Reflectorless Rotating Oscillators (RRO)

[Yoel]

Ah, sorry, now I remember that you've mentioned this rule a while ago in a comment!

I did not realize that this rule and oscillator are known for so long.

EDIT:

BTW, is there a notation for oblique hexagonal ships?

I did not know that you did.

No, not really -- I did not discover that p594, either. For example this post shows that it was already known by 2012:

[...]
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.
[...]

[hotcrystal0]

This counts, right?

Edit 2: P136 RRO:

Code: Select all

x = 4, y = 4, rule = B2n3-jkry4eiy5c7c8/S2-ci3-ac4iqy5ce
bo$3o$ob2o$bo!

Code: Select all

x = 58, y = 20, rule = B2n3-jkry4eiy5c7c8/S2-ci3-ac4iqy5ce
50b2o$49bob2o$50b2o$50bo2$bo37bo$3o35b3o$ob2o34bob2o$bo37bo3$18bo37bo
$16b2obo34b2obo$17b3o35b3o$18bo37bo2$45bo$44b2o$43b2obo$44b2o!

[hotcrystal0]

P84:

Code: Select all

x = 33, y = 33, rule = B3/S23-y4y
9bo$8bobo$8bobo$6b3ob2o$5bo$6b3ob2o16bo$8bob2o15bobo$27bobo$26b2ob3o$
32bo$26b2ob3o$26b2obo8$10b3o$12bo$3bob2o4bobo$b3ob2o$o$b3ob2o$3bobo$3b
obo15b2obo$4bo16b2ob3o$27bo$21b2ob3o$22bobo$22bobo$23bo!

It can be turned into an RRO by changing the right transitions:

Code: Select all

x = 27, y = 13, rule = B3-y4cj/S23-y4y
16b3o$15b2ob2o$14bobob2o$14bo3bo$15bo2bo$15b3o2$2b3o18b3o$bo2bo17bo2b
o$bo3bo16bo3bo$2obobo15b2obobo$2ob2o16b2ob2o$b3o18b3o!

[pifricted]

It can be turned into an RRO by changing the right transitions:

Code: Select all

x = 27, y = 13, rule = B3-y4cj/S23-y4y
16b3o$15b2ob2o$14bobob2o$14bo3bo$15bo2bo$15b3o2$2b3o18b3o$bo2bo17bo2b
o$bo3bo16bo3bo$2obobo15b2obobo$2ob2o16b2ob2o$b3o18b3o!

Another one:

Code: Select all

x = 14, y = 6, rule = B34cj/S23-y4y
o$o$b3o9bo$4b2o5b2o$4b2obo3bobo$7bo3bo!

But it’s unloopable.

Edit:
This one is loopable.

Code: Select all

x = 29, y = 13, rule = B34r/S23-y4y
20bo$18bobo$19b2o$18bo6$2bo25bo$2o24b2o$obo23bobo$o25bo!

[hotcrystal0]

Another one:

Code: Select all

x = 14, y = 6, rule = B34cj/S23-y4y
o$o$b3o9bo$4b2o5b2o$4b2obo3bobo$7bo3bo!

But it’s unloopable.

I don’t think it counts as an RRO if it’s not loopable.

[b-engine]

I don’t think it counts as an RRO if it’s not loopable.

It, does count. A reflectorless rotating oscillator doesn't need to be loopable, inferred by the name.

EDIT:

It doesn't count.

By your logic, any rotating oscillator that does not involve any reflectors would count. Including for example the blinker. Do you think the blinker is a RRO?

In my books a RRO also need it's center (the center of the entire envelope throughout the period) to be empty, so this will exclude blinker.

[confocaloid]

I don’t think it counts as an RRO if it’s not loopable.

It, does count. A reflectorless rotating oscillator doesn't need to be loopable, inferred by the name.

It doesn't count.

By your logic, any rotating oscillator that does not involve any reflectors would count. Including for example the blinker. Do you think the blinker is a RRO?

[...] In my books a RRO also need it's center (the center of the entire envelope throughout the period) to be empty, so this will exclude blinker.

But that is not explicitly mentioned either.

There can even be a completely statorless rotating oscillator with the property "the center of the entire envelope throughout the period is empty", which nevertheless is not a RRO. Imagine a statorless "ring"-shaped blob that is a period-(4N) mod-N rotating oscillator.

