Reflectorless Rotating Oscillators (RRO)

[Docsy]

Could i please perhaps see the L89 rro?

It can be found here: https://conwaylife.com/forums/viewtopic ... 716#p79716

There is a similar design of adjustable RRO that is basically the original design, turned sideways. It uses orthogonal and diagonal spaceships that are the same speed.
Are there any specific examples of this?

Nope, still up for grabs! I'd say intuitively it's likely a little less easy to find, since the fastest spaceships in many rules have the diagonal going slower than the orthogonal, but that's not really a dealbreaker.

[splitterrules]

A 4-state example:

Code: Select all

x = 41, y = 33, rule = RROdesign
14.A6.A$14.BA5.C2$19.C8.BA$19.A8.A10$A20.A$BA9.AC8.C3.AC12.AC2$CA12.C
A3.C8.CA9.AB$19.A20.A10$12.A8.A$11.AB8.C2$19.C5.AB$19.A6.A!
@RULE RROdesign
@TABLE n_states:4
neighborhood:Moore
symmetries:rotate4reflect

0 0,0,0,0,0,0,0,0 0
0 0,0,0,2,0,0,0,0 2
0 0,0,0,0,2,0,0,0 1
0 0,0,0,1,2,0,0,0 1
0 0,0,0,2,2,0,0,0 1
0 0,0,0,0,3,0,0,0 3
0 0,0,0,2,3,0,0,0 3
0 0,0,0,3,0,2,0,0 3
0 0,0,1,3,1,0,0,0 3
0 0,0,1,2,1,1,0,0 1
0 0,0,3,0,0,1,0,0 3
1 0,0,0,1,3,0,0,0 1
1 0,0,1,3,3,0,0,0 2
1 0,0,1,3,3,1,0,0 2
1 0,0,3,2,1,1,0,0 2
3 0,0,0,0,0,0,0,0 1
3 0,0,0,3,0,0,0,0 3
3 0,0,0,0,1,0,0,0 1
3 0,0,0,3,1,3,0,0 1
3 0,0,1,0,2,0,0,0 1
3 0,0,1,1,2,0,0,0 1
3 0,0,1,1,3,0,0,0 1
0 0,0,3,1,0,1,2,0 1

var a1={0,1,2,3}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var a9=a1
a1 a2,a3,a4,a5,a6,a7,a8,a9 0

[muzik]

A multistate hexagonal example would be interesting to find, since we already have an adjustable hex SMOS.

[1and0nlycordershippr]

Can you show it to me?

[pifricted]

Can you show it to me?

Arbitrary level SMOSMOS...MOS in 32 states!

[Docsy]

I realized even the design I showed earlier is not really the simplest way to do an adjustable RRO. You actually only need one kind of spaceship and a specific reaction when two of them collide just right. Here's a visual of the design. It's possible this might be more versatile for finding them in other rules.

[AforAmpere]

Here is an implementation of that design:

Code: Select all

x = 688, y = 88, rule = B2ai3aqr4aejrtw5ijnr6-ac/S2-ik3iry4-kyz5-eknq6ak7e
180bo69bo84bo44bo45bo35bo57bo29bo29bo27bo17bo17bo17bo17bo$178bobo67bob
o82bobo42bobo43bobo33bobo55bobo27bobo27bobo25bobo15bobo15bobo15bobo15b
obo$182b2o198b2o198b2o98b2o2$2bo99bo79bo19bo59bo39bo44bo34bo19bo35bo
35bo27bo29bo29bo19bo19bo17bo17bo17bo17bo7bo$2bobo97bobo97bobo57bobo37b
obo42bobo52bobo33bobo33bobo25bobo27bobo27bobo37bobo15bobo15bobo15bobo
15bobo$486bo199bo$2o98b2o98b2o98b2o98b2o98b2o98b2o$486b2o198b2o$bo99bo
99bo99bo99bo99bo99bo2$605bo2$604b2o5$286bo299bo2$286b2o194b2o102b2o94b
2o2$482bo199bo$505bo$686bo$504b2o94b2o$686b2o$601bo2$405bo199bo2$404b
2o198b2o$282b2o298b2o$386bo$282bo299bo$386b2o2$500b2o$305bo376b2o$501b
o$304b2o376bo2$486bo199bo$400b2o198b2o$486b2o198b2o$401bo199bo2$382b2o
221bo$586bo$382bo221b2o$586b2o2$300b2o$205bo299bo$301bo$204b2o298b2o$
482b2o198b2o2$482bo199bo2$686bo$600b2o$582b2o102b2o$601bo$582bo$405bo
199bo2$200b2o202b2o94b2o102b2o2$201bo299bo5$682b2o2$682bo2$86bo99bo99b
o99bo99bo99bo99bo$400b2o198b2o$86b2o98b2o98b2o98b2o98b2o98b2o98b2o$
401bo199bo$83bobo97bobo37bobo57bobo52bobo42bobo25bobo33bobo33bobo37bob
o27bobo27bobo25bobo15bobo15bobo15bobo15bobo$85bo19bo79bo39bo59bo19bo
34bo44bo27bo35bo35bo19bo19bo29bo29bo19bo7bo17bo17bo17bo17bo2$104b2o
198b2o198b2o98b2o$107bobo127bobo67bobo42bobo70bobo33bobo43bobo27bobo
27bobo37bobo15bobo15bobo15bobo15bobo$107bo129bo69bo44bo72bo35bo45bo29b
o29bo39bo17bo17bo17bo17bo!

