Thread for basic questions

[toroidalet]

Those patterns are the result of having that fuse at the end of a diagonal line of some length (without a snake head). Therefore, one could delete some amount of cleanup gliders and everything after the cutoff point to give a predecessor of bounded population.

I don't see why a pi is problematic considering that no terminations of the fuse result in a pure pi, and so disrupting the diagonal line would stop it from forming, removing the fuse cell would too, and removing a cell from the snake head would make another fuse in the opposite direction and there would be no gliders to clean up its junk.
Using a barberpole fuse eliminates the pond, traffic light, and the constellation produced from this cluster (and a few others like it):

Code: Select all

x = 59, y = 60, rule = B3/S23
bo$obo2$2bobo2$4bobo2$6bobo2$8bobo2$10bobo2$12bobo2$14bobo2$16bobo2$
18bobo2$20bobo2$22bobo2$24bobo2$26bobo2$28bobo2$30bobo2$32bobo2$34bobo
2$36bobo2$38bobo2$40bobo2$42bobo2$44bobo2$46bobo2$48bobo2$50bobo2$52bo
bo2$54bobo2$56bobo2$58bo!

In the unlikely chance that something is creatable by both fuses or glider phases and was not already explicitly taken care of, there are many more fuses to choose from:

Code: Select all

x = 75, y = 90, rule = B3/S23
4bo5bo15bo15bo15bo15bo$4b2o4bo6b3o6bo6b3o6bo6b3o6bo6b3o6bo$4bo5bo15bo
15bo15bo15bo10$2o$obo$2bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o$obo$2o8$2bo2bo
3bo3bo3bo3bo3bo3bo3bo3bo$2bobobobobobobobobobobobobobobobobobobo$2bo2b
o3bo3bo3bo3bo3bo3bo3bo3bo26$2bo2b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b
2o3b2o3b2o3b2o$2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo
2bobo2bobo2bo$2bo2b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o
16$3b2obo3bobo3bobo3bobo3bobo3bobo3bobo3bobo$3bo2b2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2o2$3b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$4bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo11$7b2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$7b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2o2$5bo2bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$4b2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o!

muzik: Although it seems like one should be able to come up with more examples, the only things I've found are sort of trivial:

Code: Select all

x = 12, y = 23, rule = B3/S23
5b2o$2o2bo2bo2b2o$o3b4o3bo$2bobo2bobo$b2obo2bob2o$2bobo2bobo$2bob4obo$
b2obo2bob2o$2bobo2bobo$2bobo2bobo$b2ob4ob2o$2bobo2bobo$2bobo2bobo$b2ob
o2bob2o$2bob4obo$2bobo2bobo$b2obo2bob2o$2bobo2bobo$2bob4obo$b2obo2bob
2o$4bo2bo$4bo2bo$5b2o!

Code: Select all

x = 15, y = 14, rule = B3/S23
8b2o$6bo2bo$6b3o2$4b7o$2obo7bob2o$2obob2ob2obob2o$3bobo3bobo$3bo7bo$4b
7o2$6b3o$6bo2bo$8b2o!

And this horribly unoptimized cuphook variant:

Code: Select all

x = 16, y = 17, rule = B3/S23
6bo2bo$6b4o2$4b8o$3bo8bo$3bob2o2b2obo$2obobo4bobob2o$2obobo4bobob2o$3b
ob2o2b2obo$2obobo6bob2o$2obobo3b2obob2o$3bob2o3bobo$3bo8bo$4b8o2$6b4o$
6bo2bo!

[MathAndCode]

I don't get why those in particular are problematic.

The block was problematic because the fuse is stabilized at one end by a hook. Pi ash was problematic because the fuse would create that without any gliders. Beehives, ponds, and traffic lights were problematic because they can form from subsets of a glider. The other constellation that I mentioned was problematic because one can remove part of the hook, most of the fuse, and all of the gliders.

Why does mirage have so many unnecessary cells?

It's supposed to look like it came out of nowhere.

[muzik]

muzik: Although it seems like one should be able to come up with more examples, the only things I've found are sort of trivial:

Code: Select all

x = 12, y = 23, rule = B3/S23
5b2o$2o2bo2bo2b2o$o3b4o3bo$2bobo2bobo$b2obo2bob2o$2bobo2bobo$2bob4obo$
b2obo2bob2o$2bobo2bobo$2bobo2bobo$b2ob4ob2o$2bobo2bobo$2bobo2bobo$b2ob
o2bob2o$2bob4obo$2bobo2bobo$b2obo2bob2o$2bobo2bobo$2bob4obo$b2obo2bob
2o$4bo2bo$4bo2bo$5b2o!

