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)

Code: Select all

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

Code: Select all

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)

Code: Select all

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

Code: Select all

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--

Code: Select all

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

--and a p76:

Code: Select all

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

Both are unloopable.

[Mathemagician314]

1/2-fold p80:

Code: Select all

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:

Code: Select all

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:

Code: Select all

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:

Code: Select all

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:

Code: Select all

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

[hotcrystal0]

2-able P160 RRO by rabbit on the Discord:

Code: Select all

x = 20, y = 6, rule = B3-ceky/S237
2b3o$2o$bo2bo11b3o$b3o11bo2bo$18b2o$15b3o!

[Mathemagician314]

P1428 RRO, not loopable:

Code: Select all

x = 6, y = 5, rule = B2n3acijn4aejknq/S2-in3-aeky4awz5aiq
3o$ob3o$5bo$2bobo$3bo!

[hotcrystal0]

P1428 RRO, not loopable:

Code: Select all

x = 6, y = 5, rule = B2n3acijn4aejknq/S2-in3-aeky4awz5aiq
3o$ob3o$5bo$2bobo$3bo!

Is it still considered an RRO if it's not loopable?

[Mathemagician314]

Is it still considered an RRO if it's not loopable?

I thought it was an RRO if it was statorless, but I could be wrong; there was a dispute over this earlier in the thread with no clear conclusion. In my example above, I don't think you can reasonably argue that there's a "reflector" there, and so I thought it satisfied the restrictions; although technically there could be a statorless reflector, in which case my definition doesn't hold up. Maybe we should have another discussion about what defines an RRO, to end the debate?

[confocaloid]

P1428 RRO, not loopable:

Code: Select all

x = 6, y = 5, rule = B2n3acijn4aejknq/S2-in3-aeky4awz5aiq
3o$ob3o$5bo$2bobo$3bo!

Is it still considered an RRO if it's not loopable?

I thought it was an RRO if it was statorless, but I could be wrong; there was a dispute over this earlier in the thread with no clear conclusion. In my example above, I don't think you can reasonably argue that there's a "reflector" there, and so I thought it satisfied the restrictions; although technically there could be a statorless reflector, in which case my definition doesn't hold up. Maybe we should have another discussion about what defines an RRO, to end the debate?

One could simply say "rotating oscillator", when the entire oscillator rotates 90 or 180 degrees after some number of ticks, regardless of whether or not there is a nonempty stator, and regardless of whether or not the oscillator is a loopable RRO.

Alternatively, one could describe the above p1428 as a "period-1428 mod-357 oscillator":

• The pattern reappears (not necessarily in the same orientation) after 357 ticks, which is its mod.
• The pattern reappears again in the same orientation after 1428 ticks, which is its period.

With this description, again there are no implications about loopability / stator.

[LaundryPizza03]

Massive p3128 1/2-loopable RRO with an 824*824 bounding box, totaling 234304 rotor cells.

Code: Select all

x = 42, y = 132, rule = R6,C0,M1,S47..76,B44..62,NM
3b7o$2b9o$2b10o$2b10o$b4o3b5o$b3o5b5o$4o6b4o$3o7b4o$4o6b4o$b2o6b4o$2b
2o4b4o$3b3o2b2o$4b6o96$21b2o14bo$19b6o5b10o$14b7o3b3o2b13o$14b7o4b5o5b
7o$13b7o5b4o6b6o$13b7o5b3o5b7o$13b7o6b3o4b4o$14b4o9b2o4b3o$13b6o14b3o$
13b5o15b3o$13b5o16b2o$14b3o16b3o$14b3o16b3o$14b3o15b4o$15b2o14b4o$16b
3o11b3o$16b3o12b2o$16b3o11b2o$16b4o10bo$16b4o9bo$16b2ob2o6b2o$17b8ob2o
$18b9o$20bo3bo!

