B3/S2-a358

[Mathemagician314]

This is a fun rule I've been experimenting with in apgsearch and golly over the past month or so. (If anybody else has investigated this rule in-depth before, sorry about this post.) It has an abundance of common spaceships and oscillators, and you can view the natural ones in the C1 census (which doesn't have many soups since I'm the only one who's searched it so far). The most common object is the following 20-bit still life, small lake, which arises from the traffic light sequence:

Code: Select all

x = 18, y = 9, rule = B3/S2-a358
4bo$3bobo$3bobo$b2o3b2o7bo$o7bo4b2ob2o$b2o3b2o7bo$3bobo$3bobo$4bo!

Just slightly less common is the block, which functions as it does in Life. Then comes the blinker, which functions normally, and then an alien oscillator that's in Day and Night and some other OCA's:

Code: Select all

x = 3, y = 3, rule = B3/S2-a358
o$b2o$bo!

As you continue down the top few, you see a few more alien period-2 oscillators (there are a lot of those) and many common still lives from Life. One outlier is that the barge siamese loaf occurs very commonly -- it often comes from this eight-cell predecessor:

Code: Select all

x = 4, y = 3, rule = B3/S2-a358
b3o$ob2o$2o!

Before moving on, it's important to note that the line-of-six spark (and the line of four, one of its great-great-grandparents) is extremely common in this rule and lasts for fifty generations (in that time it grows quite a bit, and it also has some hassling potential - see below):

Code: Select all

x = 6, y = 1, rule = B3/S2-a358
4o!

But what I haven't mentioned yet are the spaceships; this rule is full of common spaceships (all found so far being orthogonal). One of the most common is the following c/3o spaceship, which often arises from a pi-heptomino:

Code: Select all

x = 5, y = 3, rule = B3/S2-a358
2bo$bobo$2ob2o!

There are also many common c/2o spaceships of different periods -- the periods found so far being 2, 4, 6 and 8:

Code: Select all

x = 68, y = 7, rule = B3/S2-a358
2bo6bo6bo6bo4bo6bo6b3o7bo5b3o5bo$b3o4b3o4b3o4b3o2b3o4b3o5bo2bo5b3o4b3o
4b3o$o3bo2bo3bo3bobo4bobo2bobo4bobo4bo2b2o5bobo3bobobo3bobo$3bo6bo4bob
o4bo6bo4bobo4bobo6bo6b2o8bo$7b2o12b3ob2ob3o2b2ob2o5bo6bo7bo6bo$7bo$23b
o4bo!

Apsgsearch also lets us find some stranger speeds; here's the other speeds known so far, a 2c/5o, a c/4o (period eight), a c/21o, and a c/43o (period 86):

Code: Select all

x = 67, y = 10, rule = B3/S2-a358
2b3o14b4o20bo18b2o$bo2bo13bob2obo18b3o15b2ob2o$b3o14bo4bo19bo17bo$b2o
14b2ob2ob2o15b2obo$o17bob2obo16bo$o16b2ob2ob2o15b3o21b2o$19bo2bo41b2o$
61b2o3bo$61bo2b2o$61bobobo!

There is likely some way to arrange some c/2o spaceships in way to make a puffer, but as of yet I have not found one (and none has appeared naturally). Looking at oscillators, many periods have been found (including an extendable period-2 family), and they are shown below:

Code: Select all

x = 183, y = 70, rule = B3/S2-a358History
.3D12.3D15.D.D12.3D11.3D13.3D20.3D15.3D11.D.3D12.D.D.D8.D.3D$3.D14.D
15.D.D12.D13.D17.D20.D.D15.D.D11.D.D.D12.D.D.D8.D.D.D7.3D.3D$.3D12.3D
15.3D12.3D11.3D15.D20.3D15.3D11.D.D.D12.D.3D8.D.3D9.D.D$.D16.D17.D14.
D11.D.D15.D20.D.D17.D11.D.D.D12.D3.D8.D.D.D7.3D.3D$.3D12.3D17.D12.3D
11.3D15.D20.3D15.3D11.D.3D12.D3.D8.D.3D9.D.D.D$176.3D.3D4$13.A6.A12.
4A11.2A12.A15.A23.3A14.A3.A11.3A13.A3.A12.2A$.3A8.A.2A2.2A.A15.A9.A.A
13.4A10.3A38.A.A.A.A25.A.A.A.A7.6A7.A3.A$11.A.A2.2A2.A.A9.3A2.A9.A.2A
12.3A10.3A.A38.A3.A10.5A12.A3.A20.3A.3A$12.A2.A2.A2.A11.A.A.A7.3A27.A
.A.3A19.A3.A70.A.A.A.A$16.2A16.2A.A6.A4.A24.3A.3A19.A.A.A.A14.A13.3A
39.A3.A$35.A8.3A.A4.A19.3A.A.A17.A3.A.A.A3.A11.A42.6A$.A44.A4.A.3A18.
A.3A18.A4.A.A4.A11.A31.A10.2A$2.2A46.A4.A19.3A19.A3.A.A.A3.A11.A31.A$
2.A49.3A8.A.A10.A23.A.A.A.A14.A31.A$49.2A.A9.2A.2A34.A3.A15.A10.3A4.
3A11.A$12.2A36.A.A9.A4.A85.A$11.A2.A19.A15.2A11.2A.2A51.A3.A7.5A2.5A
10.A$.A10.2A19.2A29.A.A11.A5.A17.3A13.A.A.A.A$.2A10.A18.A.A2.A39.A.A
3.A.A33.A3.A8.3A4.3A$2.A10.A18.A.A.2A40.A.A.A.A$14.2A16.A.A2.A10.A31.
A.A68.A3.A$16.A16.2A12.A.A24.A4.A3.A4.A11.A49.A.A.A.A$16.A3.A13.A13.A
24.A.A3.5A3.A.A9.A.A49.A3.A$2.A14.3A.A44.A7.A2.2A5.2A2.A10.A.3A33.3A$
.2A16.A.A24.5A14.A.A7.2A.A5.A.2A9.2A3.2A$3.A16.A25.A4.A13.A2.A9.A5.A
11.A6.A32.5A$.A44.3A2.A2.A7.A3.2A7.2A.A5.A.2A9.2A5.3A$2.2A43.A.A.A.A.
A6.2A3.A6.A2.2A5.2A2.A9.2A5.2A24.A5.3A$2.A12.A32.2A.A2.A6.A2.A8.A.A3.
5A3.A.A8.3A5.2A21.A.A.A18.4A$14.A.A15.A3.A12.3A10.A.A9.A4.A3.A4.A12.A
6.A20.A.A.A18.A2.A$14.A2.2A14.2A2.A25.A16.A.A18.2A3.2A21.A.A.A2.2A4.A
10.2A$A12.2A.A2.A13.A3.2A39.A.A.A.A16.3A.A25.A4.2A2.A.A.A$.2A10.A2.A
2.A13.A.A41.A.A3.A.A17.A.A34.A.A.A7.4A$.A12.2A.2A.A11.A4.A40.A5.A19.A
35.A.A.A$3.2A11.A4.A112.3A5.A$3.A12.A.3A$17.2A84.2A28.5A$48.6A48.A2.A
$47.A.4A.A9.2A12.A22.A.2A.A27.3A15.4A$3.A31.3A9.2A4.2A8.A2.A10.A.A22.
A2.A$4A14.A13.2A2.A.A8.2A.2A.2A6.A2.2A2.A8.3A73.2A$.A.A13.A.A11.A.3A.
2A8.2A.2A.2A7.6A7.2A75.A2.A$.4A11.A.A.A10.A4.A.A8.2A4.2A7.6A6.A.A.A
20.A8.A43.4A$.A14.A3.A11.2A2.A10.A.4A.A9.2A9.2A3.2A18.2A4.2A$14.2A2.A
2.2A11.A.2A10.6A9.A2.A12.A2.A12.A4.A6.A4.A$13.A4.A4.A10.A2.A26.2A13.A
2.A11.A.A5.4A5.A.A$12.A.A.2A.2A.A.A10.2A43.2A11.A.A6.A2.A6.A.A$13.A4.
A4.A69.A.A6.A2.A6.A.A$14.2A2.A2.2A71.A.A5.4A5.A.A$16.A3.A74.A4.A6.A4.
A$16.A.A.A79.2A4.2A$17.A.A57.2A20.A8.A$18.A57.A2.A$75.A2.A.A$76.3A.A
2.A18.A2.A$79.2A.A.A16.A.2A.A$72.A7.A2.A18.A2.A$71.A.A6.A22.2A$70.A2.
A4.2A$70.A.2A3.A$71.A2.A2.A$72.5A2$74.A$73.A.A$74.A!