This clearly works for all loopabilities, and there is always an oscillator at p(18*n) with loopability n>1.

[Docsy]

RRO definition: You can't do reflector loops, that's cheating!
Spaceships: Fine, we'll do it ourselves.

Reflectorless relays are fun.

[AforAmpere]

An improved version, with a p14 minimal spacing. 100 copies evenly fit in this example:

Code: Select all

x = 700, y = 700, rule = B2a3akqr4acjrt5-akq6aek7c8/S2-kn3iry4ajr5enry6kn78
8bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13b
o13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo$6bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo2$3bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13b
o13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo5b2o$3bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo$2o693bo$698bo$bo$4bo693b2o2$3b2o
7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$
4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b
2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo
$4bo693b2o2$3b2o7$695b2o2$2o693bo$698bo$bo$4bo693b2o2$3b2o7$695b2o2$2o
693bo$698bo$bo$4bo693b2o$8bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo$3b2o5bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo2$5bobo11bobo11bobo11b
obo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo
11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bobo11bo
bo$5bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo13bo!

[muzik]

How easy would it be to write a program that checks for the loopability of some given input oscillator? There have been some mentions of scripts in this thread, but none posted outright from what I can see. I'd imagine it'd work in this manner (for the square grid):

- calculate the period of the oscillator: let's call this p
- verify that the oscillator's kinetic symmetry is one of the following: n.c, n.e, n.k, nrc, nrk
- factorize the period of the oscillator
- for all factors of the oscillator's period from 1 to p/2: place the oscillator, advance p/[factor] generations, then place another copy of the oscillator at the initial position and verify that doing so doesn't break everything
- if the period is reduced by the expected amount, list that as a valid loopability

Of course, this wouldn't check for nontrivial interactions in the center that don't happen for single copies but still reduce the overall period, but the system seems functional enough after rotating it in 3D in my mind a bunch.

[Docsy]

- verify that the oscillator's kinetic symmetry is one of the following: n.c, n.e, n.k, nrc, nrk

As a note, while every loopable pattern I've seen has some rotational symmetry, in principle loopability doesn't require any symmetry, so fully requiring this would break the script for some (undiscovered?) edge cases.
Edit:
A bit of trivia that I think belongs in this thread, loopability as a concept can actually be generalized to spaceships, and there's a known example by hotcrystal0 and FWKnightship here:

I think I found a SMORRO

Code: Select all

x = 34, y = 5, rule = 2-cn3-acky4ityz5k/2k3-ekny4ijqy6i78/3
2A30.2A$A.A28.A.A$A.2A26.2A.A$B2A28.2AB$.A30.A!

A 6c/52 based on it:

Code: Select all

x = 48, y = 15, rule = 2-cn3-acky4ityz5k/2k3-ekny4ijqy6i78/3
7.A32.A$6.B2A30.2AB$8.2A28.2A$7.2A30.2A6$.B44.B$2A9.2A22.2A9.2A$.B8.A
.A22.A.A8.B$9.2A2.2B.A14.A.2B2.2A$10.2A.2B2A14.2A2B.2A$11.3A.A16.A.3A
!

[muzik]

- verify that the oscillator's kinetic symmetry is one of the following: n.c, n.e, n.k, nrc, nrk

As a note, while every loopable pattern I've seen has some rotational symmetry, in principle loopability doesn't require any symmetry, so fully requiring this would break the script for some (undiscovered?) edge cases.

Are you referring to items such as these?:

By the way, how does one classify this P75 oscillator? (in a custom rule, just to demonstrate the concept)

Code: Select all

x = 2, y = 3, rule = modrrotest
.A$BA$BA!

It can even be made into a P25 using 3 copies:

Code: Select all

x = 13, y = 12, rule = modrrotest
4.D$2.2CD.A$2.2CF$2.2CA3$10.D$9.3D$8.2D.2D$.A6.2D$BA$BA!