[Mathemagician314]

1/2-loopable p516:

Code: Select all

x = 93, y = 48, rule = B2e3aijk4cjw5aciny6-en78/S1c2aek3-aceq4acjntwz5acejq6eik7e8
2obo2bo$b2o2bobo61b2obo2bo$obo2b3o62b2o2bobo$69bobo2b3o$4b2o13b3o$4b2o
12bobobo50b2o13b3o$16b2obobobo49b2o12bobobo$bobo10bob3ob3o62b2obobobo$
b3o13b2o51bobo10bob3ob3o$14bo2bobo50b3o13b2o$6b2o9b2o64bo2bobo$4bobo7b
ob3o2bo53b2o9b2o$3bobobo8b2o2bobo50bobo7bob3o2bo$3bobo14b3o49bobobo8b
2o2bobo$3b3o66bobo14b3o$72b3o18$84b3o$67b3o14bobo$67bobo2b2o8bobobo$
68bo2b3obo7bobo$71b2o9b2o$70bobo2bo$71b2o13b3o$67b3ob3obo10bobo$66bobo
bob2o$67bobobo12b2o$68b3o13b2o2$82b3o2bobo$82bobo2b2o$83bo2bob2o!

[AforAmpere]

1,2,3,4,5,6,7,8,10-able p840:

Code: Select all

x = 116, y = 120, rule = R6,C0,S25-26,31,34,36-38,46-80,95-96,98,101-105,110-111,B47-52,56,63-71
13b3o$12b5o$11b8o$10b9o$10b3o3b4o$10b3o3b4o25b3o40b3o$10b3o3b4o24b5o
38b5o$10b9o24b8o35b7o$11b7o24b11o32b10o$12b5o24b3o4b5o31b3o4b5o$41b2o
6b5o30b2o5b5o$40b3o6b5o29b3o6b5o$40b3o6b5o29b3o6b5o$41b4o3b5o31b3o4b5o
$42b11o32b4ob6o$43b8o34b9o$43b7o36b7o$44b5o38b5o$46bo42bo2$109b2o$107b
6o$106b8o$105b3o4b3o$104b4o5b3o$104b4o5b3o$103b5o4b4o$104b4o4b4o$104b
11o$105b9o$106b8o$107b7o$108b4o12$8b4o$7b6o$6b8o$6b8o$5b10o$5b4o3b4o$
4b4o4b5o$4b4o4b5o$5b2o5b4o$6b3o3b3o$6b8o$7b6o$9b2o7$105b2o$103b6o$102b
8o$101b3o3b3o$100b4o5b2o$99b5o4b4o$99b5o4b4o$100b4o3b4o$101b10o$102b8o
$102b8o$103b6o$104b4o12$4b4o$2b7o$2b8o$2b9o$b11o$4o4b4o$4o4b5o$3o5b4o$
3o5b4o$b3o4b3o$2b8o$3b6o$5b2o2$26bo42bo$24b5o38b5o$23b7o36b7o$22b9o34b
8o$20b6ob4o32b11o$20b5o4b3o31b5o3b4o$19b5o6b3o29b5o6b3o$19b5o6b3o29b5o
6b3o$20b5o5b2o30b5o6b2o$20b5o4b3o31b5o4b3o24b5o$21b10o32b11o24b7o$23b
7o35b8o24b9o$24b5o38b5o24b4o3b3o$25b3o40b3o25b4o3b3o$96b4o3b3o$97b9o$
97b8o$99b5o$100b3o!

1,2,4,8-able, but can fit 11:

Code: Select all

x = 131, y = 130, rule = R6,C0,S19,23,25,29,31,34,36-38,46-80,93,98-100,102-105,B47-52,56,63-71
45bo$43b5o$14b3o25b7o$13b5o2bo20b10o$12b7o21b3o3b6o37b4o$11b4o2b4o19b
3o4b5o36b6o$11b3o3b4o18b3o5b5o35b9o$10b4o4b3o19b2o5b5o34b11o$11b3o3b4o
19b3o3b6o33b3o5b5o22bob3o$12b8o21b10o34b3o5b5o23b6o$13b6o23b8o35b3o5b
5o22b9o$14b4o25b5o37b3o5b5o19bob4o2b5o$15bo28b3o39b3o3b5o21b2obo4b3o$
86b11o20b4o3bo2b4o$87b8o22b4o6b4o$88b6o23b4o6b4o$90b2o26b3o4b6o$117bob
3o3b5o$119b11o$121b7o$122bob2o$123b2o25$123b2o$121b6o$120b8o$119b4o2b
4o$118b4o4b3o$118b4o4b4o$118b4o4b4o$118b5o2b5o$119b10o$120b8o$120b8o$
9b5o107b6o$8b3ob3o107b3o$8b8o$7b9o$6b5ob5o$6b4o4b4o$5b4o5b4o$6b3o5b4o$
6b3o5b3o$7b4o2b3o$8b7o$9b5o$11bo22$120b4o$119b6o$118b8o$117b3o4b3o$
116b3o5b4o$116b4o4b4o$116b4o4b4o$116b5o2b5o$117b10o$118b8o$118b8o$119b
6o2$6b2o$4b6o$4b6o$3b8o$2b10o$b5o2b5o$5o4b5o$4o6b4o$4o6b4o$b4o5b3o14bo
$2b4o3b3o13bob3o41b3o$3b8o13b7o39b5o$4b6o12b10o37b7o$5b4o12b6ob5o34b
10o$21b4o4b4o33b6ob5o34bo$20b5o6b3o32b5o4b3o33bo2b3obo$20b5o6b3o31b5o
6b3o31bob6obo$20b5o6b3o31b5o6b3o30bo2b7obo$21b5o4b3o33b5o4b3o33b8o$21b
11o34b6o2b3o34b2ob6o$23b8o36b10o33b7ob2o$25b5o39b6o36bo2b6o$26b3o41b4o
38b3ob2o$72bo40b4o2bo2$118bo!