Period 2: very common, not much to say.
Period 3: no results in C1 yet, but common in other symmetries -- can any of them be monomerized?
Period 4: the only "rare" period in C1, there are quite a few of these.
Period 5: much rarer than P4, but the heart is common with different induction coils.
Period 6: there's a very common P6, shown at the top in the demonstration above, and there are quite a few other P6's as well.
Period 7: very uncommon except in some symmetries.
Period 8: more common than P7, there are a few of these.
Period 9: only one so far is a line-of-six hassler and stator variants. I hope to find more.
Period 10: has a common oscillator just a bit less common than the P6 -- all other P10's are variants thereof.
Period 14: two unrelated oscillators; the first being a line of six hassler similar to the P9.
Period 18: the oscillator shown was recently found, no others found.
Period 36: very common oscillator, but no others are known in that period.

Any smaller variants of these oscillators would be cool to find, and there are others scattered throughout the b3s2-a358 census.

I think this rule needs a name, but I don't know what a good name would be -- any suggestions? Anyway, goals would be to find new spaceship speeds and slopes, including a diagonal ship, and new oscillator periods. It would also be nice to find a linear or even nonlinear infinite growth mechanism, naturally or by constructing it. This rule, to me, seems similar enough to Life to carry knowledge over, but different enough that it feels refreshing.

Can people help apgsearch this? Because I think that's what's going to give us the most info in the end.

[silversmith]

Firstly, I would like to say this is a pretty good first post for a rule thread, and it is nice to see someone promoting a rule do plenty of their own exploration of the rule.

As for the rule itself, the dynamics are really sparse. On one hand, this allows the rule to be searched at tens of thousands of soups per second. On the other hand, patterns are very fragile and most interactions leave nothing behind.

The tub and a few similar still lifes can acts as catalysts, as demonstrated in some of the previously mentioned oscillators and this p16 oscillator:

Code: Select all

x = 17, y = 17, rule = B3/S2-a358
4b6o3$4bo7bo$o2bobo5bobo$o3bo7bo$o$o15bo$o15bo$o15bo$16bo$4bo7bo3bo$3b
obo5bobo2bo$4bo7bo3$7b6o!

I'll contribute to apgsearching this rule, maybe it will lead to some more discoveries.

[Mathemagician314]

WHOA! I would like to say a huge thank you to everybody who helped apgsearch this -- especially silversmith and FWKnightship -- as I never imagined the censuses would accumulate this many objects. There's been so many new discoveries that I just saw, so let me try to enumerate them:

Talking about oscillators, the first period 3 oscillator appeared naturally (it was already known from symmetric searches, but it's still cool to know that it's natural):

Code: Select all

x = 12, y = 5, rule = B3/S2-a358
2bo6bo$bob2o2b2obo$obo2b2o2bobo$bo2bo2bo2bo$5b2o!

In new discoveries, all periods up to 14 are now known, with the following p11, p12, and p13 oscillators respectively appearing in symmetric soups:

Code: Select all

x = 58, y = 25, rule = B3/S2-a358
2b2o3b2o10bo5bo16b2o3b2o$bo7bo8b2o5b2o14bo2bobo2bo$o2bo3bo2bo9bo3bo16b
2obobob2o$obo5bobo32b2ob2o$bo3bo3bo31b2obobob2o$2b7o13bo17bo3bobo3bo$
22bo17bob3ob3obo$2b7o13bo15b2o11b2o$bo3bo3bo12bo11b2obo15bob2o$obo5bob
o11bo10bobobobo11bobobobo$o2bo3bo2bo11bo10bo2bo2bo11bo2bo2bo$bo7bo12bo
11b6o11b6o$2b2o3b2o13bo$34b6o11b6o$33bo2bo2bo11bo2bo2bo$20bo3bo8bobobo
bo11bobobobo$18b2o5b2o7b2obo15bob2o$19bo5bo12b2o11b2o$40bob3ob3obo$40b
o3bobo3bo$41b2obobob2o$43b2ob2o$41b2obobob2o$41bo2bobo2bo$42b2o3b2o!

