OCA B24/S23V has several non-trivial oscillators

[bruberu]

While searching through rules with a Von-Neumann neighborhood, I found B24/S23V (B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e).
In a random soup, usually this segments itself very quickly, mostly into several simple oscillators and objects bounded by a rectangle, which encapsulates their inner pattern (as long as nothing disturbs it).

However, there are two rather interesting behaviors shown in this rule.

First of all, objects not bounded in a rectangle are usually extremely unstable, and if these objects are large enough, these can create extremely long methuselahs, taking over 10,000 generations to finally encase themselves.

What I found most interesting was that of these encapsulated patterns, most of them were extremely high-period non-trivial oscillators. For example, take the pattern below, which is the master list of oscillators that have been found so far:

Code: Select all

x = 33, y = 569, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
3o4b5o2b3o$2bo4b2ob2o2bobo$3o4b5o2b3o$o6b2ob2o$3o4b5o7$3o4b6o$2bo4bo4b
o$3o4b6o$2bo$3o7$obo4bo4bo2b3o2b7o$obo4b2o4bobobo2b2o3b2o$3o4b3o4b2obo
2bo2bo2bo$2bo4bo7b3o2b2o3b2o$2bo4b3o10b7o$7bo6$3o4b6o2b7o2b9o$o6bo2bob
o2bobo2b2o2bo7bo$3o4bo2bobo2bobobobo2b9o$2bo4b3ob2o2b3o3bo$3o4bo3b2o2b
o3b3o$7b2o2b2o2bobobobo$7b2o2b2o2b2o2bobo$7bo4bo2b7o$7b6o3$3o5bo4b7o2b
o5b4o$o6b4o2bob3obo3bo5bobo$3o4bo2bo2bo2bo2bo4bo4bobo$obo4b4o2bo2bo2bo
5bo3b3o$3o7bo2bob3obo$13b7o6$3o4b5o2b6o$2bo4b2ob2o2bob2obo$2bo4bo3bo2b
2o2b2o$2bo4bo3bo2bob2obo$2bo4bo3bo2b6o$7bo3bo$7b2ob2o$7b5o4$3o4b7o$obo
4b7o$3o6bobobo$obo7b4o$3o7$3o4b11o$obo4bob2o3b2obo$3o4b2o7b2o$2bo4bob
2o3b2obo$3o4b11o7$ob3o4b4o$obobo4bo2bo$obobo4b4o$obobo5b3o$ob3o5bo7$ob
o4b18o$obo4b7o4b7o$obo4b18o$obo$obo7$ob3o4b14o$o3bo4bobo2b3o5bo$ob3o4b
14o$obo$ob3o7$ob3o$o3bo$ob3o$o3bo$ob3o7$obobo4b10o$obobo4b2ob2o4bo$ob
3o4bo4bo3bo$o3bo4b10o$o3bo7$ob3o4b9o$obo6bob2ob2obo$ob3o4bo2bobo2bo$o
3bo4bob5obo$ob3o4bobo3bobo$9b4ob4o$9bo2b3o2bo$9b3o3b3o$9b9o3$ob3o4b7o
3b7o$obo6bobob3o3b3o3bo$ob3o4bo2bob2o3bo5bo$obobo4bo5bo3bo5bo$ob3o4bo
2bob2o3bo3b3o$9bobob3o3b7o$9b7o5$ob3o4b8o$o3bo4bobob4o$o3bo4b2o2bo2bo$
o3bo4bobob4o$o3bo4b8o7$ob3o4b11o$obobo4bob3o5bo$ob3o4b11o$obobo$ob3o7$
ob3o$obobo$ob3o$o3bo$ob3o7$3ob3o4b10o$2bobobo4bob2o2b2obo$3obobo4b2o6b
2o$o3bobo4bob2o2b2obo$3ob3o4b10o7$3obo6b7o$2bobo6b4o2bo$3obo6bo2b2obo$
o3bo6b2o2b3o$3obo6b2o7$3ob3o4b9o$2bo3bo4bo2bobo2bo$3ob3o4bo2b3o2bo$o5b
o4bo2b3o2bo$3ob3o4bo2bobo2bo$11b9o6$3obobo4b7o$2bobobo4b3ob3o$3ob3o4bo
5bo$o5bo4bo5bo$3o3bo4bo5bo$11bobobobo$11b7o5$3ob3o4b12o$2bo3bo4bo2bob
2obo2bo$3o3bo4b2obob2obob2o$o5bo4bo10bo$3o3bo4b2obob2obob2o$11bo2bob2o