[muzik]

Are any [1,2,3,4,5,6,7,8]-able examples in isotropic non-totalistic rules known? I believe the above post is the first example of [1,2,3,4,5,6,7,8] so far in any rule, but I could be wrong. Have any pattern collections been made?

I believe these are the lowest periods for which no reflectorless rotating oscillators (including loopability-1 cases) are known so far: 228, 248, 268, 276, 280, 296, 312, 328, 332, 336, 344, 348, 356, 360, 380, 388, 396, 400

HexInverseFire's p594 also fits in this thread as a [1,2,3]. Are there any other loopable RROs in a hexagonal rule other than this one and AlephAlpha's, or indeed any at all in a triangular rule?:

Code: Select all

x = 63, y = 47, rule = B2-m4-m56/S2m34m56H
10bobo$13bo$11b2obo$12b4o$12bob3o$13bo$13bo2bo2$o2bo$3bo$3obo$b4o$2bo
b2o$3bo25bo$4bobo23b2o$32b2o$29bob3obo$31b2o$31b5o$57bobo$57b2o$57b3o
$57bobob2o$57bob3o$60bo$59bo15$10bobo37bobo$13bo39bo$11b2obo36b2obo$12b
4o36b4o$12bob3o35bob3o$13bo39bo$13bo2bo36bo2bo!
[[ STARTFROM 594 ZOOM 5 ]]

[confocaloid]

[...]
I believe these are the lowest periods for which no reflectorless rotating oscillators (including loopability-1 cases) are known so far: 228, 248, 268, 276, 280, 296, 312, 328, 332, 336, 344, 348, 356, 360, 380, 388, 396, 400
[...]

Here is a "nontrivial" "reflectorless" "rotating" p248 oscillator:

Code: Select all

x = 60, y = 60, rule = B3/S234c
21bo2$19bob3o$21b2obo$21bob2o$22b3obo2$24bo11$26bo$25b3o28bo$24b2o2bo27b2o$
26b3o26b2obo$54bo2b3o$53bobobo$52bobobo$27b2o9bo11b3o2bo$27b2o9b2o11bob2o$37b
ob2o11b2o$32b2o3bobo13bo$32b2o3b2o$19b2o3b2o$18bobo3b2o$17b2obo$3b3o12b2o9b2o
$3b3o13bo9b2o$3b3o$3o$3o$3o26b3o$29bo2b2o$30b3o$31bo11$33bo$32b3o$31b3obo$32b
o3bo$33bo3bo$34bob3o$35b3o$36bo!

Obviously it is not an example of the kind of object this thread is about. (Even though it is statorless, and it rotates 90 degrees after 62 ticks.)

To capture the idea of a RRO, one needs to add the requirement of loopability. It must be possible to combine two or more non-interacting instances of the object, sharing the same envelope, into a lower-period oscillator whose period divides the period of one instance. Without that requirement, the above p248 mod62 oscillator, xp4_y1g8021aozwox10bay0ooez77pos440607jw1166711zy38k0h05czy611, and perhaps even the blinker would all qualify, losing an interesting idea of a RRO for a relatively boring notion of a statorless oscillator with a certain kind of kinetic symmetry.

[muzik]

[...]
I believe these are the lowest periods for which no reflectorless rotating oscillators (including loopability-1 cases) are known so far: 228, 248, 268, 276, 280, 296, 312, 328, 332, 336, 344, 348, 356, 360, 380, 388, 396, 400
[...]