[Docsy]

Yes. In principle, loopability for oscillators is just the property that you can layer non-overlapping, non-interacting copies of itself to produce oscillators of a lower period. Rotation makes this a lot easier to achieve, often you just have a "failed" spaceship that produces a rotated copy of itself before evaporating, but in principle as long as an oscillator only would interact with itself with small offsets in time relative to the period, it doesn't have to rotate. Rotation is also helpful cuz if a pattern ever produces a rotated copy of itself in its entirety with nothing else, it's instantly an oscillator, so it could even wander in a way unlike a spaceship and still be an RRO.

You could have an RRO-like pattern that has a backend that fluctuates until it's completed what resembles a full rotation, thus technically not rotating. You could also have an amoeba that just sorta wanders around and happens to end up in the same spot and the same phase (admittedly unlikely to line up perfectly). You could also have two RROs that interact yet don't break each other for a small portion of their phase, maintaining much of their loopability while not being an RRO in totality.

[yyh_baboon]

Yes. In principle, loopability for oscillators is just the property that you can overlap non-overlapping, non-interacting copies of itself to produce oscillators of a lower period. Rotation makes this a lot easier to achieve, often you just have a "failed" spaceship that produces a rotated copy of itself before evaporating, but in principle as long as an oscillator only would interact with itself with small offsets in time relative to the period, it doesn't have to rotate. Rotation is also helpful cuz if a pattern ever produces a rotated copy of itself in its entirety with nothing else, it's instantly an oscillator, so it could even wander in a way unlike a spaceship and still be an RRO.

You could have an RRO-like pattern that has a backend that fluctuates until it's completed what resembles a full rotation, thus technically not rotating. You could also have an amoeba that just sorta wanders around and happens to end up in the same spot and the same phase (admittedly unlikely to line up perfectly). You could also have two RROs that interact yet don't break each other for a small portion of their phase, maintaining much of their loopability while not being an RRO in totality.

Agree. Loopable flipping oscillators exist;

Code: Select all

  x = 88, y = 169, rule = B2i3-jkny4qz5cy6cn/S2aek3-aky4eiyz5knq6-kn
20bob2o$21b4o$25bo$22b3obo$21bo3bo$21bob2o2$19b2o$19b2o$17bobo$17b3o$
18bo4$18bo$17b3o$17bobo$19b2o$19b2o2$21bob2o$21bo3bo$22bo2bo2$21b2obo
$20bobo2b2o$21b6o$24bo$23b2o$20b3o3b2o$20bo7bo$20bobo$21b2o3$19b3o$19b
o$19b3o2$36b2o5b2o$37bo5bo$34b4o5b4o$26bobo6bo9bo6bobo$28bo2b2o15b2o2b
o$28b4o17b4o$28bo3bo15bo3bo$28bo3bo15bo3bo$29b3o17b3o11$35bo$34b2o$31b
o3bo$30b3o2bo$34bo$31bobo$31b3o9$3b3o2$4ob4o$o7bo$o2b3o2bo$b2obob2o3$
8bo11bo46b2o9b2o$7b2o11b2o44bobo9bobo$6b2obo9bob2o42b2obo9bob2o$7bobo
9bobo44b2o11b2o$8b2o9b2o46bo11bo3$80b2obob2o$79bo2b3o2bo$79bo7bo$79b4o
b4o2$82b3o9$54b3o$54bobo$53bo$52bo2b3o$52bo3bo$52b2o$52bo11$36b3o17b3o
$35bo3bo15bo3bo$35bo3bo15bo3bo$35b4o17b4o$35bo2b2o15b2o2bo$33bobo6bo9b
o6bobo$41b4o5b4o$44bo5bo$43b2o5b2o2$66b3o$68bo$66b3o3$65b2o$65bobo$59b
o7bo$60b2o3b3o$63b2o$63bo$61b6o$61b2o2bobo$63bob2o2$62bo2bo$62bo3bo$63b
2obo2$67b2o$67b2o$68bobo$68b3o$69bo4$69bo$68b3o$68bobo$67b2o$67b2o2$63b
2obo$62bo3bo$61bob3o$62bo$63b4o$64b2obo!

I think it’s only a matter of time before completely asymmetrical loopable oscillators are found.