[wwei47]

P88 RRO. Not evenly loopable.

Code: Select all

x = 14, y = 9, rule = B2c3-cjkr4cerw5acqy6ce7c8/S2-i3-ar4ceiqrtz6-n7c8
11bo2$10b4o$9bo2bo$8bo2bo$2bo6bobo$b3o5b3o$bo$3o!

[confocaloid]

The idea of loopability is to reduce the period. In this case, even though two noninteracting instances of the (strict) statorless oscillator can "follow each other" with the same shared envelope, the period of the resulting (non-strict) oscillator does not change from p88 to p44 (as one would expect for a loopable oscillator), which means it is not loopable.

(Note also that writing this directly and explicitly provides a better description of the posted pattern, compared to just writing "not evenly loopable", regardless of whether the latter is correct or not.)

[hotcrystal0]

P88 RRO. Not evenly loopable.

Code: Select all

x = 14, y = 9, rule = B2c3-cjkr4cerw5acqy6ce7c8/S2-i3-ar4ceiqrtz6-n7c8
11bo2$10b4o$9bo2bo$8bo2bo$2bo6bobo$b3o5b3o$bo$3o!

The idea of loopability is to reduce the period. In this case, even though two noninteracting instances of the (strict) statorless oscillator can "follow each other" with the same shared envelope, the period of the resulting (non-strict) oscillator does not change from p88 to p44 (as one would expect for a loopable oscillator), which means it is not loopable.

(Note also that writing this directly and explicitly provides a better description of the posted pattern, compared to just writing "not evenly loopable", regardless of whether the latter is correct or not.)

An additional constraint is that that it must be possible to arrange two or more non-interacting copies of the oscillator to produce a new oscillator with a lower period.

So is it a true RRO or not? It’s loopable, it’s just that it can’t be evenly looped to produce a P44.

[confocaloid]

"With a lower period"

It is not loopable, because it is impossible to produce a lower period by putting >= 2 noninteracting instances with a single shared envelope.

[...]

An additional constraint is that that it must be possible to arrange two or more non-interacting copies of the oscillator to produce a new oscillator with a lower period.

So is it a true RRO or not? It’s loopable, it’s just that it can’t be evenly looped to produce a P44.

[confocaloid]

Both the copperhead and the fireship from Conway's Life are supported: [...]

2-loopable p1684 mod421 statorless rotating oscillator in a CA supporting the copperhead and the fireship:

Code: Select all

x = 108, y = 73, rule = B3-e4eq6n7c/S234ey6ei:T421,200
bo79bo$b2o78b2o$2o78b2o19$106b2o$105b2o$106bo42$14bo7bob2o25bob2o$13b
3o5bo6bo21bo6bo$12bo4bo2b2o3bo2bo20b2o3bo2bo$11b3o4bobo5b2o18b2obo5b2o
$11b3o4bobo5b2o18b2obo5b2o$12bo4bo2b2o3bo2bo20b2o3bo2bo$13b3o5bo6bo21b
o6bo$14bo7bob2o25bob2o!

EDIT 1 (2024-12-27): the ear is a 2-loopable p656 mod164 statorless rotating oscillator, endemic to this CA within the space of 2-state isotropic CA with range-1 Moore neighbourhood:

Code: Select all

x = 88, y = 20, rule = B34eqz6ei7c8/S234e5e
23bob3o55bob3o$23b2o58b2o17$3b2o$3obo!
#C [[ GRID THEME MCell ]]

Two instances can be arranged to make a p656 glider gun (and four instances make a p328 glider gun):

Code: Select all

x = 96, y = 50, rule = B34eqz6ei7c8/S234e5e
2o$2o4$85bo$84bobo$10bo61b3o9bobo$9bobo60b3o10bo$9bobo9b3o48b2o$10bo
10b3o46bob2o$22b2o49b2o9bo2bo$22b2obo42bo3bobo8bo4bo$8bo2bo9b2o44bo4bo
16bo$7bo4bo8bobo3bo39bob5ob2o8bo3bo$6bo16bo4bo38b3obo4b2o5bo5bo$6bo3bo
8b2ob5obo39bo3bo3b2o6bo3bo$6bo5bo5b2o4bob3o40bobo13b3o$7bo3bo6b2o3bo3b
o42b4o$8b3o13bobo44b2o$22b4o$23b2o7$71b2o$70b4o$23b2o31b3o13bobo$22b4o
29bo3bo6b2o3bo3bo$21bobo13b3o14bo5bo5b2o4bob3o$20bo3bo3b2o6bo3bo13bo3b
o8b2ob5obo$19b3obo4b2o5bo5bo12bo16bo4bo$19bob5ob2o8bo3bo13bo4bo8bobo3b
o$19bo4bo16bo14bo2bo9b2o$20bo3bobo8bo4bo29b2obo$25b2o9bo2bo30b2o$22bob
2o32bo10b3o$24b2o31bobo9b3o$24b3o10bo19bobo$24b3o9bobo19bo$36bobo$37bo
3$65bo$66bo27b2o$64b3o27b2o!
#C [[ MAXGRIDSIZE 9 GRID THEME Catagolue ]]