To capture the idea of a RRO, one needs to add the requirement of loopability. It must be possible to combine two or more non-interacting instances of the object, sharing the same envelope, into a lower-period oscillator whose period divides the period of one instance. Without that requirement, the above p248 mod62 oscillator, xp4_y1g8021aozwox10bay0ooez77pos440607jw1166711zy38k0h05czy611, and perhaps even the blinker would all qualify, losing an interesting idea of a RRO for a relatively boring notion of a statorless oscillator with a certain kind of kinetic symmetry.

This definition is obviously agreed on by most people here including myself, so I fail to see why you felt the need to reiterate it.

[muzik]

EDIT, this one can fit 74, but is only 2/4:

Code: Select all

x = 8, y = 6, rule = B2n3-k4ejqz5ek6-e78/S2n3-jk4-cjnw5cey678
2o2b2o$b4obo$2b4obo$2b6o$2bob2obo$3bob2o!

3 and 6 also work:

Code: Select all

x = 1211, y = 827, rule = B2n3-k4ejqz5ek6-e78/S2n3-jk4-cjnw5cey678
893b3o$892bobobo$892b4obo$893b5o$893b4o$892b4obo$893b2ob2o$896bo4$893b
2o$894b2o$894bo$894bobo2$894bo$895bo104$389bo388bo5bo$388b5o2bo381b10o
$2b3o382b7o3bo378b11o$bobo382b9ob2o377b10obo$2obob2o380b8o381b5ob3o$o
3bo383bo3bo384bo3bo2b2o$392bo390b3o262$893b3o$892bobobo$892b4obo$893b
5o$892bob3o$892bob3o2$893b4o$893b2o$892b4o$893b4o$894b3o$894b2o24$315b
2o$314b3o$314b4o$315b4o$316b2o$314b4o2$314b3obo$314b3obo$313b5o$313bo
b4o$314bobobo$315b3o262$425b3o390bo$425b2o2bo3bo384bo3bo383bo3bo$426b
3ob5o381b8o380b2obob2o$424bob10o377b2ob9o382bobo$424b11o378bo3b7o382b
3o$424b10o381bo2b5o$426bo5bo388bo104$315bo$316bo2$314bobo$316bo$315b2o
$316b2o4$314bo$313b2ob2o$313bob4o$314b4o$313b5o$313bob4o$314bobobo$315b
3o!

As does 12:

Code: Select all

x = 1211, y = 1211, rule = B2n3-k4ejqz5ek6-e78/S2n3-jk4-cjnw5cey678
892b2o$893b2o$895bo$893b3o$892bo2bo$893bo$893bo186$893b3o$892bobobo$892b
4obo$893b5o$893b4o$892b4obo$893b2ob2o$896bo4$893b2o$894b2o$894bo$894b
obo2$894bo$895bo104$194b2ob2o190bo193b2o193bo5bo$193bob2ob2o6bo181b5o
2bo186bob3obo2b2o184b10o$2b3o187bob4o6bo4bo177b7o3bo183bob4obob4o182b
11o$bobo188b7o4b4obo177b9ob2o183b6ob6o181b10obo$2obob2o185bob5o4bo183b
8o186bob2o3b4o184b5ob3o$o3bo188b2o2bo190bo3bo189b2ob2o3bo186bo3bo2b2o
$392bo390b3o67$894bo$893b3o$892b5o$893b5o$893b4o$893b4o$891b6o$893b3o
$893b2o$896bo$894bo$894b2o27$314b3o$314b2o2b2o$313b7o$314b4obo$314b4o
$314b3obo$314b4o$314b4o$313b5o$314b5o$315b3o$316bo146$893b3o$892bobob
o$892b4obo$893b5o$892bob3o$892bob3o2$893b4o$893b2o$892b4o$893b4o$894b
3o$894b2o24$315b2o$314b3o$314b4o$315b4o$316b2o$314b4o2$314b3obo$314b3o
bo$313b5o$313bob4o$314bobobo$315b3o146$894bo$893b3o$892b5o$893b5o$893b
4o$893b4o$892bob3o$893b4o$891bob4o$891b7o$891b2o2b2o$894b3o27$315b2o$
316bo$314bo$316b2o$315b3o$314b6o$314b4o$314b4o$313b5o$314b5o$315b3o$316b
o67$425b3o390bo$425b2o2bo3bo186bo3b2ob2o189bo3bo190bo2b2o188bo3bo$426b
3ob5o184b4o3b2obo186b8o183bo4b5obo185b2obob2o$424bob10o181b6ob6o183b2o
b9o177bob4o4b7o188bobo$424b11o182b4obob4obo183bo3b7o177bo4bo6b4obo187b
3o$424b10o184b2o2bob3obo186bo2b5o181bo6b2ob2obo$426bo5bo193b2o193bo190b
2ob2o104$315bo$316bo2$314bobo$316bo$315b2o$316b2o4$314bo$313b2ob2o$313b
ob4o$314b4o$313b5o$313bob4o$314bobobo$315b3o186$317bo$317bo$315bo2bo$
315b3o$315bo$316b2o$317b2o!