[Docsy]

Agree. Loopable flipping oscillators exist;

Code: Select all

  x = 88, y = 169, rule = B2i3-jkny4qz5cy6cn/S2aek3-aky4eiyz5knq6-kn
20bob2o$21b4o$25bo$22b3obo$21bo3bo$21bob2o2$19b2o$19b2o$17bobo$17b3o$
18bo4$18bo$17b3o$17bobo$19b2o$19b2o2$21bob2o$21bo3bo$22bo2bo2$21b2obo
$20bobo2b2o$21b6o$24bo$23b2o$20b3o3b2o$20bo7bo$20bobo$21b2o3$19b3o$19b
o$19b3o2$36b2o5b2o$37bo5bo$34b4o5b4o$26bobo6bo9bo6bobo$28bo2b2o15b2o2b
o$28b4o17b4o$28bo3bo15bo3bo$28bo3bo15bo3bo$29b3o17b3o11$35bo$34b2o$31b
o3bo$30b3o2bo$34bo$31bobo$31b3o9$3b3o2$4ob4o$o7bo$o2b3o2bo$b2obob2o3$
8bo11bo46b2o9b2o$7b2o11b2o44bobo9bobo$6b2obo9bob2o42b2obo9bob2o$7bobo
9bobo44b2o11b2o$8b2o9b2o46bo11bo3$80b2obob2o$79bo2b3o2bo$79bo7bo$79b4o
b4o2$82b3o9$54b3o$54bobo$53bo$52bo2b3o$52bo3bo$52b2o$52bo11$36b3o17b3o
$35bo3bo15bo3bo$35bo3bo15bo3bo$35b4o17b4o$35bo2b2o15b2o2bo$33bobo6bo9b
o6bobo$41b4o5b4o$44bo5bo$43b2o5b2o2$66b3o$68bo$66b3o3$65b2o$65bobo$59b
o7bo$60b2o3b3o$63b2o$63bo$61b6o$61b2o2bobo$63bob2o2$62bo2bo$62bo3bo$63b
2obo2$67b2o$67b2o$68bobo$68b3o$69bo4$69bo$68b3o$68bobo$67b2o$67b2o2$63b
2obo$62bo3bo$61bob3o$62bo$63b4o$64b2obo!

As a small note, I think people use RFO to mean two different things at times. One is an RRO that rotates 180 degrees halfway through the period without ever rotating 90 degrees. The other is a pattern that mirrors itself halfway through. The former is known and I quite like them, the one you shared is an example, and I'd love to see how you could make one adjustable. For the latter, loopability for such oscillators is only possible for odd loopabilities, and as far as I know, no example is known, at least not in INT.

As noted earlier with the generations ship I shared, loopability does generalize to spaceships as well, but not many examples are known either. I'd love some more exploration into loopability in the broad sense.

[1and0nlycordershippr]

Yes. In principle, loopability for oscillators is just the property that you can overlap non-overlapping, non-interacting copies of itself to produce oscillators of a lower period. Rotation makes this a lot easier to achieve, often you just have a "failed" spaceship that produces a rotated copy of itself before evaporating, but in principle as long as an oscillator only would interact with itself with small offsets in time relative to the period, it doesn't have to rotate. Rotation is also helpful cuz if a pattern ever produces a rotated copy of itself in its entirety with nothing else, it's instantly an oscillator, so it could even wander in a way unlike a spaceship and still be an RRO.

You could have an RRO-like pattern that has a backend that fluctuates until it's completed what resembles a full rotation, thus technically not rotating. You could also have an amoeba that just sorta wanders around and happens to end up in the same spot and the same phase (admittedly unlikely to line up perfectly). You could also have two RROs that interact yet don't break each other for a small portion of their phase, maintaining much of their loopability while not being an RRO in totality.

Agree. Loopable flipping oscillators exist;

Code: Select all

  x = 88, y = 169, rule = B2i3-jkny4qz5cy6cn/S2aek3-aky4eiyz5knq6-kn
20bob2o$21b4o$25bo$22b3obo$21bo3bo$21bob2o2$19b2o$19b2o$17bobo$17b3o$
18bo4$18bo$17b3o$17bobo$19b2o$19b2o2$21bob2o$21bo3bo$22bo2bo2$21b2obo
$20bobo2b2o$21b6o$24bo$23b2o$20b3o3b2o$20bo7bo$20bobo$21b2o3$19b3o$19b
o$19b3o2$36b2o5b2o$37bo5bo$34b4o5b4o$26bobo6bo9bo6bobo$28bo2b2o15b2o2b
o$28b4o17b4o$28bo3bo15bo3bo$28bo3bo15bo3bo$29b3o17b3o11$35bo$34b2o$31b
o3bo$30b3o2bo$34bo$31bobo$31b3o9$3b3o2$4ob4o$o7bo$o2b3o2bo$b2obob2o3$
8bo11bo46b2o9b2o$7b2o11b2o44bobo9bobo$6b2obo9bob2o42b2obo9bob2o$7bobo
9bobo44b2o11b2o$8b2o9b2o46bo11bo3$80b2obob2o$79bo2b3o2bo$79bo7bo$79b4o
b4o2$82b3o9$54b3o$54bobo$53bo$52bo2b3o$52bo3bo$52b2o$52bo11$36b3o17b3o
$35bo3bo15bo3bo$35bo3bo15bo3bo$35b4o17b4o$35bo2b2o15b2o2bo$33bobo6bo9b
o6bobo$41b4o5b4o$44bo5bo$43b2o5b2o2$66b3o$68bo$66b3o3$65b2o$65bobo$59b
o7bo$60b2o3b3o$63b2o$63bo$61b6o$61b2o2bobo$63bob2o2$62bo2bo$62bo3bo$63b
2obo2$67b2o$67b2o$68bobo$68b3o$69bo4$69bo$68b3o$68bobo$67b2o$67b2o2$63b
2obo$62bo3bo$61bob3o$62bo$63b4o$64b2obo!