[hotcrystal0]

P76:

Code: Select all

x = 35, y = 15, rule = B2c3ainr/S2-ci3-a4ci
b3o26b3o$bo2bo25bo2bo$o3bo24bo3bo$3o2bo23b3o2bo$bo2bo25bo2bo$3b2o27b2o
4$21b2o$21bo2bo$20bo2b3o$21bo3bo$21bo2bo$22b3o!

[AforAmpere]

1/2/3/4/6/7/11/12/14-able:

Code: Select all

x = 9, y = 8, rule = R5,C0,S13-16,18-19,21,25,33-57,65,67,74,B34-45,74-76
4b3o$b7o$b4o2b2o$4o3b2o$5o2b2o$b5ob2o$2b6o$4b3o!

1/2/4/8/16-able:

Code: Select all

x = 10, y = 10, rule = R5,C0,S1,3,5-6,8,11,13-14,16-20,22,25,33-57,65-66,69,72,B34-45,74
4b2o$3b5o$2b2o3b2o$b2o5bo$4o3b3o$b4ob4o$b8o$2b7o$2b6o$3b4o!

[confocaloid]

1/2/3/4/6/7/11/12/14-able:

Code: Select all

x = 9, y = 8, rule = R5,C0,S13-16,18-19,21,25,33-57,65,67,74,B34-45,74-76
4b3o$b7o$b4o2b2o$4o3b2o$5o2b2o$b5ob2o$2b6o$4b3o!

1/2/4/8/16-able:

Code: Select all

x = 10, y = 10, rule = R5,C0,S1,3,5-6,8,11,13-14,16-20,22,25,33-57,65-66,69,72,B34-45,74
4b2o$3b5o$2b2o3b2o$b2o5bo$4o3b3o$b4ob4o$b8o$2b7o$2b6o$3b4o!

"Soup-friendly" versions, looped with highest specified loopability:

p66 oscillator, 14 instances of the statorless loopable bug sharing the same envelope

