Reflectorless Rotating Oscillators (RRO)

[yaochen2]

Period 13528 RRO from a rulespace rich in high period spaceships with loopability 3

Code: Select all

x = 524, y = 276, rule = B2in3-ekn4ckqtz5ekr6ci8/S2aek3-ae4ceiyz5-jqy6ac7e
463bo2$461bob2o$462bo$460bo2bo$461b3o$461bobo$461bo3$461b2o$459b2o$
458bo2b2o$457bobo2bo$458bo2bo$459bobo$460bo3$459b3o$459bobo8bobo$459bo
bo8bo2bo$428bo30b2o7bo3b2o$427bobo26b2o$455b2ob2o$427bobo25b4obo$456b
4o$455bobobo$455b2o2bo23bo$458bo23b3o2b3o$458bo2bo19bo2bo2b2o$462bo18b
obo4bo2bo$458b2obobo17bobo5b2o$457b3o4bo17b3o4bobo$459bo2b2o21b2o3bo$
458bobob3o20b2ob2o2bo$462b2o21bob2ob3o$486bo3bo$485b2ob2o$484bob2o$
485b2o19$451bo$450b3o$450bob2o2$448b2o2bo$447bob2o2b2o$447b2ob3ob2o$
448bo2bo2bo$448b2o2bobo$449b5o$451bo2$434b2o8bo$434b2o7b4o$433bobo7bo
2bo$435b3o4bo2b2o$432b5obob2obobo$432bo5b2obo$432b3o2bo5b4o$433bo2b3o
2bo4bobo$440bo2bobob2o$441bob2obobo$443b2o2$442bo$442bobo$443bobo2$
445bo7$503b3o$502b3obo$502bo2bo$501b4obobo5b2o$500b2o5bo5b5o$501b2o5bo
b2o6b2o$503bo3b4obo2bo3bobobo$500b2ob2obobobo3b5o2bobo$498b4o2bobo3b2o
3bo7bo$498b2o2b3o2bo3b2obo4bobo$498bobob2o2bobo3bobobo3b3o$501bobob4o
3bo5b4o$327bo3b3o170bob2o3bobobo$326b3obo2bo171b3o6bo$325b2obobo2bo
178bo2bo$10bo314bobo5b2o179bo$4b3o2b3o314b3obo2bo$3bo2bobo2b2o309b2obo
2bobobo$3b4o3b2o310b2ob3o3b2o$3bobob2obobo310bob2ob2ob3o$2bobobo3b3o
312b3o3b2o$3bo2bobob2o$2bob2o2bobo$7ob4o$5b2o4bo$4bo103$459b3o16bo$
458bo3bo$458b2o2$462bo$456b2o3bobo2bo$454bobo8b2o$459bo2bob3o$454b4o7b
o$453bob2o2b3ob2o$453bobo2bob2ob2o$453b2obo$454b2o5bo$454b3o5bo$450b2o
6bo2bobo$451bo4bo2b2o2bo4b2o$462bobo2bo2b2o$451bo3bo2bo6b2obo3bo$450bo
5b2o3bo2b2obo4b2o$449bob3o5b3o8b3o$449b3obo2bo2bob3o5b3o$449bob3o2bobo
bobo$449b2o5b2ob2o2bo$448bo10bob4o2b4o$459bobobo6b2o$459b3o7b3o$448bo
11b3o5b4o$448b2o20bobo$448b3o$451b2o$449b2ob2o$449b2obo$439b2o9bobo$
431bo3b2ob3o9b2o$429b2o3b2o2bobo3bo$428b2ob2o3bo4b2o2bo12bo$429b3obobo
bo2b5obo3bob2o2b4o$430bobobobobo2b2o6bo2bobobo3bo$437bob2ob4o4bob2o2bo
3b2o$436b4o3bo7b2obo3b3o$438b2o9b3o6b2o$435bo3bo5bo2bobo$436bo7bobob2o
$437bo5bo3b2o$438bo3bob4o$439bob4obo$440b2o3bobo2$444b3o$444bo$443b2o
2b2o$444bo2b2o$445b3o$446bo!

Loopability 13 p3908 RROMOS

Code: Select all

x = 491, y = 255, rule = B2en3aeiy4cijnrtw5-acy6-ik/S01c2aei3jkqy4aijnqrw5aiq6-ak8
242bobo$246b2o$242b2o2bo$242b2o$244bo2bo$o244b2o15bo74bo74bo$b2o4b2o
254b2o5b2o66b2o30b2o41b2o55b2o12bo$o6bo235b3o3b2o11bo6b3o65bo31b3o40bo
56b3o$7b2o236bo4bo19b2o98b2o98b2o12b3o$247b2o234b6o$245bob2o235b7o$
482b3o2b4o$482b4ob4o$482b3ob3o$482bobo2bo$481b3obo$482bo44$245bo2$244b
obo17$484b3o$485bo17$245b3o$245b3o$246bo6$483b3o$483bobo29$245bo2$244b
obo17$484b3o$485bo42$245b3o$245b3o$246bo6$483b3o$483bobo4$245bo2$244bo
bo17$484b3o$485bo7$237bo$241bob2o$236b2o2bob3o$235bobo2b2o$235b2obo2b
2o$239bo2b3o230bo$238b2o2b4o229bo$245bo65b2o98b2o60bob2o$244bo35b2o27b
3o43b2o52b3o18b2o42bobo2bo$244bo37bo28b2o44bo53b2o19bo42b2o3bo$244bo
35b2o73b2o73b2o41b2obo2bo4bo$473b2obo7bo$475b2obo4b2o$475bo2bob2o2bo$
476bo2b2o$477b2ob2o2$477bo!