Code: Select all

x = 15, y = 14, rule = B3/S23
8b2o$6bo2bo$6b3o2$4b7o$2obo7bob2o$2obob2ob2obob2o$3bobo3bobo$3bo7bo$4b
7o2$6b3o$6bo2bo$8b2o!

And this horribly unoptimized cuphook variant:

Code: Select all

x = 16, y = 17, rule = B3/S23
6bo2bo$6b4o2$4b8o$3bo8bo$3bob2o2b2obo$2obobo4bobob2o$2obobo4bobob2o$3b
ob2o2b2obo$2obobo6bob2o$2obobo3b2obob2o$3bob2o3bobo$3bo8bo$4b8o2$6b4o$
6bo2bo!

Indeed these results seem unsatisfactory. It may be worth adding the requirement that all four sides must interact with rotor cells (thus disqualifying the orthogonal on-off), but even this admits cases such as the following:

Code: Select all

x = 25, y = 25, rule = B3/S23
8b2o2b2o$9bo2b2o$8bo7bo$8b9o2$6b13o$5bo13bo$5bob2obo3bob2obo$2b2obob2o
b2ob2ob2obob2obo$3bobo13bobob2o$3bobob2ob2ob2ob2obobo$2obobo2bob2ob2ob
o2bobo$2obobo13bobob2o$3bobo2bob2ob2obo2bobob2o$3bobob2ob2ob2ob2obobo$
2obobo13bobo$ob2obob2ob2ob2ob2obob2o$5bob2obo3bob2obo$5bo13bo$6b13o2$
8b9o$8bo7bo$11b2o2bo$11b2o2b2o!

Having the rotor touch all four sides and be fully continuous seems overly restrictive on the other hand, possibly blocking out legitimate desirable examples, and there could probably be some sort of boring exception created anyway.

[praosylen]

Are there any other known non-period-1 billiard table oscillators where the rotor is bounded by four diagonally connected line segments, opposite ends parallel and equal length, and the rotor makes direct contact with this bounding region without ever killing it?

Code: Select all

rle

Here are two 5x7 ones I found the last time someone asked the question: viewtopic.php?p=53933#p53933. I don't know of any other nontrivial ones beyond the ones you mentioned and those two, but I'd imagine they exist at larger sizes.

[creeperman7002]

Is B2c/S2c the simplest omniperiodic rule? Oscillators with periods 1-10:

Code: Select all

x = 264, y = 123, rule = B2c/S2c
169bo$168bobo$169bo$166bo5bo$169bo$166bo5bo$169bo$166bo5bo$161bobobobo
3bobobobo$160bobobo3bobo3bobobo$161bobobobo3bobobobo$160bobobo3bobo3bo
bobo$157bobo9bo9bobo$160bobobo3bobo3bobobo$157bobo9bo9bobo$154bobobo7b
o5bo7bobobo$157bobo9bo9bobo$152bo7bobobo3bobo3bobobo7bo$157bobo9bo9bob
o$150bo3bobobo7bo5bo7bobobo3bo$157bobo9bo9bobo$148bo3bo7bobobo3bobo3bo
bobo7bo3bo$157bobo9bo9bobo$146bo3bo3bobobo7bo5bo7bobobo3bo3bo$157bobo
9bo9bobo$146bo3bo3bobobo7bo5bo7bobobo3bo3bo$157bobo9bo9bobo$142bobo3bo
3bo7bobobo3bobo3bobobo7bo3bo3bobo$157bobo9bo9bobo$140bo5bo3bo3bobobo7b
o5bo7bobobo3bo3bo5bo$157bobo9bo9bobo$140bo5bo3bo3bobobo7bo5bo7bobobo3b
o3bo5bo$137bobobobobobobobobobo5bobobobo3bobobobo5bobobobobobobobobobo
$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$135bo21bobo9bo9bobo21bo$140b
o5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$135bo21bobo9bo9bobo21bo$140bo5bo
3bo3bobobo7bo5bo7bobobo3bo3bo5bo$131bobo3bobobobobobobobobobo5bobobobo
3bobobobo5bobobobobobobobobobo3bobo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo
3bo5bo$129bo5bo21bobo9bo9bobo21bo5bo$140bo5bo3bo3bobobo7bo5bo7bobobo3b
o3bo5bo$127bo3bobo3bobobobobobobobobobo5bobobobo3bobobobo5bobobobobobo
bobobobo3bobo3bo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$125bo3bo5bo
21bobo9bo9bobo21bo5bo3bo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$123b
o3bo3bobo3bobobobobobobobobobo5bobobobo3bobobobo5bobobobobobobobobobo
3bobo3bo3bo$44bobo93bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo48bobo$43bobo
bo75bo3bo3bobo3bobobobobobobobobobo5bobobobo3bobobobo5bobobobobobobobo
bobo3bobo3bo3bo$42bo5bo71bobobobobobobobobobo3bobo3bo3bo7bobobo3bobo3b
obobo7bo3bo3bobo3bobobobobobobobobobo26bo5bo$43bobobo75bo3bo3bobo3bobo
bobobobobobobobo5bobobobo3bobobobo5bobobobobobobobobobo3bobo3bo3bo$40b
o3bobo3bo69bobobobobobobobobobo3bobo3bo3bo7bobobo3bobo3bobobo7bo3bo3bo
bo3bobobobobobobobobobo26bo5bo$43bobobo69bobobo3bo3bo5bo21bobo9bo9bobo
21bo5bo3bo3bobobo$38bo3bo5bo3bo63bobo21bo5bo3bo3bobobo7bo5bo7bobobo3bo
3bo5bo21bobo22bo5bo$37bobobo7bobobo63bobobo3bo3bo5bo21bobo9bo9bobo21bo
5bo3bo3bobobo$38bo3bo5bo3bo63bobo21bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo
5bo21bobo16bobobo3bobo3bobobo$35bo7bobobo7bo21bo39bobobo3bo3bo5bo21bob
o9bo9bobo21bo5bo3bo3bobobo$38bo3bo5bo3bo36bobobobobobobo14bobo21bo5bo
3bo3bobobo7bo5bo7bobobo3bo3bo5bo21bobo16bobobo3bobo3bobobo$13bo19bo3bo
bobo7bobobo3bo19bo33bobobo7bo3bo3bobo3bobobobobobobobobobo5bobobobo3bo
bobobo5bobobobobobobobobobo3bobo3bo3bo7bobobo$32bobobo3bo3bobo3bo3bobo
bo28bo15bo12bobo21bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo21bobo12bobo7bo
5bo7bobo$bo11bo6bobobobo4bo3bo7bobobo7bo3bo17bo31bo7bobobo3bo3bo5bo21b
obo9bo9bobo21bo5bo3bo3bobobo7bo$obo2bobo2bobobobo15bobobo3bo3bobo3bo3b
obobo4bobobobo2bobobobobobo4bo15bo4bobobobo5bobobobobobobobobobo3bobo
3bo3bo7bobobo3bobo3bobobo7bo3bo3bobo3bobobobobobobobobobo5bobobobo2bo
5bobobo3bobo3bobobo5bo$bo11bo6bobobobo4bo3bo7bobobo7bo3bo17bo31bo7bobo
bo3bo3bo5bo21bobo9bo9bobo21bo5bo3bo3bobobo7bo$32bobobo3bo3bobo3bo3bobo
bo28bo15bo12bobo21bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo21bobo12bobo7bo
5bo7bobo$13bo19bo3bobobo7bobobo3bo19bo33bobobo7bo3bo3bobo3bobobobobobo
bobobobo5bobobobo3bobobobo5bobobobobobobobobobo3bobo3bo3bo7bobobo$38bo
3bo5bo3bo36bobobobobobobo14bobo21bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo
21bobo16bobobo3bobo3bobobo$35bo7bobobo7bo21bo39bobobo3bo3bo5bo21bobo9b
o9bobo21bo5bo3bo3bobobo$38bo3bo5bo3bo63bobo21bo5bo3bo3bobobo7bo5bo7bob
obo3bo3bo5bo21bobo16bobobo3bobo3bobobo$37bobobo7bobobo63bobobo3bo3bo5b
o21bobo9bo9bobo21bo5bo3bo3bobobo$38bo3bo5bo3bo63bobo21bo5bo3bo3bobobo
7bo5bo7bobobo3bo3bo5bo21bobo22bo5bo$43bobobo69bobobo3bo3bo5bo21bobo9bo
9bobo21bo5bo3bo3bobobo$40bo3bobo3bo69bobobobobobobobobobo3bobo3bo3bo7b
obobo3bobo3bobobo7bo3bo3bobo3bobobobobobobobobobo26bo5bo$43bobobo75bo
3bo3bobo3bobobobobobobobobobo5bobobobo3bobobobo5bobobobobobobobobobo3b
obo3bo3bo$42bo5bo71bobobobobobobobobobo3bobo3bo3bo7bobobo3bobo3bobobo
7bo3bo3bobo3bobobobobobobobobobo26bo5bo$43bobobo75bo3bo3bobo3bobobobob
obobobobobo5bobobobo3bobobobo5bobobobobobobobobobo3bobo3bo3bo$44bobo
93bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo48bobo$123bo3bo3bobo3bobobobobo
bobobobobo5bobobobo3bobobobo5bobobobobobobobobobo3bobo3bo3bo$140bo5bo
3bo3bobobo7bo5bo7bobobo3bo3bo5bo$125bo3bo5bo21bobo9bo9bobo21bo5bo3bo$
140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$127bo3bobo3bobobobobobobobobo
bo5bobobobo3bobobobo5bobobobobobobobobobo3bobo3bo$140bo5bo3bo3bobobo7b
o5bo7bobobo3bo3bo5bo$129bo5bo21bobo9bo9bobo21bo5bo$140bo5bo3bo3bobobo
7bo5bo7bobobo3bo3bo5bo$131bobo3bobobobobobobobobobo5bobobobo3bobobobo
5bobobobobobobobobobo3bobo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$
135bo21bobo9bo9bobo21bo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$135bo
21bobo9bo9bobo21bo$140bo5bo3bo3bobobo7bo5bo7bobobo3bo3bo5bo$137bobobob
obobobobobobo5bobobobo3bobobobo5bobobobobobobobobobo$140bo5bo3bo3bobob
o7bo5bo7bobobo3bo3bo5bo$157bobo9bo9bobo$140bo5bo3bo3bobobo7bo5bo7bobob
o3bo3bo5bo$157bobo9bo9bobo$142bobo3bo3bo7bobobo3bobo3bobobo7bo3bo3bobo
$157bobo9bo9bobo$146bo3bo3bobobo7bo5bo7bobobo3bo3bo$157bobo9bo9bobo$
146bo3bo3bobobo7bo5bo7bobobo3bo3bo$157bobo9bo9bobo$148bo3bo7bobobo3bob
o3bobobo7bo3bo$157bobo9bo9bobo$150bo3bobobo7bo5bo7bobobo3bo$157bobo9bo
9bobo$152bo7bobobo3bobo3bobobo7bo$157bobo9bo9bobo$154bobobo7bo5bo7bobo
bo$157bobo9bo9bobo$160bobobo3bobo3bobobo$157bobo9bo9bobo$160bobobo3bob
o3bobobo$161bobobobo3bobobobo$160bobobo3bobo3bobobo$161bobobobo3bobobo
bo$166bo5bo$169bo$166bo5bo$169bo$166bo5bo$169bo$168bobo$169bo!