Code: Select all

x = 215, y = 185, rule = R6,C0,S642-643,645-646,692,695-696,742-743,745-746,793,795,891,894,937-938,940,942-944,1038-1039,1041-1042,1232-1234,1236-1239,1622-1632,1671-1681,1720-1730,1769-1779,1818-1829,1865,1867-1877,1915-1926,1964-1975,2012-2025,2061-2074,2110-2124,2156,2159-2172,2208-2221,2254,2258-2270,2306-2318,2354-2366,2405-2415,2450,2454-2465,2501-2516,2550-2563,2597,2599-2611,2613,2648,2650-2660,2695-2696,2698-2709,2744,2746-2757,2795-2806,3187,3189,3191-3193,3290,3630,B1670-1679,1681,1720-1729,1769-1778,1819-1827,1867-1878,1917-1926,1967-1975,2016-2025,2064,2066-2073,2109,2113-2122,2162-2171,2205,2210-2220,3629,3683,3724,3731,NW01010101010101010101010101013131313131313131313131010131313131313131313131310101313131313131313131313101013131313131313131313131010131313131313131313131310101313131313100313131313101013131313131313131313131010131313131313131313131310101313131313131313131313101013131313131313131313131010131313131313131313131310101010101010101010101010101
75b2o$73b6o$71b6ob2o20b4o$70b5o4bo19b6o$70b4o5b2o17b8o$70b4o5b2o16b9o$
70b4o4b3o15b5o3b3o$71b9o16b4o5b2o35b4o$72b8o16b4o6bo34b5o$73b6o17b5o4b
2o32b8o$74b4o19b5o2b2o32b10o$98b7o33b4o4b2o$100b4o34b4o5bo$138b5o3b2o$
139b5o2bo$140b6o$142b3o19$41b3o$39b6o$37b5o2b2o$37b4o4b2o128b4o$37b4o
5b2o126b6o$37b4o4b3o125b8o$37b5o2b3o125b9o$38b8o125b5o3b3o$39b7o125b5o
4b2o$40b6o125b5o4bo$41b4o127b5o2b2o$173b7o$175b4o21$208b3o$207b6o$206b
2ob5o$206b2o2b5o$206b2o3b4o$26b3o177b2o2b4o$24b3ob2o177b7o$23b2o3b3o
177b3o$22b2o5b3o$22b3o4b4o$22b3o4b3o$23b4ob4o$23b8o$24b6o$24b6o$25b4o
18$186b4o$185b6o$185b6o$184b8o$183b4ob4o$183b3o4b3o$182b4o4b3o$183b3o
5b2o$4b3o177b3o3b2o$b7o177b2ob3o$b4o2b2o177b3o$4o3b2o$5o2b2o$b5ob2o$2b
6o$4b3o21$36b4o$35b7o$34b2o2b5o127b4o$34bo4b5o125b6o$33b2o4b5o125b7o$
33b3o3b5o125b8o$34b9o125b3o2b5o$34b8o125b3o4b4o$35b6o126b2o5b4o$36b4o
128b2o4b4o$169b2o2b5o$170b6o$171b3o19$70b3o$69b6o$68bo2b5o$67b2o3b5o$
67bo5b4o34b4o$67b2o4b4o33b7o$67b10o32b2o2b5o19b4o$68b8o32b2o4b5o17b6o$
69b5o34bo6b4o16b8o$69b4o35b2o5b4o16b9o$108b3o3b5o15b3o4b4o$109b9o16b2o
5b4o$109b8o17b2o5b4o$110b6o19bo4b5o$111b4o20b2ob6o$136b6o$138b2o!

p62 oscillator, 16 instances of the statorless loopable bug sharing the same envelope

Code: Select all

x = 251, y = 251, rule = R6,C0,S51,150,249,299,397-398,544-545,641,643-645,692-695,792-795,837,839,842,844-845,890-892,894,940-944,988-993,1088-1090,1236-1239,1621,1623-1633,1670-1682,1720-1731,1768-1780,1817-1828,1866-1877,1914,1916-1927,1964-1976,2013-2025,2062-2073,2112-2123,2160-2171,2209-2220,2258-2269,2307-2318,2356-2367,2405-2416,2453-2464,2501,2503-2513,2549-2550,2552-2563,2597,2600-2610,2646,2648-2660,2696,2699-2708,2745-2758,2793,2796-2805,3187-3189,3191-3194,3237-3239,3242,3382-3383,3385-3387,3532,B1671-1682,1719-1730,1769-1779,1818-1829,1867-1877,1917-1926,1967-1976,2015-2025,2065-2074,2113-2122,2162,2164-2171,2211-2220,3629,NW01010101010101010101010101013131313131313131313131010131313131313131313131310101313131313131313131313101013131313131313131313131010131313131313131313131310101313131313100313131313101013131313131313131313131010131313131313131313131310101313131313131313131313101013131313131313131313131010131313131313131313131310101010101010101010101010101
133bo$131b4o$129b7o$128b6ob2o$128b5o3b2o$128b4o4b2o$128b5o3bo$129b5ob
2o$130b6o$132b2o10$97bo$95b4o$93b5ob2o$92b5o3b2o$92b4o5bo$91b4o6b2o$
92b4o4b2o$92b5ob4o$93b8o65b5o$94b7o64b6o$95b5o64b7o$97bo65b9o$163b4o2b
4o$163b3o4b3o$163b3o5bo$164b3o3bo$165b5o$167b2obo13$65b2o$64b4obo$62b
5obobo$61b4o4bo$60b5o4b2o$60b4o4b3o$60b5o3b3o$61b9o$62b8o$63b6o$64b5o$
195b3o$194b5o$193b7o$192b8o$191b5ob4o$191b4o4b3o$191b4o4b3o$191b4o5bo$
191b6o2bo$193b6obo$195b3obo8$31b2o$30b4o$27b6obobo$27b5o3bo$27b4o4b2o$
27b4o4b2o$27b5o2b2o$28b8o$29b6o$30b4o4$226bo$103b2o119b5o$102b6o115b7o
$101bo2b5o113b8o$100bo4b5o111b5ob4o$99b2o5b4o111b4o3b3o$99b3o4b4o110b
4o5b3o$100b3o3b4o111b4o5bo$100b10o111b4o4bo$100b9o113b4o2b2o$101b7o
116b5o$102b5o119bo11$4b2o$3b5o$2b2o3b2o$b2o5bo$4o3b3o$b4ob4o$b8o$2b7o$
2b6o$3b4o6$244b4o$243b6o$242b7o$242b8o$241b4ob4o$241b3o3b4o$242bo5b2o$
242b2o3b2o$243b5o$245b2o11$24bo$22b5o$21b2o2b4o$21bo4b4o$20bo5b4o$19b
3o5b4o$20b3o3b4o$20b4ob5o109b5o$21b8o109b7o$21b7o109b9o$22b5o109b10o$
24bo111b4o3b3o$136b4o4b3o$136b4o5b2o$136b5o4bo$137b5o2bo72b4o$138b6o
72b6o$141b2o72b8o$215b2o2b5o$214b2o4b4o$214b2o4b4o$215bo3b5o$214bobob
6o$217b4o$218b2o8$51bob3o$50bob6o$51bo2b6o$50bo5b4o$49b3o4b4o$49b3o4b
4o$50b4ob5o$51b8o$51b7o$52b5o$53b3o$182b5o$182b6o$181b8o$181b9o$180b3o
3b5o$180b3o4b4o$180b2o4b5o$181bo4b4o$180bobob5o$181bob4o$184b2o13$80bo
b2o$81b5o$80bo3b3o$79bo5b3o$78b3o4b3o$78b4o2b4o$79b9o65bo$80b7o64b5o$
80b6o64b7o$80b5o65b8o$149b4ob5o$149b2o4b4o$148b2o6b4o$149bo5b4o$149b2o
3b5o$150b2ob5o$152b4o$153bo10$117b2o$115b6o$114b2ob5o$114bo3b5o$113b2o
4b4o$113b2o3b5o$114b2ob6o$115b7o$116b4o$117bo!