In addition, many new oscillators of different periods were discovered, including new p7's, p8's, and p14's. My favorite is a semi-natural monomerization of an already known p14:

Code: Select all

x = 22, y = 15, rule = B3/S2-a358
b4o$bo2bo$2b2o2$b4o8bo6bo$12b2o6b2o$14bo4bo4$b4o10b4o2$2b2o12b2o$bo2bo
10bo2bo$b4o10b4o!

Finally, silversmith found the first p16, which is shown in their post above. (By the way, how did you find it -- did you just experiment with different catalysts and reactions or did you use some search tool?)

In terms of spaceships, a new c/4 spaceship was discovered, the first period-4 of its velocity:

Code: Select all

x = 15, y = 4, rule = B3/S2-a358
6b3o$6bobo$5obobob5o$3bobo3bobo!

Also, a new 2c/86 was discovered (closely related to the more common one, but it pushes a blinker):

Code: Select all

x = 7, y = 13, rule = B3/S2-a358
6bo$6bo$6bo$2b2o$bo2bo$b3o$3bo$bobo$2bo3bo$2b5o$2b2ob2o$5o$b3o!

All credit goes to the people who apgsearched these, mainly Silversmith and FWKnightship -- I never thought this rule would have so many cool objects! Is there more to be discovered, like a diagonal spaceship or linear growth? Only apgsearch and courage will tell...

[wildmyron]

Is there more to be discovered, like a diagonal spaceship or linear growth? Only apgsearch and courage will tell...

Here are a few c/4 diagonal spaceships found with ikpx2:

Code: Select all

x = 69, y = 30, rule = B3/S2-a358
3bo19bo19bo$2b2o18b2o18b2o$2o3bo14b2o3bo14b2o3bo$2o3bo14b2o3bo14b2o3bo
$3bo3bo15bo3bo15bo3bo$b2o5bo12b2o5bo12b2o5bo$3bo4b2o13bo4b2o13bo4b2o$
7bo19bo19bo$4b2o18b2o18b2o$4bobo17bobo17bobo$28b4obo14b4obo$29bo3b2o
14bo3b2o$29bobo17bobo$30bo3bo15bo3bo$30bobob2o14bobob2o$36bo19bo$33b2o
3b3o12b2o3bo$35bo2b3o14bo2b3o$59b2o$36b2obo16b2ob2o$35bo3bo16b2ob2o2bo
$35bo21bobob5obo$37bo19bo5bo2b3o$59b3o6bo2$62bo$62bo$62bo$61bo$61bo!

Because of the addition of S5 to the mostly Life rule, the diagonal speed limit is c/3, and here are some spaceships of that speed:

Code: Select all

x = 78, y = 15, rule = B3/S2-a358
6bo19bo19bo19bo$4b2ob2o15b2ob2o15b2ob2o15b2ob2o$3bo4b2o13bo4b2o13bo4b
2o13bo4b2o$2b2o3bo2bo11b2o3bo2bo11b2o3bo2b3o9b2o3bo2b3o$bo2bob2ob2ob2o
7bo2bob2ob2ob2o7bo2bob2o3b2o8bo2bob2o3b2o$bo6bo12bo6bo12bo10bo8bo10bob
o$o3bo2bo2b3o7bo3bo2bo2b3o7bo3bo2b2o11bo3bo2b2o$bob2ob6o9bob2ob6o9bob
2ob2o13bob2ob2o5b2obo$b2o3bobo12b2o3bobo12b2o2bob3o11b2o2bob3o4bobo$2b
o5b2o2b2o8bo5b2o2b2o8bobo2bobo12bobo2bobo6b2o$3bo9b2o8bo9b2obo6b2ob2o
15b2ob2o7bo$3b2o18b2o8bo12b2o18b2o8b2o$3b3o17b3o9bo8bobo2bo14bobo2bo$
44bo4b2o13bo4b2o$50bo19bo!

I also tried searching c/5d, c/6d, c/7d, and c/8d but didn't find anything after brief searches.

