
10bo2$10bobo$9bobob2o$14bo$12b5o$12b3obo$13bob2o$14b4o$16b2o$o15bo2bo$
b3o13bobo$o3b2o12b3o$3bo2bo13b2o$4bobo12bobo$5b2o8b2obo$5b3o7b2o2b2o6b
o$5b4obo2bo2bo2b2ob3obo$8bobo10b2ob3o2bo$9bo2bo2bo5bo2bo3b3o$12bo2bo4b
o9bo$12b3o2b3o$14bo16b2o$17b3o11bobo$17b3o7b4obo$17b2o7b2o$16bobo8bo2b
ob2o$18bo8b3obo2bo$16bo5b3o2b2o2bo2bo$17bobobobo4bo2bo3bo$18b4obob2o2b
4o3bo$20b2obobo4b3o7bo$21b2ob3o2b3o5b4o$23bob2obo2bob2ob3o4b2o$25bo2bo
2bo3bo2b3o2bo$26bobo2bo2bo4bo3bo$31b3o4b2ob3o$30b4o4bo$29b3o4b3o4b4o$
29bo2b2o2b3o4b4o$30bob7o2bo3b4o$31b3obo2b5o3b2o$33b6obo$34bo5bo5bo$32b
obo5bo2bo2bo$33bobo6bo3bo$37b2ob2o2bobo$38b2ob2o2bo$40bo!

@velcorex: a nice collection of results there. What do you think of the possibility of c/2 orthogonal and c/5 diagonal?

Here is a c/5 diagonal partial, bilateral symmetry, width 19 - from a width 21 gfind search (there were no good width 21 partials)

Code: Select all

x = 28, y = 28, rule = B34/S267
6bo$4bo2bo$2bo3bobo$4bo$bobo5bo$5b3obo$obo2b2o2bo2bo$bo3bo3b2o3bo$2bo
7bo$4b4o2bo2b2obo$7b3obo2bobo$10bo5bo$6bo5b2o2bob2obo$9bo2bo2b5o2bo$7b
ob2o5bo2bo$13bo6bo2bo$9b6o2b2ob2o2bo$13bo2bob2obo3b2o$12b2o2b3obob2o2b
o$12b3o2bo5bo2b2o$15b2obobo4b3o$12bo3b2o6b4o$13bo4bo4b4o$15bo2b2o2b2ob
o$16bo4b2obo$17bo2b4o$17b6o$19b3o!

This search took 1.5 hr so a width 23 search is feasible - I should run that tonight.

c/2 orthogonal appears to be so sparse that it seems to me very unlikely that anything exists at that speed.

[velcrorex]

Your c/5 diagonal partial is promising, so I'd keep searching in that direction.
I think it's rather unlikely that there is a c/2 ship. All of my searches have gone very poorly. I usually do some searching with wls to get a visual on what's happening and any partials for c/2 are very very shallow.

EDIT: Anyone is welcome to prove me wrong by finding a c/2 ship in this rule.

[velcrorex]

c/6 diagonal with glide reflect symmetry.

Code: Select all

x = 22, y = 23, rule = B34/S267
16bo$17bo$15b2obo$18bo2bo$12bobob3o$12bo2bob2o2bo$12bo2bo3bobo$
13b2o3b2o$14bo4bo$17b3o$7b3o3b2o2b3o$9bobo2bo2b2o$9b2obobo$9b2o3b
o$3b2o4b5o$2b2ob2o2b2o$2bo3bobobo$7bobo$bo4b2obo$b3ob3o$2o2b3obo
$bo5bo$2b4o!

EDIT:
c/8 diagonal with glide reflect symmetry.

Code: Select all

x = 14, y = 13, rule = B34/S267
5bo$b3o$o3b3obo$o3b3o2bo$b2o4b4o$4b4ob3o$5b2o2bo2bo$6bo6bo$6bobo$6bo6b
o$4b2o2bo$5bob3obobo$7bo3b2o!

[Bullet51]

P8, P9, P24 and a c/3 wickstretcher:

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x = 76, y = 50, rule = B34/S267
69b4o$68bob2obo$70b2o$68bo4bo$68b6o$68bo4bo$69bo2bo$68b6o$67bo2b2o2bo$
66bob6obo2$66bo8bo$67bo6bo$67bobo2bobo$67b2o4b2o$70b2o$68b6o$68bo4bo$
67b2ob2ob2o$67b3o2b3o$59bo2bo5b6o$58b6o4b2o2b2o2$40bo4bo14b2o8b2o2$38b
ob2o2b2obo12b2o8b2o$5bo18bo$4b2obo12b3ob3o9bobob6obobo10b2o8b2o$bo2bo
15bo5bo11bobo4bobo$4b2o13b2o5bo13bo4bo14b2o8b2o$2obo2b3o31bo4bo$b3o2bo
b2o10bo5b2o10bobo4bobo12b2o8b2o$4b2o14bo5bo9bobob6obobo$5bo2bo11b3ob3o
33b2o8b2o$2bob2o16bo15bob2o2b2obo$4bo55b2o8b2o$40bo4bo$60b2o8b2o2$60b
2o8b2o2$60bobo6bobo2$59bobo8bobo$62bo6bo$61b3o4b3o$64bo2bo$62bob4obo$
64b4o$65b2o!