I think it’s only a matter of time before completely asymmetrical loopable oscillators are found.

This is an example:

How does one classify this P75 oscillator? (in a custom rule, just to demonstrate the concept)

Code: Select all

x = 2, y = 3, rule = modrrotest
.A$BA$BA!

It can even be made into a P25 using 3 copies:

Code: Select all

x = 13, y = 12, rule = modrrotest
4.D$2.2CD.A$2.2CF$2.2CA3$10.D$9.3D$8.2D.2D$.A6.2D$BA$BA!

[NimbleRogue]

A bit of trivia that I think belongs in this thread, loopability as a concept can actually be generalized to spaceships, and there's a known example by hotcrystal0 and FWKnightship here:

I think I found a SMORRO

Code: Select all

x = 34, y = 5, rule = 2-cn3-acky4ityz5k/2k3-ekny4ijqy6i78/3
2A30.2A$A.A28.A.A$A.2A26.2A.A$B2A28.2AB$.A30.A!

A 6c/52 based on it:

Code: Select all

x = 48, y = 15, rule = 2-cn3-acky4ityz5k/2k3-ekny4ijqy6i78/3
7.A32.A$6.B2A30.2AB$8.2A28.2A$7.2A30.2A6$.B44.B$2A9.2A22.2A9.2A$.B8.A
.A22.A.A8.B$9.2A2.2B.A14.A.2B2.2A$10.2A.2B2A14.2A2B.2A$11.3A.A16.A.3A
!

Found a 4c/72o RRS in INT with loopability 1,2

Code: Select all

x = 57, y = 14, rule = B2i3aiy4ekntyz5e6c8/S2aek3-aeky4iz5acikq6aci
3o11b3o23b3o11b3o$o15bo23bo15bo$2o13b2o23b2o13b2o7$2b2o9b2o$2bobo7bobo
$4bo7bo$bob2o7b2obo$b2o11b2o!

Can anyone find one with a higher loopability?

[splitterrules]

A 1,2,4-loopable SMORRO in the L89 rule:

Code: Select all

x = 32, y = 15, rule = B2i3-k4cjqyz5ey6-en78/S2n3-j4-jnwy5cky678
4bo22bo$4b2o20b2o$b6o18b6o$ob3obo18bob3obo$b5o20b5o$2b2obobo16bobob2o$
bobobobo16bobobobo$bobobobo16bobobobo$bob3o20b3obo$2b4o20b4o$2b4o20b4o
$2b5o18b5o$b5o20b5o$2b3o22b3o$3bo24bo!

A 1,3-loopable SMORRO:

Code: Select all

x = 346, y = 150, rule = B2n3-kq4ejz5eky6-en78/S2n3-jk4-cjnwy5cey678
266bo36bo$250b2o10bob4o34b4obo10b2o$250bo10bob6o32b6obo10bo$252bo8bob
7o30b7obo8bo$251bo9b2ob5o32b5ob2o9bo$263bo3bo34bo3bo49$271bo26bo$271b
2o24b2o$271b2obo20bob2o$270b5o20b5o$271b3obo18bob3o$270bob2obo18bob2o
bo$270bob3o20b3obo$271b5o18b5o$270b4obo18bob4o$270bobobo20bobobo$271b
3o22b3o15$226bo116bo$225b6o108b6o$224b11o100b11o$225b10o100b10o$226b8o
102b8o$227bo4b2o102b2o4bo56$2bo24bo$bo26bo$4bo20bo$2bobo20bobo$b4o20b
4o$b4o20b4o$b5o18b5o$5o20b5o$b3o22b3o$2bo24bo!

EDIT: A 1/2/4/5/10/20:

Code: Select all

x = 28, y = 10, rule = B2n3-k4cj5ek67/S2n3-jk4acikrty5cr678
2bobo18bobo2$2o24b2o$bo24bo$b3obo16bob3o$b4o18b4o$b5o16b5o$5o18b5o$b3o
20b3o$2bo22bo!

