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)

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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.

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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!