[muzik]

(The 66 doesn't count, because they interact outside the loop.)

Yes, but, still it is an 33-cyclic RRO by considering two 'ships' in a row.

Would this simply be a 2,3,4,6,11,12,22,31,33 then, with 44 and above invalid?

Code: Select all

x = 39, y = 7, rule = B2n3-k4ej5ey6-e78/S2n3-jk4-cjnwy5cky678
3bo30bo$2b5o2bo23b5o$b7obo22b7o$6ob2o22b8o$b7o24b5o$2bo5bo24bo$6bo!

[ababa11e]

My first real RRO [p324]:

Code: Select all

x = 4, y = 3, rule = B3-e4c5ei6n/S23-a4i5er6en7c
2bo$b3o$2obo!

this x-shaped RFO moving in a way i have never seen before:

Code: Select all

x = 4, y = 3, rule = B3-e4c5ri6n/S23-a4i5r6e
2bo$b3o$2obo!

[BOTH CROSSPOSTED FROM MY RULES]

[hotcrystal0]

1, 2, 4-able P236:

Code: Select all

x = 73, y = 21, rule = B2k3-ckny4jy/S2-in3ijnqr4ityz5n
o29bo29bo$2o28b2o28b2o$b2o28b2o28b2o$2o28b2o28b2o3$b2o28b2o28b2o$b3o27b
3o27b3o$69bob2o$59bo5b2o2b3o$54bo3b2o5b2o3bo$53b3o2b2o5bo$52b2obo$31b
3o27b3o$32b2o28b2o3$33b2o28b2o$32b2o28b2o$33b2o28b2o$34bo29bo!

[Yoel]

P594 in a self-complementary hexagonal rule:

Code: Select all

x = 5, y = 5, rule = B2-m4-m56/S2m34m56H
3bo$ob3o$3o$bobo$b3o!

[confocaloid]

Code: Select all

x = 5, y = 5, rule = B2-m4-m56/S2m34m56H
3bo$ob3o$3o$bobo$b3o!

This p594 is long known, and it's a large part of what makes HexInverseFire an interesting CA.

[Yoel]

I've discovered it, together with this rule, in 2023, but did not bother to post it. I did not know that you did. It was a part of this research, which I am now reviewing:

viewtopic.php?f=11&t=6125

Code: Select all

x = 5, y = 5, rule = B2-m4-m56/S2m34m56H
3bo$ob3o$3o$bobo$b3o!

This p594 is long known, and it's a large part of what makes HexInverseFire an interesting CA.

[confocaloid]

I did not know that you did.

No, not really -- I did not discover that p594, either. For example the following post shows that it was already known by 2012. (In fact, I did crosspost it to the thread you linked to: viewtopic.php?p=180739#p180739 )

[...]
But beyond that, here's a really neat pattern:

Code: Select all

x = 158, y = 19, rule = HexInverseFire
151bo2$149bobobobo$152b2o$70bobobo76b5o$obo68b2ob2o77b2o$2o70b5o74bobo
bobo$3o65bo$obob2o63b2o4b2o68b3o7bo$ob3o68bo70b3o$3bo69bobo70b3o$2bo
67bo4bo70b2o$70b2o76bo$69bo77b4o$146b6o$145b7o$149bob4o$149bobo2bo$
150bo!

It would be accurate to describe it as a p594 oscillator, but it seems more descriptive to describe it as a spaceship that travels in a circle. I'm including three of them -- one traveling clockwise, one traveling counter-clockwise, and one next to a p2 oscillator. If you run this pattern at just the right speed, it looks like a spaceship orbiting a star.
[...]