Code: Select all

x = 742, y = 499, rule = B2n3-k4cj5ek67/S2n3-jk4acikrty5cr678
344b3ob2o42b2ob3o$338bo3b4ob2obo40bob2ob4o3bo$337b2o2b3ob5obo38bob5ob
3o2b2o$338b4o4b6o38b6o4b4o$338b2o6bob2obo38bob2obo6b2o$347bob2o40b2obo
2$270bo200bo2$267bo3b2o3bo188bo3b2o3bo$267bo2bob6o186b6obo2bo$267bobo
4b5o184b5o4bobo$273b7o182b7o$272bob5o184b5obo$277bo186bo4$201bob2o332b
2obo$47bo150bobob2obo330bob2obobo150bo$46b3o148b2ob5obo328bob5ob2o148b
3o$45b5o149bob6o328b6obo149b5o$44b5o149bob2ob2obo328bob2ob2obo149b5o$
45b4o150bo2bob2o330b2obo2bo150b4o$45b4o644b4o$45b4o644b4o$44bob3o644b
3obo$44bob4o76b2o3bo229b3o14b3o229bo3b2o76b4obo$44bob3o77b7o228b3o14b
3o228b7o77b3obo$44bob3o76bob7o228bobo12bobo228b7obo76b3obo$44b6o73b12o
227b2o14b2o227b12o73b6o$48b2o72b2obo2b6o230b2o10b2o230b6o2bob2o72b2o$
123bobobo4bo230bo14bo230bo4bobobo$125bo490bo3$53b2obob2o622b2obob2o$
46bo5bob2ob2obo620bob2ob2obo5bo$45b3o7b5obo618bob5o7b3o$47bo6bob6o618b
6obo6bo$55b2ob2obo618bob2ob2o$57bob2o620b2obo3$358b2o22b2o$359b2o20b2o
$358bo2bo18bo2bo$359bo22bo$357bob3o18b3obo$357bob3o18b3obo$358b5o16b5o
$357b4obo16bob4o$357bobobo18bobobo$358b3o20b3o46$362bo16bo$361bobo14bo
bo$46b3o312b4o12b4o312b3o$45bobobo311bobo14bobo311bobobo$44bob4o642b4o
bo$44b5o312bo18bo312b5o$45b3obo308b2o22b2o308bob3o$44bob3o308bobobo18b
obobo308b3obo$44bob2o309b3obo18bob3o309b2obo$45b2o311b5o16b5o311b2o$
44b4o309bobob2o16b2obobo309b4o$45bo312bob3o16b3obo312bo$45bo310bobob2o
18b2obobo310bo$45bo312b4o18b4o312bo$46bobo309b4o18b4o309bobo$45b3o310b
5o16b5o310b3o$357b5o18b5o$358b3o20b3o$359bo22bo52$359bo22bo2$358b2o22b
2o$357bo26bo$356bob2obo18bob2obo$357b4obo16bob4o$358b3obo16bob3o$357bo
b3o18b3obo$358b5o16b5o$357b4obo16bob4o$357bobobo18bobobo$358b3o20b3o2$
47bo646bo$46b3o644b3o$45b5o642b5o$44b5o644b5o$45b4o644b4o$45b4o644b4o$
45b3o646b3o$45b3o646b3o$45b2obo644bob2o$44b5o644b5o$44b2o650b2o43$359b
obo18bobo2$357b2o24b2o$358bo24bo$358b3obo16bob3o$358b4o18b4o$358b5o16b
5o$357b5o18b5o$358b3o20b3o$359bo22bo20$46b3o644b3o$45bobobo642bobobo$
44bob4o642b4obo$44b5o644b5o$45b3obo642bob3o$45b4o644b4o$45bo650bo$43bo
b3o646b3obo26$359bo22bo$357bo26bo$357b5o18b5o$357b4o20b4o$357b4o20b4o$
357b5o18b5o$358b4o18b4o$358b5o16b5o$357b4obo16bob4o$357bobobo18bobobo$
358b3o20b3o38$47bo646bo$46b3o644b3o$45b5o642b5o$44b5o644b5o$45b4o644b
4o$45b4o644b4o$45b5o642b5o$43b3obobo642bobob3o$43b5o646b5o$43b3o650b3o
$44bo652bo$44bo652bo3$47bo646bo$46b2o646b2o$46bo313bo20bo313bo$44b2o
311b5o18b5o311b2o$44b3o310b6o16b6o310b3o$45bo312b4o18b4o312bo$358b4o
18b4o$358b4o18b4o$358b4o18b4o$358b5o16b5o$357b5o18b5o$358b3o20b3o$359b
o22bo13$8bo724bo$b2ob3obo724bob3ob2o$ob2o3b3o722b3o3b2obo$8ob2o720b2ob
8o$ob10o6bob4o694b4obo6b10obo$bob2o2bobo7b2obobo696bobob2o7bobo2b2obo$
2b2ob2o2bo8b5o696b5o8bo2b2ob2o2$19bo702bo2$74bo3bo4bo2b2o566b2o2bo4bo
3bo$73b5ob3o578b3ob5o$72b15o568b15o$73b10ob3o568b3ob10o$74b5o5bo572bo
5b5o$75bo590bo4$146b2ob6ob2o426b2ob6ob2o$145bob2o3b5obo424bob5o3b2obo$
145b8ob2o2bo424bo2b2ob8o$145bob7o3bo426bo3b7obo$146bob2o2b3o432b3o2b2o
bo$147b2ob2o2bo432bo2b2ob2o2$226bo288bo$224bobo3b2o278b2o3bobo$219bo5b
ob6o276b6obo5bo$218b13o280b13o$217b14o280b14o$218b10obo282bob10o$219b
5o294b5o$220bo300bo3$296b2o146b2o$291b2obob4o142b4obob2o$290bob2o3b2o
144b2o3b2obo$290b7ob3o4bo53b2o20b2o53bo4b3ob7o$290bob5o2bo2b3o54b2o20b
2o54b3o2bo2b5obo$291bob4o4b2o2bo55bo18bo55bo2b2o4b4obo$292b2o7bob4o54b
o18bo54b4obo7b2o$306bo52bo22bo52bo$358b3o20b3o$357bob3o18b3obo$357bob
3o18b3obo$358b5o16b5o$357b4obo16bob4o$357bobobo18bobobo$358b3o20b3o53$
359bo22bo$358bo24bo3$358bo24bo$359b3o18b3o$359b3o18b3o$358b4o18b4o$
358b5o16b5o$357b5o18b5o$358b3o20b3o$359bo22bo!