Here are of few more c/4 orthogonal spaceships with period 4 (including some tagalongs):

Code: Select all

x = 72, y = 36, rule = B3/S2-a358
4b2o18b2o18b2o18b2o$3bo2bo16bo2bo16bo2bo16bo2bo$2bo4bo14bo4bo14bo4bo
14bo4bo$2bo4bo15bo2bo16bo2bo16bo2bo$b2ob2ob2o12bo6bo12bo6bo12bo6bo$4b
2o15bo6bo12bo6bo12bo6bo$2bob2obo11b2ob6ob2o8b2ob6ob2o8b2ob6ob2o$2bo4bo
11b2obob2obob2o8b2obob2obob2o8b2obob2obob2o$20b10o10b10o10b10o$2bo4bo
12bobo4bobo10bobo4bobo10bobo4bobo$b3o2b3o10b2ob6ob2o8b2ob6ob2o8b2ob6ob
2o$o8bo10b2ob4ob2o10b2ob4ob2o10b2ob4ob2o$obo4bobo10b2obo2bob2o10b2obo
2bob2o10b2obo2bob2o$b2o4b2o13bo4bo14bo4bo14bo4bo$2bo4bo14b6o14b6o14b6o
$2b2o2b2o14bo4bo14bo4bo14bo4bo$2b6o13b3o2b3o12b3o2b3o12b3o2b3o$bo2b2o
2bo13b6o14b6o14b6o$ob6obo3$o3b2o3bo$10o33b4o16b4o$ob2o2b2obo32bo4bo15b
o2bo$43bo2bo16b4o$62b2o2b2o$40bobob2obobo11b3o2b3o$40bo2b4o2bo11b2o4b
2o$40bobo4bobo10b2o6b2o$40b3o4b3o10b2o6b2o$41b2o4b2o11bob2o2b2obo$41b
2ob2ob2o10bobobo2bobobo$40bo2bo2bo2bo8b2obo6bob2o$41bobo2bobo12bo6bo$
42b2o2b2o10bo12bo$59b2o8b2o!

Probably ntzfind is better suited to this specific search, but this will do for now.

There are also now a large number of c/2 and c/3 orthogonal spaceships of various periods in the ikpx2_stdin census.I was hoping a puffer or wickstretcher might appear, but no such luck (yet).

Edit: Including this p14, c/2 spaceship. I'm convinced there's a wickstretcher with a mechanism similar to this. I'll run the c/2 ikpx2 search for a bit longer, but we'll have to get lucky for a wickstretcher to appear in the search along with a fencepost so that it gets picked up by apgsearch.

[wildmyron]

Is there more to be discovered, like a diagonal spaceship or linear growth? Only apgsearch and courage will tell...

Here are a few c/4 diagonal spaceships found with ikpx2:

Code: Select all

x = 69, y = 30, rule = B3/S2-a358
3bo19bo19bo$2b2o18b2o18b2o$2o3bo14b2o3bo14b2o3bo$2o3bo14b2o3bo14b2o3bo
$3bo3bo15bo3bo15bo3bo$b2o5bo12b2o5bo12b2o5bo$3bo4b2o13bo4b2o13bo4b2o$
7bo19bo19bo$4b2o18b2o18b2o$4bobo17bobo17bobo$28b4obo14b4obo$29bo3b2o
14bo3b2o$29bobo17bobo$30bo3bo15bo3bo$30bobob2o14bobob2o$36bo19bo$33b2o
3b3o12b2o3bo$35bo2b3o14bo2b3o$59b2o$36b2obo16b2ob2o$35bo3bo16b2ob2o2bo
$35bo21bobob5obo$37bo19bo5bo2b3o$59b3o6bo2$62bo$62bo$62bo$61bo$61bo!

Because of the addition of S5 to the mostly Life rule, the diagonal speed limit is c/3, and here are some spaceships of that speed:

Code: Select all

x = 78, y = 15, rule = B3/S2-a358
6bo19bo19bo19bo$4b2ob2o15b2ob2o15b2ob2o15b2ob2o$3bo4b2o13bo4b2o13bo4b
2o13bo4b2o$2b2o3bo2bo11b2o3bo2bo11b2o3bo2b3o9b2o3bo2b3o$bo2bob2ob2ob2o
7bo2bob2ob2ob2o7bo2bob2o3b2o8bo2bob2o3b2o$bo6bo12bo6bo12bo10bo8bo10bob
o$o3bo2bo2b3o7bo3bo2bo2b3o7bo3bo2b2o11bo3bo2b2o$bob2ob6o9bob2ob6o9bob
2ob2o13bob2ob2o5b2obo$b2o3bobo12b2o3bobo12b2o2bob3o11b2o2bob3o4bobo$2b
o5b2o2b2o8bo5b2o2b2o8bobo2bobo12bobo2bobo6b2o$3bo9b2o8bo9b2obo6b2ob2o
15b2ob2o7bo$3b2o18b2o8bo12b2o18b2o8b2o$3b3o17b3o9bo8bobo2bo14bobo2bo$
44bo4b2o13bo4b2o$50bo19bo!