[wwei47]

P112 2-loopable reflectorless rotating rake gun by NimbleRogue. Oh my god wow.

Code: Select all

x = 10, y = 6, rule = B3-cer4qyz5iy7e/S2-cn3cej4-anqy5cnqry6-a7e
2b2o3bo$b9o$3bo$4o$b2o$4bo!

Code: Select all

x = 16, y = 16, rule = B3-cer4qyz5iy7e/S2-cn3cej4-anqy5cnqry6-a7e
12bo$11b2obo$11b2ob2o$12b4o$10b2o2b2o$11bob2o5$b2obo$2o2b2o$4o$2ob2o$
bob2o$3bo!

[b-engine]

I eventually came up with this defination of RRO:

• The center of the envelope must be hollow (no cell is turned on in any phase).

• The average bounding box of each phases must be significantly smaller than the bounding box of the envelope. (This should rule out some oscillators such as blinkers or a giant C4 blob that rotates itself every few generations)

• The mod is necessarily a fraction of the period, and must not be 1/2 of that. (This should rule out reflectorless flipping oscillators)

[islptng]

1,2,3

Code: Select all

x = 76, y = 13, rule = B3aeijr4aijrty5k6e/S2aek3aijr4i5an6ck
bo31bo31bo$obo29bobo29bobo$2bo31bo31bo$bo31bo31bo7b3o$2o30b2o30b2o5b3o
$72b3o$73bo2$41b2o$41bo25bo$40bo25b2o4b2o$40bobo24b2obobo$41bo25bobo!

Also 1,2,3:

Code: Select all

x = 81, y = 16, rule = B2kn3aciq4ijknwy5-iky6ci7e/S2aek3aijr4aiknty5aknr6ai
76bobo$75b2o2bo$75bobob2o$2bo31bo31bo8bo2b2o$b3o29b3o29b3o9b2o$2obo28b
2obo28b2obo4$77bo$44bob2o28bo$44b3o26bobobo$45bo26b2o4bo$71b2obobo$72b
2o3bobo$78b2o!

Only 1,2:

Code: Select all

x = 10, y = 8, rule = B2k3aeiqr4ejnqw5aqy6c/S2-n3-eknq4jryz5cjknr6cik7c
2bo$b3o$2obo3$6bob2o$6b3o$7bo!