A rule with four speeds of SMORRO:

Code: Select all

x = 37, y = 12, rule = B2n34cejqz5ek6-en78/S2n3-jk4-jnw5ceky678
2bo31bo$4bo27bo4$3b2o27b2o$b4o27b4o$b4o27b4o$b5o25b5o$5o27b5o$b3o29b3o
$2bo31bo!

Code: Select all

x = 47, y = 38, rule = B2n34cejqz5ek6-en78/S2n3-jk4-jnw5ceky678
16$11bo24bo$13bo20bo4$12b2o20b2o$10b4o20b4o$10b4o20b4o$10b5o18b5o$9b5o
20b5o$10b3o22b3o$11bo24bo!

Code: Select all

x = 95, y = 41, rule = B2n34cejqz5ek6-en78/S2n3-jk4-jnw5ceky678
28$19bo27bo$21bo23bo4$20b2o23b2o$18b4o23b4o$18b4o23b4o$18b5o21b5o$17b
5o23b5o$18b3o25b3o$19bo27bo!

Code: Select all

x = 27, y = 12, rule = B2n34cejqz5ek6-en78/S2n3-jk4-jnw5ceky678
2bo21bo$4bo17bo4$3b2o17b2o$b4o17b4o$b4o17b4o$b5o15b5o$5o17b5o$b3o19b3o
$2bo21bo!

[Docsy]

These are incredible splitter!

also, as a note, I said earlier that 89-loopability was the record for RROs, but that's not true. Ampere found a 104-loopable RRO here:
https://conwaylife.com/forums/viewtopic ... 05#p135905

Might be a useful seed for SMORROs as well.

[splitterrules]

Two diagonal RRSes:
{1,2,4}:

Code: Select all

x = 537, y = 537, rule = B3acir4eknqyz5ej6ik7e/S3-kn4-jq5-qy6
362b3o$360bob3o$358b2obobo$358b5o$358b2obo3bo$360b3obo$361bo3bo$363bo
159$528b3o$528b3o$527bobo3b2o$526b5ob3o$527bobobobob2o$525bo4b7o$527bo
bobobobo$526bob3o$190b2ob2o333b2o$190b5o$191bobo$190b3o4bo$190b3o12$
174b2ob2o$174b5o$175bob2o$174b3o$174b2o3$177bo136$361bo$359bo3bo$358b
3ob3o$357bobo3bob2o$357b2obob5o$355bob3obobob2o$354b3obob3o$354bo2bobo
bobob2o$354b13o$355bobobobobob2o$358b3o$359bobo2$357bo2bo$358bob2o$
357bo3bo$359bo5$339b3o$338b2ob2o$339bobo$336b3ob3o3bobo$2b3o330bob3obo
bo3bo$2b3o329b3obob5o4bo$bobobo329bobobobobo2b2o$2b5o326bo4b5obo2b2o$
2obobo329bobobobo$3o4bo326b5ob3o$2o3bo329bobo3bo$4bobo329b3ob3o$336b3o
b3o159$171bo$169bo3bo$168b3obo$166b2obo3b2o$166b5ob3o$166b2obobobo$
170b3o$169bobo$168b5o$168b2obo$170b3o$170b2o!