[C28]

is there a way to stabilize this?

Code: Select all

x = 22, y = 12, rule = B3/S23
bo$obo3b2obo$o2bo2bob2o$b2o2$9bo$7bobo$6bobo$2o3bo2bo11b2o$2o4bobo11b
2o$7bobo$9bo!

[ihatecorderships]

Can someone explain to me all the different catagolue symetries? some examples would also be helpful.
Edit. Thanks!

[yujh]

Can someone explain to me all the different catagolue symetries? some examples would also be helpful.

symmetry

[mniemiec]

symmetry

This article mentions D8_2, which I had never heard of before (and seems counter-intuitive). Does anyone know any rules that support it?

[bubblegum]

This article mentions D8_2, which I had never heard of before (and seems counter-intuitive). Does anyone know any rules that support it?

It also mentions a checklist for constructing rules that support it, from which I derived this rule:

Code: Select all

x = 32, y = 31, rule = B3-kqy6i/S2-in3-aey4ait6ai7e
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o4bo$o
8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o6bobo
5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!

[mniemiec]

This article mentions D8_2, which I had never heard of before (and seems counter-intuitive). Does anyone know any rules that support it?

It also mentions a checklist for constructing rules that support it, from which I derived this rule: ...

It appears that such rules are of the form that the parity of the line of symmetry is irrelevant, which means that any suitable pattern in such a rule has exactly the same behavior and census under D8_1, D8_2, and D8_4 - making D8_2 always redundant in any rule in which it is valid. (I.e. useful as an academic footnote, but not useful for soup searching).

[dvgrn]

what's our attitude towards money related things in the field of CA patterns.

1. could patreons be allowed?
2. would money rewards be accepted?

Lifenthusiasts tend to be wonderfully ornery and opinionated. So "our attitude" isn't just NP-complete, it's undecidable -- each of us has our own attitude, and any kind of consensus is very, very unlikely.

There is no governing body that could possibly forbid Patreons, Kickstarters, monetary rewards, etc., so they're allowed by default. But apparently everyone who has considered setting up donation-based funding for CA projects ... has concluded that it's much less bother to just get a regular job and self-fund whatever they want to accomplish.