Crossposting

Nice rule with a common P80 1/2/4 RRO:

Code: Select all

x = 75, y = 11, rule = B2cen3aenr4aeikw5iqy/S2aik3-ikqy4jknryz5in6cin
6o26b6o26b6o4bo$5b2o30b2o30b2o3bo$5bo31bo31bo4bo$74bo$65bo8bo$64b3o5b
3o$64bo8bo$64bo$37bo26bo4bo$36b2o26bo3b2o$37b6o21bo4b6o!

Another 1,2

Code: Select all

x = 7, y = 13, rule = B3-enry4ik5jnqr6ik7e/S2-c3aijr4aijntz5n
4bo$4b2o$5b2o$4b2o6$b2o$2o$b2o$2bo!

A P184, but sadly only 1,2

Code: Select all

x = 7, y = 13, rule = B3-jkny4cinrt5cer6cik7c/S2-n3-cnqy4aeikqy5aeqr6cn7e
4bo$3b3o$3bob2o8$2obo$b3o$2bo!

This tiny thing is 1,2,3!?

Code: Select all

x = 9, y = 11, rule = B3aij4rt5jnr6cen/S2-in3aijkr4in5ajkr
bo5b2o$o5b2o$obo4bo$b3o$4o$bo2$5b2o$6b2o$4bobo$4b2o!

1,2,4

Code: Select all

x = 81, y = 17, rule = B3-eqr4aikwyz5cjqry6cn7c/S2-c3ijr4-jtwz5inqr6-en7
77bo$76b2o$75b2o$2obo28b2obo28b2obo8b2o$b3o29b3o29b3o$2bo31bo31bo6$46b
o31bo$45b3o29b3o$45bob2o18b2o8bob2o$68b2o$67b2o$67bo!

[AforAmpere]

1/2/4/8-able RRG:

Code: Select all

x = 53, y = 53, rule = B3aijr4ejk7c8/S2aek3-acek4ceinty5aj6ack
5b3o$4bo2bo$4bo3bo$3b2o2b2o12b2o26bo$4b2o16b2o6bo17b4o$9b3o14bo3b2o16b
o3bo$11bo13bob2o2b2o19bo$9bobo17bobo17bob2o$9b2o15bo2b2o18b2o$27b2o15b
2obo$44bo2bo$45b3o9$6bo$5b3o41bo$4b2o2bo39b2o$7b2o39bo$6bo2bo$6bo2bo
36bo$5bo2bo35bo2bo$6bo36bo2bo$43bo2bo$4bo39b2o$3b2o39bo2b2o$3bo41b3o$
46bo9$5b3o$5bo2bo$5bob2o15b2o$2b2o18b2o2bo15b2o$2obo17bobo17bobo$o19b
2o2b2obo13bo$o3bo16b2o3bo14b3o$b4o17bo6b2o16b2o$3bo26b2o12b2o2b2o$44bo
3bo$45bo2bo$45b3o!

[muzik]

Not sure if this has been documented here:

Code: Select all

x = 18, y = 11, rule = R2,C2,S2,5,8,11,15,19,22-26,29,32,43,46-47,49-50,52-53,55-56,67,70-71,73-74,76-77,79-80,82-83,91,94-95,97-98,100-101,103-104,106-107,109-111,B3,6,9,12,27,30,33,36,51,54,57,60,75,78,81,84,99,102,105,108,NW000000000001041c0401041c001c0400040104000000000000L
$10b2obo$8bo7bo$9bo2$5bo$3b2o5b3o3bo$12bo$bo11bo3bo$bo14b2o$o!
[[ ZOOM 4 ]]

Code: Select all

x = 40, y = 29, rule = R2,C2,S2,5,8,11,15,19,22-26,29,32,43,46-47,49-50,52-53,55-56,67,70-71,73-74,76-77,79-80,82-83,91,94-95,97-98,100-101,103-104,106-107,109-111,B3,6,9,12,27,30,33,36,51,54,57,60,75,78,81,84,99,102,105,108,NW000000000001041c0401041c001c0400040104000000000000L
$32b2obo$30bo7bo$31bo2$27bo$25b2o5b3o3bo$34bo$23bo11bo3bo$23bo14b2o$22b
o9$18bo$b2o14bo$bo3bo11bo$6bo$2bo3b3o5b2o$13bo2$9bo$2bo7bo$5bob2o!
[[ ZOOM 4 ]]

[muzik]

p29792:

Code: Select all

x = 8, y = 7, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
2bo$5bo$7bo$2bo4bo3$bo!