{1,7} (a new loopability):

Code: Select all

x = 294, y = 294, rule = B3aciq4enqt5aejy/S3-kn4-qz5-qy6-a
219bo$218b3o$217b2ob2o$218b3o$215b3obo$215b6o$215b3obob2o$220b3o$220b
2obo$222bo2bo$224bo$223bobo21$176b3o$176b3o$174b2ob2o$174b3o$172b2ob2o
$172b3o$170b2ob2o$170b3o$164bo3b2ob2o$162b3o3b3o$162b2obobob2o$161b2o
3b3o$162b2obobo$162b3obob2o$165bo3bo$165b2ob2o$166b3o9$275bo$274b3o$
274b3o$272b2obo$272b5o$272b2obob2o$274bob3o$276b2ob2o$278b3o$278b2ob2o
$280b3o$280b2ob2o$282b3o$282b2ob2o$284b3o$284b2ob2o$286b3obo$286b2ob2o
$288bo2b2o$287b2ob2o$289b3o$289bo22$110b2ob2o$110b5o$111bob2o$110b3o$
110b3o$111bo4$287bo$100b2ob2o180b5o$100b6o179b2ob2o$101bob2o179b2o3bob
o$100b3o183bob5o$100b3o184bobobo$286b3o4bo$284b2obo3bo$284b3o3bobo$
282b2ob2o$281b2obo$282b3o$283bo30$161bobo$162bo$161bo2bo$163bob2o$164b
3o$164b2ob2o$166b3o$166b2ob2o$168b3o$168b2obob2o$43bo107bobo16b6o$41b
5o106bo18bob2o$41b2ob2o105bo2bo15b3o$40b2o3bo107bob2o13b3o$42bobob2o
106b3o13b3o$43bobob2o105b2ob2o68bo$42b3o3bo107b3o67b3o$40b2obobob2o
107b2ob2o64b2ob2o$40b3o2b3o110b3o65b3ob2o$38b2ob2o115b2obob3o61bobob2o
$38b3o119b6o60b3o3bo$36b2ob2o120bob3o58b2obobob2o$36b3o121b3o61b3o2b3o
$34b2ob2o121b3o59b2ob2o$34b3o124bo60b3o$32b2ob2o183b2ob2o$32b3o185b3o$
32b3o183b2ob2o$218b3o$216b2ob2o$216b3o$214b2ob2o$214b3o$212b2ob2o$212b
3o$212b3o26$184b3o$184b3o$182b2ob2o$4b3o175b3o$4b3o173b2ob2o$2bob3o
173b3o$b3obo172b2ob2o$2ob4o171b3o$b3obob2o167b2ob2o$2bo3b3o167b3o$6b2o
bo164b2ob2o$8bo2bo162b3o$10bo161b2ob2o$9bobo156bo3b3o$167b3obob2o$166b
2ob4o$167b3obo$168bobob2o$169bo3bo$169b2ob2o$170b3o40$60b3o$60b3o$58b
2obobo$57b6o$58b2obob2o$62b3o$62b2ob2o$64b3o$64b2ob2o$66b3o50bo$66b2ob
2o47b3o$68b3o47bob2o$68b2ob2o39bo3b2ob2o$70b3o37b3o3b3o$70b2ob2o35b2ob
obob2o$72b3obo32b2o3b3o$72b2ob2o33b2obobo$74bo2b2o31b5o$73b2ob2o35bo3b
o$75b3o34b3obo$75bo37bo3bo$115bo!

[splitterrules]

A RRS made of two RFOs:

Code: Select all

x = 51, y = 19, rule = B2k3aik4j5iry6i/S2-ci3-acey4i5eq7e8
21bo7bo$20b3o5b3o$19b2obo5bob2o$2b2o16bo9bo16b2o$bobo17bo7bo17bobo$2o
bo43bob2o$b3o5bo31bo5b3o$3bo6bo29bo6bo$5bo3bo31bo3bo$6b3o33b3o$6b3o33b
3o$7bo35bo2$11b2o25b2o$11b2o25b2o$11bo27bo$12bob2o19b2obo$12b3o21b3o$
13bo23bo!