I also tried searching c/5d, c/6d, c/7d, and c/8d but didn't find anything after brief searches.

Here are of few more c/4 orthogonal spaceships with period 4 (including some tagalongs):

Code: Select all

x = 72, y = 36, rule = B3/S2-a358
4b2o18b2o18b2o18b2o$3bo2bo16bo2bo16bo2bo16bo2bo$2bo4bo14bo4bo14bo4bo
14bo4bo$2bo4bo15bo2bo16bo2bo16bo2bo$b2ob2ob2o12bo6bo12bo6bo12bo6bo$4b
2o15bo6bo12bo6bo12bo6bo$2bob2obo11b2ob6ob2o8b2ob6ob2o8b2ob6ob2o$2bo4bo
11b2obob2obob2o8b2obob2obob2o8b2obob2obob2o$20b10o10b10o10b10o$2bo4bo
12bobo4bobo10bobo4bobo10bobo4bobo$b3o2b3o10b2ob6ob2o8b2ob6ob2o8b2ob6ob
2o$o8bo10b2ob4ob2o10b2ob4ob2o10b2ob4ob2o$obo4bobo10b2obo2bob2o10b2obo
2bob2o10b2obo2bob2o$b2o4b2o13bo4bo14bo4bo14bo4bo$2bo4bo14b6o14b6o14b6o
$2b2o2b2o14bo4bo14bo4bo14bo4bo$2b6o13b3o2b3o12b3o2b3o12b3o2b3o$bo2b2o
2bo13b6o14b6o14b6o$ob6obo3$o3b2o3bo$10o33b4o16b4o$ob2o2b2obo32bo4bo15b
o2bo$43bo2bo16b4o$62b2o2b2o$40bobob2obobo11b3o2b3o$40bo2b4o2bo11b2o4b
2o$40bobo4bobo10b2o6b2o$40b3o4b3o10b2o6b2o$41b2o4b2o11bob2o2b2obo$41b
2ob2ob2o10bobobo2bobobo$40bo2bo2bo2bo8b2obo6bob2o$41bobo2bobo12bo6bo$
42b2o2b2o10bo12bo$59b2o8b2o!

Probably ntzfind is better suited to this specific search, but this will do for now.

There are also now a large number of c/2 and c/3 orthogonal spaceships of various periods in the ikpx2_stdin census.I was hoping a puffer or wickstretcher might appear, but no such luck (yet).

Edit: Including this p14, c/2 spaceship. I'm convinced there's a wickstretcher with a mechanism similar to this. I'll run the c/2 ikpx2 search for a bit longer, but we'll have to get lucky for a wickstretcher to appear in the search along with a fencepost so that it gets picked up by apgsearch.

Edit 2: Unfortunately I can't continue this search because ikpx2 is consistently crashing

[Mathemagician314]

I found this c/5o spaceship using ikpx2:

Code: Select all

x = 14, y = 25, rule = B3/S2-a358
2b2o6b2o$b2ob2o2b2ob2o$o12bo$o3b2o2b2o3bo$2bo8bo$b3o6b3o$2b2o6b2o$3b2o
4b2o$3b2o4b2o$4b2o2b2o$3b3o2b3o$2bo2bo2bo2bo$3bobo2bobo$4b6o$5bo2bo$5b
o2bo$5bo2bo$6b2o$2b3o4b3o$2bobo4bobo$2bo2bo2bo2bo$2bob6obo$4bob2obo$3b
2o4b2o$4b6o!
[[ TRACK 0 -1/5 GPS 10 ZOOM 13.4 ]]

EDIT: And this one:

Code: Select all

x = 14, y = 33, rule = B3/S2-a358
2b2o6b2o$bo2bo4bo2bo$o3b2o2b2o3bo$obob2o2b2obobo$b2o8b2o$2bo8bo$3bo6b
o$3bo6bo$4bo4bo$4bo4bo$3b2o4b2o$2bo3b2o3bo$3b2o4b2o$6b2o$5bo2bo$5bo2b
o$6b2o$3bo2b2o2bo$3bo6bo$2bobo4bobo$3bo6bo$3b3o2b3o$3b2ob2ob2o$4bo4bo
$5b4o$5bo2bo2$5bo2bo$5bo2bo$5b4o$4bo4bo$5bo2bo$5bo2bo!
[[ TRACK 0 -1/5 GPS 10 ]]

EDIT 2: And here's a period-10 c/2:

Code: Select all

x = 23, y = 35, rule = B3/S2-a358
2$5bo6bo$4b3o4b3o$4bobo4bobo$3bo2bo4bo2bo$4b4o2b4o$3b2o8b2o$4b2o6b2o$
3bo2bo4bo2bo$7bo2bo$6bo4bo$6bo4bo$6bob2obo$8b2o$5b2ob2ob2o$4bobob2obob
o$4bo8bo$5bobo2bobo2$8b2o$7bo2bo$7bo2bo$6b2o2b2o2$7bo2bo$7b4o$7b4o!
[[ TRACK 0 -1/2 GPS 8 ]]

[Mathemagician314]

Sorry for the doublepost, but ikpx2 finally yielded infinite growth -- a period 16 c/2o backrake:

Code: Select all

x = 13, y = 45, rule = B3/S2-a358
3bo5bo$2b3o3b3o$2bobo3bobo$bo2bo3bo2bo$2b4ob4o$b2o7b2o$2b3o3b3o$bo9bo
$o2b2o3b2o2bo$bob2o3b2obo$o4bobo4bo2$2o2b2ob2o2b2o$obo2bobo2bobo$2b2o
bobob2o$2bo2bobo2bo2$2b2ob3ob2o$2bo7bo$6bo$4bo3bo$4bo3bo$4b2ob2o2$4bo
3bo$b3o5b3o$2obob3obob2o$bobob3obobo$2obob3obob2o$bobob3obobo$bobob3o
bobo$2obo5bob2o$3bobobobo$3bo2bo2bo$2b2o2bo2b2o2$3bobobobo$6bo$5bobo2$
4bo3bo$3bo5bo$4bo3bo$5b3o$6bo!

[silversmith]

Congratulations on finding a linear growth pattern!

(By the way, how did you find it -- did you just experiment with different catalysts and reactions or did you use some search tool?)

I did a bit of both; I tested placing different still lifes around the 6 cell line, but I used a tool to speed up the placement. More specifically, I used this setup on my online CA simulator which shifts the still life every time I restart the simulation, so I only have to move things manually when switching to a new row or new still life:
https://silversimulations.com/caplayer/ ... Reset,When

[azulavoir]

an alien oscillator that's in Day and Night and some other OCA's:

Code: Select all

x = 3, y = 3, rule = B3/S2-a358
o$b2o$bo!

Maybe I'm simply too splatoonbrained but I've always thought "torpedo" would be a good name for this osc:

[Mathemagician314]

I've got nothing against that name... if you want to take that to the "thread for currently unnamed patterns" you can!

[May13]

an alien oscillator that's in Day and Night and some other OCA's:

Code: Select all

x = 3, y = 3, rule = B3/S2-a358
o$b2o$bo!

Maybe I'm simply too splatoonbrained but I've always thought "torpedo" would be a good name for this osc:

This oscillator is already known as "fish" (in LaundryPizza03's oscillator database):

Code: Select all

#C The Fish (oscillator 57), period 2 (mod 1)
#C Discovered by Harry J. Riley, 1972
#C
#C B012345678 S012345678
#C  ---X        --X
#C
x = 3, y = 3, rule = B3/S3
2bo$2o$bo!

Another 4-cell oscillator is bleeper:

Code: Select all

#C The Ant (oscillator)/Bleeper (oscillator 43), period 2 (mod 1)
#C Discovered by Mark Niemiec and Harry J. Riley, 1972
#C
#C B012345678 S012345678
#C  ---X         -X
#C
x = 3, y = 2, rule = B3/S3
b2o$2o!