[confocaloid]

A previously known orthogonal c/3 spaceship just appeared in the C1 census:

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#C https://catagolue.hatsya.com/object/xq3_o46ena6z122/b34s267
#C https://catagolue.hatsya.com/hashsoup/C1/k_n8VXm5icrnCM42434648/b34s267
#C Soup k_n8VXm5icrnCM42434648 was found on 2024-07-13 at 17:09:55 UTC and is owned by Anonymous
x = 16, y = 16, rule = B34/S267
oooboobobboboooo$
oobbboboobbbbbob$
bobobbobboboobbo$
obboobboboboooob$
oooobbbbboobbbob$
obobooobboobbbbb$
boboobobooobbbbb$
oobobbooboooobbo$
booboobobboboobb$
boobbbboooobbooo$
oobbobooboobooob$
bbbobbooboboboob$
obobobooboobbbob$
ooooooobobbbobob$
bbobooobbbobobbo$
bbobboooboboboob!

Since soups quickly settle and the most common spaceship is very rare, I tried to find something in the [R]Investigator version of the CA. I wonder if it would be possible to create a gun using SI cells. The following predecessors settle into a p411 oscillator, a p911 oscillator and a p2247 oscillator respectively:

Code: Select all

x = 36, y = 22, rule = B34/S267Investigator
25B$25C19$H29.H$4.I30.I!

[confocaloid]

A p14 oscillator appeared in the census D4_+2:

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#C https://catagolue.hatsya.com/object/xp14_40hrlr4aevvea4rlrh04/b34s267
x = 18, y = 7, rule = B34/S267
2b2o10b2o$4bo8bo$o2bo3b4o3bo2bo$o2bo4b2o4bo2bo$o2bo3b4o3bo2bo$4bo8bo$
2b2o10b2o!

Code: Select all

#C https://catagolue.hatsya.com/hashsoup/D4_+2/k_EYEMPthnHa6w13948906/b34s267
#C Soup k_EYEMPthnHa6w13948906 was found on 2024-07-19 at 10:50:54 UTC and is owned by Anonymous
x = 32, y = 31, rule = B34/S267
b3obo2b2o2bob4obo2b2o2bob3o$b2o2b2o3bo2b6o2bo3b2o2b2o$3bobob2o2b3o4b3o
2b2obobo$3o2bo2b2o3b6o3b2o2bo2b3o$2b3obob3ob8ob3obob3o$o2b3o2bo5b4o5bo
2b3o2bo$2ob2o2b2o5bo2bo5b2o2b2ob2o$b2ob3o4b3ob2ob3o4b3ob2o$4o5bo12bo5b
4o$o2b3obo3bob2o2b2obo3bob3o2bo$3obobob2ob3o4b3ob2obobob3o$o3bo5b2obo
4bob2o5bo3bo$bob7ob2o6b2ob7obo$3b2ob3o2bo2b4o2bo2b3ob2o$2ob2ob2ob2o3bo
2bo3b2ob2ob2ob2o$b4ob4ob2o2b2o2b2ob4ob4o$2ob2ob2ob2o3bo2bo3b2ob2ob2ob
2o$3b2ob3o2bo2b4o2bo2b3ob2o$bob7ob2o6b2ob7obo$o3bo5b2obo4bob2o5bo3bo$
3obobob2ob3o4b3ob2obobob3o$o2b3obo3bob2o2b2obo3bob3o2bo$4o5bo12bo5b4o$
b2ob3o4b3ob2ob3o4b3ob2o$2ob2o2b2o5bo2bo5b2o2b2ob2o$o2b3o2bo5b4o5bo2b3o
2bo$2b3obob3ob8ob3obob3o$3o2bo2b2o3b6o3b2o2bo2b3o$3bobob2o2b3o4b3o2b2o
bobo$b2o2b2o3bo2b6o2bo3b2o2b2o$b3obo2b2o2bob4obo2b2o2bob3o!

Code: Select all

#C https://catagolue.hatsya.com/hashsoup/D4_+2/k_2haUhcMq9FV223173169/b34s267
#C Soup k_2haUhcMq9FV223173169 was found on 2024-07-19 at 12:26:07 UTC and is owned by Anonymous
x = 32, y = 31, rule = B34/S267
5bo3b2o4b2o4b2o3bo$4b2ob2o2b2o2b2o2b2o2b2ob2o$4bobo18bobo$bobo8bo6bo8b
obo$2b2obo2b3ob2o4b2ob3o2bob2o$ob7obo3b4o3bob7obo$b2o2b2ob4o2b4o2b4ob
2o2b2o$b6o3b4ob2ob4o3b6o$bob2obo3bo2bob2obo2bo3bob2obo$b2ob4obob2obo2b
ob2obob4ob2o$3o6bobo2b4o2bobo6b3o$bo4bob2ob2obo2bob2ob2obo4bo$b6obo3bo
b4obo3bob6o$bo2bob2o2bobobo2bobobo2b2obo2bo$2b3o2b2obo3bo2bo3bob2o2b3o
$bo2b2ob2ob2o2b4o2b2ob2ob2o2bo$2b3o2b2obo3bo2bo3bob2o2b3o$bo2bob2o2bob
obo2bobobo2b2obo2bo$b6obo3bob4obo3bob6o$bo4bob2ob2obo2bob2ob2obo4bo$3o
6bobo2b4o2bobo6b3o$b2ob4obob2obo2bob2obob4ob2o$bob2obo3bo2bob2obo2bo3b
ob2obo$b6o3b4ob2ob4o3b6o$b2o2b2ob4o2b4o2b4ob2o2b2o$ob7obo3b4o3bob7obo$
2b2obo2b3ob2o4b2ob3o2bob2o$bobo8bo6bo8bobo$4bobo18bobo$4b2ob2o2b2o2b2o
2b2o2b2ob2o$5bo3b2o4b2o4b2o3bo!