Code: Select all

x = 16, y = 20, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
10bo$13bo$15bo$10bo4bo3$9bo7$6bo3$o4bo$o$2bo$5bo!

Code: Select all

x = 24, y = 24, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
15bo3$16bobo2$3bo11bo$12bo$3bo$o4bo$10bo$14bo$6bo$17bo$9bo$13bo$18bo4b
o$20bo$11bo$8bo11bo2$5bobo3$8bo!

[muzik]

Crossposting these two from the PCA thread (a huge thank you to phpBB for discarding my first draft of this permanently when I went to preview it after finishing it):

RRO, p67292:

Code: Select all

x = 6, y = 7, rule = PCA_4
5.H3$H.L.D3$5.B!

Of course, it's loopable:

Code: Select all

#C p16823
x = 30, y = 30, rule = PCA_4
22.H3$17.H.L.D3$22.B$D5.A$3.B2$3.F2$3.D5$26.A2$26.I2$26.H$23.D5.A$7.H
3$8.A.C.B3$7.B!

Code: Select all

x = 30, y = 16, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
D5.A$3.B2$3.F2$3.D5$26.A2$26.I2$26.H$23.D5.A!

p1812 RRO:

Code: Select all

x = 4, y = 3, rule = PCA_4
A.B$3.B$2.F!

Funnily enough this is loopable despite not having a hole in the middle of its envelope. I assume INT examples of this with no interaction are, in fact, known?:

Code: Select all

x = 12, y = 10, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
3$2.I$.H$2.H.D$7.A.B$10.B$9.F!

Code: Select all

x = 12, y = 12, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
3.A$2.H$3.B2$3.H.D2$7.A.B$10.B$3.C5.F$H$.H$2.H!

Code: Select all

x = 10, y = 10, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
6.A$5.A.C$.I$H4.H$.H.D$6.A.B$4.B4.B$8.F$2.L.D$3.D!

[muzik]

p94428:

Code: Select all

x = 4, y = 5, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
obo2$o$ob2o$3bo!

Code: Select all

x = 14, y = 27, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
$o$2obo$3bo2$bobo17$10bobo2$10bo$10bob2o$13bo!

Code: Select all

x = 28, y = 33, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
$25bo2$22bo$27bo$23bobo$20bo6bo15$5bo3$2bo$3b2o$2bo$o$22bobo$o$22bo$22b
ob2o$25bo!

[muzik]

B3/S23 has this near-miss:

Code: Select all

x = 9, y = 7, rule = B3/S23
4b3o$3b2o3bo$2ob3o2bo$2o3bo2bo$o2bo2b2o$bo2b2o$2b4o!
[[
PASTET EVERY 152 38 PASTE o! -10 -3
PASTET EVERY 152 76 PASTE o! -2 -11
PASTET EVERY 152 114 PASTE o! 6 -3
PASTET EVERY 152 PASTE o! -2 5
]]

Twofold:

Code: Select all

x = 21, y = 19, rule = B3/S23
3b4o$3b2o2bo$b2o2bo2bo$o2bo3b2o$o2b3ob2o$o3b2o$2b3o6$16b3o$15b2o3bo$12b
2ob3o2bo$12b2o3bo2bo$12bo2bo2b2o$13bo2b2o$14b4o!
[[
PASTET EVERY 76 38 PASTE o! 2 9
PASTET EVERY 76 PASTE o! 10 1
PASTET EVERY 76 38 PASTE o! 18 9
PASTET EVERY 76 PASTE o! 10 17
]]

[yaochen2]

Crazy p1372 RROMOS

Code: Select all

x = 9, y = 4, rule = B2e3-cjqr4eiknqwz5cijkn6ak7e/S01c2-ck3cjkny4acijqwy5iknr6ckn7c8
8bo$2o4bo$bo6bo$2o!

Crazier p1516 RROMOS

Code: Select all

x = 11, y = 4, rule = B2e3-cjnr4-acjk5-aeny6-ck7c8/S01c2aen3jkny4aiw5-aeqy6-n7e8
8b2o$2o8bo$bo6b2o$2o!