bo2bo$11b12o5$3ob3o4b8o$2bobobo4bo4b3o$3ob3o4bo2bo2b2o$o5bo4bob3o2bo$
3ob3o4bo2b3obo$11b2o2bo2bo$11b3o4bo$11b8o4$3ob3o4b8o$2bo3bo4bo2bo2b2o$
3ob3o4bo5b2o$2bobo6bo3bo2bo$3ob3o4b8o7$3ob3o4b7o$2bo3bo4bo2b4o$3ob3o4b
o2b4o$2bo3bo4bo3b3o$3ob3o4bo5bo$11bo5bo$11b7o5$3obobo4b7o$2bobobo4b4ob
2o$3ob3o4bo5bo$2bo3bo4bobo2b2o$3o3bo4bo2bo2bo$11b7o6$3ob3o4b7o$2bobo6b
obobobo$3ob3o4b3ob3o$2bobobo4bob3obo$3ob3o4bob3obo$11bob3obo$11b3ob3o$
11bobobobo$11b7o3$3ob3o4b13o$2bo3bo4bob3ob2o3b2o$3o3bo4b4ob2o5bo$2bo3b
o4b4ob2o5bo$3o3bo4bob3ob2o3b2o$11b13o6$obob3o4b13o$obobobo4b2o3bobo3b
2o$3obobo4bo11bo$2bobobo4bo11bo$2bob3o4b2o3bobo3b2o$11b13o6$obob3o4b
12o$obo3bo4b2o7b3o$3ob3o4bo10bo$2bobo6b2o7b3o$2bob3o4b12o7$obobobo4b
12o$obobobo4bo2b2o2b2ob2o$3ob3o4bobo2b4o2bo$2bo3bo4bo2b2o2b2ob2o$2bo3b
o4b12o7$obob3o4b9o$obobo6bo7bo$3ob3o4bo5b3o$2bobobo4bo3b3obo$2bob3o4bo
5b3o$11bo7bo$11b9o5$3ob3o4b7o$o5bo4bob5o$3ob3o4bo2b4o$2bo3bo4bo2b4o$3o
b3o4bo4b2o$11b2o4bo$11b7o5$3ob3o4b10o$o3bo6bo8bo$3ob3o4b2o6b2o$2bobobo
4b3o4b3o$3ob3o4b2o6b2o$11bo8bo$11b10o5$3ob3o4b11o$o5bo4b3obo3bobo$3o3b
o4bo5b2ob2o$2bo3bo4bo5b2ob2o$3o3bo4b3obo3bobo$11b11o6$3obobo4b11o$o3bo
bo4bo2bob2o2b2o$3ob3o4bo2bobo2bobo$obo3bo4bo2bob2o2b2o$3o3bo4b11o7$3ob
3o4b7o$o3bo6bobobobo$3ob3o4bo5bo$obobobo4bobobobo$3ob3o4bobobobo$11bob
obobo$11b2o3b2o$11b7o4$3ob3o$2bobobo$2bobobo$2bobobo$2bob3o7$3obobo4b
10o$obobobo4bobobo3b2o$3ob3o4b2o3bob3o$obo3bo4bobobo3b2o$3o3bo4b10o7$
3ob3o4b8o$obobo6bo4b3o$3ob3o4bo3bob2o$obobobo4bo3bob2o$3ob3o4bo4b3o$
11b8o6$3ob3o4b8o$obo3bo4bob3ob2o$3ob3o4bo2b5o$2bobo6bo3b2obo$3ob3o4bo
6bo$11bo3b2obo$11bo2b5o$11bob3ob2o$11b8o3$obob3o4b6o$obobobo4bo4bo$obo
bobo4bobob2o$obobobo4bo2b3o$obob3o4bo4bo$11bob4o$11b6o5$ob3ob3o4b10o$o
bo3bobo4bob3o4bo$ob3obobo4bob3o2bobo$obobobobo4b4ob2ob2o$ob3ob3o4bo2bo
2bo2bo$13b4ob2ob2o$13bob3o2bobo$13bob3o4bo$13b10o3$ob3ob3o4b12o$o3bo3b
o4bo2b5o2b2o$o3bob3o4bobob3ob4o$o3bobo6bo2b5o2b2o$o3bob3o4b12o7$ob3ob
3o4b10o$o3bobobo4bo2bo5bo$o3bob3o4bo3bob4o$o3bobobo4bo6bobo$o3bob3o4bo
3bob4o$13bo2bo5bo$13b10o5$3ob3ob3o4b10o$2bo3bobobo4b2o2bo4bo$3ob3ob3o
4b2o7bo$o5bobobo4b2obo2bo2bo$3ob3ob3o4bo4b3obo$15b3o3b4o$15b10o5$3obob
obobo4b9o$2bobobobobo4bobo3bobo$3ob3ob3o4bo2bobo2bo$o5bo3bo4bo3bo3bo$
3o3bo3bo4bo3bo3bo$15b4ob4o$15bo2bobo2bo$15b9o4$3ob3obo4b7o$o3bo3bo4bo
5bo$3ob3obo4bo5bo$obobobobo4bo5bo$3ob3obo4bo3b3o$13b2ob4o$13b3o2b2o$
13b7o4$obob3ob3o2b16o$obo3bo3bo2bobobobob2ob5o$obob3ob3o2bo5bo4bo3bo$o
bobo3bo4bobobobo4bo3bo$obob3ob3o2bobobobo4bo3bo$13bobobobo4bobobo$13b
2o3b2ob2ob2ob2o$13b16o4$3obobob3ob3o4b9o$2bobobo3bo3bo4bo7bo$3ob3o3bob
3o4b3o5bo$o5bo3bobo6bo2bo4bo$3o3bo3bob3o4b6o2bo$19b3obobobo$19b9o5$3ob
ob3ob3o4b9o$o3bobobobobo4b4o4bo$3obob3ob3o4bo7bo$2bobo3bobobo4b2o6bo$
3obob3ob3o4bobo2b4o$17b2o5b2o$17bob4ob2o$17b9o!