Monetary rewards for specific discoveries are in fact very traditional in this business -- John Conway Himself used them on multiple occasions to encourage early discoveries. (Along similar lines, Donald Knuth's reward checks come to mind, though these would not usually be Conway's-Life-related).

A $50 reward was what got me in to Life research back in 2001, though the money got recycled back into a new reward that was eventually sent to Mike Playle for finding the Snark. And MikeP has since recycled his prize money into another reward, and added more $ for other discoveries. Fortunately or unfortunately, CA research really isn't much of a money-making business.

[Macbi]

Is there a list somewhere of the bounties currently on offer?

[dvgrn]

Is there a list somewhere of the bounties currently on offer?

Not really. I've been trying to get Ed Pegg to update the mathpuzzle.com Prize Page, but it just acknowledges that Mike Playle won the post-boojum reflector prize, without listing his replacement prizes.

[wwei47]

The Mine function uses your CPU and an algorithm to process and discover interesting long living BIOs on 17*17 or 35*35 grids. Mining randomly processes through 4 different types of symmetrical forms and loop possibilities.

I'm wondering if we should create our own algorithm to do this just to show them off.
EDIT: Oops wrong tag

[PC101]

Is there a reaction like this that can be used to turn an XWSS into a HWSS?

Code: Select all

x = 15, y = 19, rule = B3/S23
11b2o$10b2ob2o$11b4o$12b2o3$bo$2o$obo3$4b2o$4bobo$4bo3$9bo$8b2o$8bobo!

[cgoler2]

Where's the POTD voting thread?

[bubblegum]

Where's the POTD voting thread?

It got locked because I'm terrible at managing these

[hotdogPi]

We've looked at (via script) every pattern with 9 or fewer cells and everything with 10 in a single cluster. What is the minimum number of cells (known) that we'll never finish since absolutely everything constructible is included?

From what I understand, anything constructible can be made with 13 gliders — 17 are required for it to be clean, but that's not a requirement here. It includes 3 glider-producing switch engines (10 cells each), but I don't know how many cells are needed in place of the remaining 4 gliders.

[C28]

what is the name of this 10-cell pattern?

Code: Select all

x = 4, y = 4, rule = B3/S23
2o$obo$b3o$b3o!

[mniemiec]

what is the name of this 10-cell pattern? ...

I don't think it has a name. There are so many life patterns, that have no particular interesting behaviors, that the vast majority of them don't have individual names. This is true for larger still-lifes and oscillators (but generally not spaceships, as they tend to be fragile and rare, at least in Life). This is especially true for patterns that are unstable.

[MathAndCode]

what is the name of this 10-cell pattern? ...

I don't think it has a name. There are so many life patterns, that have no particular interesting behaviors, that the vast majority of them don't have individual names. This is true for larger still-lifes and oscillators (but generally not spaceships, as they tend to be fragile and rare, at least in Life). This is especially true for patterns that are unstable.

This particular pattern is fairly common, though. C28 presented it in ten-cell form, but it has a six-cell predecessors and at least three seven-cell predecessors (and I wouldn't be surprised if that number turned out to be higher).

Code: Select all

x = 41, y = 41, rule = B3/S23
o$o34bo$o34b2o$36bobo$2o35b2o$2bo30$o$o$o36bo$o2bo32b2o$b2o34bo2bo$38b2o!

While I've never heard an official name for it, I've always called it the U-turner in my head because the activity makes several 180° turns.



Edit: I just realized that I forgot to include the six-cell predecessor's child and grandchild in the number of seven-cell predecessors. There is also o$bo$o$b2o$2b2o, so the number of seven-cell predecessors is at least six, and I wouldn't be surprised if it turned out to be even higher.

[hotdogPi]

It has an 8-cell 33-generation predecessor.

Code: Select all

x = 5, y = 4, rule = B3/S23
2b2o$bo2bo$o2bo$o2bo!

It's actually quite similar to this century predecessor: in both cases 8 cells enters the sequence of something with a minimum of 6 cells many generations later.

Code: Select all

x = 3, y = 5, rule = B3/S23
bo$obo$obo$b2o$bo!

[MathAndCode]

I just found two more seven-cell predecessors.

Code: Select all

x = 17, y = 4, rule = B3/S23
2bo11bobo$b2obo8b2o$o11bo$2o10b2o!

[wwei47]

I didn't know about this 5-cell pi predecessor until I found it by accident — what is it actually used in?

Code: Select all

x = 3, y = 4, rule = B3/S23
bo$3o2$bo!

I know the question is kind of old, but most of the uses I've seen for it are in Lifecompetes, where it's used to cheaply launch pis faster than the other 5-cell pi predecessor.