Reflectorless Rotating Oscillators (RRO)

[NimbleRogue]

Why does the definition for a RRO require that "two non-interacting copies of the pattern could be combined into an oscillator with a period equal to exactly half of that of the component oscillators" according to the wiki.

Why should this not count?(Note with 2 copies extra cells are formed, but with 3 they do not interact)

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x = 44, y = 10, rule = B3-ejq4w6c/S2-c3-a4i
3o17b3o17b3o$2bo19bo19bo$b2o18b2o18b2o$20bo14b3o$35bobo$18bo15bo2bo4b
o$16b2o14b2o6b4o$16bo15b2o6bo$16b3o13b3o5bo2bo$37bo3b3o!

And why not this? even though it is not loopable, it rotates itself every 117 generations

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x = 4, y = 3, rule = B3-cjry4jryz5iknqy6i7e/S2aek3-anry4-acntz5-aij67e
4o$obo$3o!

That definition ensures that only RROs are counted, but I feel it is too restrictive, leaving out some RROs.

[confocaloid]

Why should this not count?(Note with 2 copies extra cells are formed, but with 3 they do not interact)

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x = 44, y = 10, rule = B3-ejq4w6c/S2-c3-a4i
3o17b3o17b3o$2bo19bo19bo$b2o18b2o18b2o$20bo14b3o$35bobo$18bo15bo2bo4b
o$16b2o14b2o6b4o$16bo15b2o6bo$16b3o13b3o5bo2bo$37bo3b3o!

I think this also counts as a loopable RRO, and the intended meaning was "two or more non-interacting copies ... with a lower period ..."

And why not this? even though it is not loopable, it rotates itself every 117 generations

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x = 4, y = 3, rule = B3-cjry4jryz5iknqy6i7e/S2aek3-anry4-acntz5-aij67e
4o$obo$3o!

Because this is just a p468 mod117 oscillator. There are very many oscillators whose mod is strictly lower than their period.
I think the underlying idea of a "reflectorless rotating oscillator" is narrower than that. Intuitively, a RRO should look and feel like a "looped spaceship" which is actually an oscillator rather than a spaceship.
In Life, roteightor is a mod2 p8 oscillator, and gourmet is a mod8 p32 oscillator, but those oscillators are not RROs.

That definition ensures that only RROs are counted, but I feel it is too restrictive, leaving out some RROs.

Well there is already a way to say that the oscillator rotates 90 degrees in 1/4 of its period, without implying anything else: "period-4N mod-N oscillator".

RROs should be loopable, or at least it should be possible to see how the oscillator "looks like a "spaceship" which doesn't actually move away, but instead reappears in a rotated form and subsequently returns back to the starting location". Removing that requirement will include very many oscillators that are "boring" in this context (i.e. are not the kind of thing one is usually looking for, when one is looking for known examples of RROs).

[NimbleRogue]

Well there is already a way to say that the oscillator rotates 90 degrees in 1/4 of its period, without implying anything else: "period-4N mod-N oscillator".

Sorry, I should have included the requirement that the oscillator is In C1.
To the point about It needing to look like a ship, I never knew that it should look like that, but it makes sense.

[Mathemagician314]

Here's a rule with both an organic-looking p20--

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x = 5, y = 4, rule = B2i3-ckq4eqtwz6n/S2ace3-ckq4ceirwyz5er6-ci8
2bo$b3o$o2b2o$2bo!

--and a p76:

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x = 4, y = 4, rule = B2i3-ckq4eqtwz6n/S2ace3-ckq4ceirwyz5er6-ci8
3o$ob2o$o2bo$obo!

Both are unloopable.

[Mathemagician314]

1/2-fold p80:

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x = 24, y = 14, rule = B2i3-ek4rtw5n6i7c/S2-ck3-ay4jkrt5ejnry6n7c8
16bo$15b3o$12bo5bo$15b4o$16bobo$15bo3$3bo16bo$obo14bobo$4o13b4o$o5bo10b
o5bo$b3o14b3o$2bo16bo!

[Mathemagician314]

Very sparky 1/2/3-fold p156 RRO in a generations rule:

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x = 116, y = 28, rule = 2-ak34/2kn3-r4aijnr5c/5
.3A46.3A46.3A$.ABA46.ABA46.ABA$DAD2A44.DAD2A44.DAD2A$.ABADC44.ABADC
44.ABADC$.3A2B44.3A2B44.3A2B4$93.CB$92.DCDC$91.C3.2D$92.2D3.C13.A$93.
CD3.B11.4A$86.D7.BC3.B9.AC2B2A$86.D9.D3.C8.2A.D2A$89.D7.C2D10.DA2D2A$
88.D2C5.B14.CB2A$89.BABD.DC2A14.DC$52.2B3A32.A2B3.B2A$52.CDABA33.A2B.
2BA$53.2ADAD32.2A3B2A$54.ABA35.3A$54.3A3$109.2A$109.3A$110.A!

It's almost 4-fold as well, but a tub ends up doubling the period:

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x = 23, y = 23, rule = 2-ak34/2kn3-r4aijnr5c/5
8.3A$8.ABA$7.DAD2A$8.ABADC$8.3A2B3$20.D$18.5A$18.ABDBA$3.CB13.5A$2.AD
B13.BDA$5A13.BC$ABDBA$5A$2.D3$10.2B3A$10.CDABA$11.2ADAD$12.ABA$12.3A!

It can be combined to make a double-barrelled gun:

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x = 6, y = 23, rule = 2-ak34/2kn3-r4aijnr5c/5
2.AB$.3AC$.ABD.B$.5A$2.3A14$.3A$5A$ABD.B$3AC$.AB!

EDIT: Adding S5j turns it into an 8c/38 spaceship instead:

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x = 6, y = 5, rule = 2-ak345j/2kn3-r4aijnr5c/5
.3A$.ABA$DAD2A$.ABADC$.3A2B!