Notably, all of these are highly non-trivial. Even though it makes sense that such complex oscillators would fit in a rule where all objects encased inside a simple rectangle are automatically stable, most oscillators with similar periods still have no correlation with each other.

Even more interestingly, there seem to be several stable patterns that can attach to these as long as they can fit, such as this 3-wide "hat" attached to this period 4 oscillator:

Code: Select all

x = 10, y = 5, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
10o$7ob2o$ob3obo2bo$7ob2o$10o!

Or even this, a small pattern attached on the rectangle next to another period 10 oscillator:

Code: Select all

x = 4, y = 17, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
2bo$2b2o$2b2o$2b2o$3bo$2b2o$2b2o$2b2o$3bo$4o$o2bo$ob2o$4o$ob2o$4o$ob2o
$4o!

One open question that still remains is whether or not all periods exist within this rule. I have yet to see any simple oscillators with period 13 or 19 yet, although their non-existence would be quite difficult to prove. I also ran this quite a while in apgluxe 5, but considering how long some of these take to stabilize, quite a lot of objects get labeled as pathological, and soups per second turn quite quickly into seconds per soup (I got 4 seconds per soup on a fairly bad laptop).

[bruberu]

As an update, I did find two p5 oscillators so far:

Code: Select all

x = 15, y = 9, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
6o2b7o$o2bobo2bobo2b2o$o2bobo2bobobobo$3ob2o2b3o3bo$o3b2o2bo3b3o$2o2b
2o2bobobobo$2o2b2o2b2o2bobo$o4bo2b7o$6o!

What's rather interesting about the first one in particular is that it seems to be stabilized by the block near the bottom. I wonder if there's a way to shorten the block in any way, although so far I have not figured out a method by which to do so.

I have also not found any of the other missing periods so far, but I'll keep you posted if I do.

[bprentice]

A very interesting rule!

Another P5 and a P11:

Code: Select all

x = 18, y = 13, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
9A$A7.A$9A8$18A$7A4.7A$18A!

Square Cell reports a period of 66 for your 8th oscillator in your 1st pattern.

Brian Prentice

[bruberu]

Yes, I noticed that discrepancy after making it

There is actually a P23, though:

Code: Select all

x = 13, y = 10, rule = B2ei3ajr4-cjnry5acjkr6-ak7c8/S2ei3aejr4-ceny5-ce6-cn7e
2$b9o$bo2bobo2bo$bo2b3o2bo$bo2b3o2bo$bo2bobo2bo$b9o!

I'm also going to edit the original post with a new, updated master list of oscillators.