[muzik]

Could an adjustable family of reflectorless rotating oscillators exist, in which a small, fast spaceship chases an adjustable-speed spaceship? This seems easy to model with a multistate rule, but I don't know if a 2-state solution would be easy to find.

[AforAmpere]

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?

Now there are, a 1/2/3-able p342:

Code: Select all

x = 60, y = 13, rule = B2o3-o4m6/S2-o34p5H
47bo$48bo$48bo$47b2o$5bo2bo39bo$5b4o4$55b2o$56bo$4o43b4o6bo$o2bo43bo2b
o7b2o!

1/2-able p324:

Code: Select all

x = 5, y = 17, rule = B2-p3o4-o6/S2m3-oH
2bo$2b3o$2b2o$3bo$3bo8$bo$bo$b2o$3o$2bo!

EDIT, what I'm pretty sure is a loopability record in this space, 1/2/3/4-able:

Code: Select all

x = 37, y = 41, rule = B2-m4-o/S23p4m5H
2bo$2b3o$2bo$2b3o$18b2o$19bo2$10b2o$b2o6b5o7b2o$3o7bo2bo8bo$bo8b2ob2o
7bo$b2o8b4o9b2o$2bo2b3o5bo$6bo14$30bo$23bo5b3o2bo$11b2o9b4o8b2o$14bo7b
2ob2o8bo$14bo8bo2bo7b3o$14b2o7b5o6b2o$25b2o2$17bo$17b2o$32b3o$34bo$32b
3o$34bo!

[muzik]

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?

Now there are,

Excellent! I was confident this entire rulespace had been exhausted already.

...Frustratingly however, all three of these rules are explosive, so I can't search them, nor can I figure out the canonical apgcodes using the box on Catagolue...

Are there reflectorless rotating oscillators that travel in a triangular path, rather than a hexagonal path? Much like this object, but actually loopable:

Code: Select all

x = 8, y = 5, rule = B256/S34mH
3b3o$2bobo2bo$bob3o$obobob2o$2b2o!

Another question: are there any objects like that above object where it rotates 120 degrees around a cell, rather than a vertex, so that the central cell has a period of p/3?

[73times137]

Here is a p152 with loopability 2 in a rule with many spaceships:

Code: Select all

x = 36, y = 12, rule = B2n3-qy4t5ek/S235ac6c
2bo21bo$bobo19bobo$o2bo18bo2bo$3o19b3o5$33b3o$32bo2bo$32bobo$33bo!

Spaceships in this rule include the glider, xWSSes, the W-pentomino which is 4c/17d, a small c/3d, and a 6c/12:

Code: Select all

x = 53, y = 7, rule = B2n3-qy4t5ek/S235ac6c
42b3o$34b3o4bo2bo5b3o$26b3o4bo2bo7bo4bo2bo$b3o21bo2bo7bo3bo3bo7bo$o7b
2o9bo8bo3bo3bo3bo3bo3bo3bo$obo5bobo7b2o8bo7bo7bo4bobo$o2bo4bo8b2o6bobo
5bobo5bobo7bo!

This seems like an interesting rule to apgsearch- I especially find it interesting how much the presence of two spaceships in the same direction with very close speeds (the glider and W-pentomino) affects the performance. If only running a few symmetries, do C1, D4_+2, and D8_1- this should find odd, even, and diagonally-symmetric patterns, while finding more possible asymmetric spaceships.
EDIT:
Adding B3y also adds a 2c/5 spaceship while keeping the other spaceships and makes the rule much more active. However, the p152 does not work.

[yyh_baboon]

P412 4-loopable RRO:

Code: Select all

x = 4, y = 7, rule = B3-n5y6c/S2-n3-y4iq
2bo$2obo$b2o$2bo$2bo$bobo$bobo!
[[ THEME INVERSE ]]

[yyh_baboon]

First 2-loopable RFO(rotatorless flipping oscillator)?

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!

[1and0nlycordershippr]

Hey, here’s an RRO in the Single Rotation cellular automaton. Unfortunately, it isn’t loopable.

Code: Select all

x = 7, y = 7, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$3bo2$3bo2bo$4bo2$obo!

[1and0nlycordershippr]

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.

The first one is a pseudo-RRO. Pseudo-RROs are n-loopable RROs that interact with each other with n evenly spaced copies. One value of n is enough. Also, Pseudo-RROs are a kind of RROs. The spark interaction can change the period (commonly period doubled) or not do anything to the period (typical n-loopable RROs have a specific period, but n copies evenly spaced usually reduce it to init period/n)
The second one has a stator part, just like the blinker. Yes, it rotates itself, but there’s a stator.

[yyh_baboon]

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!

Actually I think they might be counted as “interacting”. My definition of “interaction” means that there exists one cell which is in the neighbourhood of both regions(even if nothing happens).

[I6_I6]

First 2-loopable RFO(rotatorless flipping oscillator)?

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!

Huh? How is that a flipper?

[yyh_baboon]

First 2-loopable RFO(rotatorless flipping oscillator)?

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!

Huh? How is that a flipper?

I put two non-interacting copies together to show its loopability.
this one half is a flipping oscillator:

Code: Select all

 x = 55, y = 87, 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$
8bo11bo$7b2o11b2o$6b2obo9bob2o$7bobo9bobo$8b2o9b2o!

[1and0nlycordershippr]

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!

Actually I think they might be counted as “interacting”. My definition of “interaction” means that there exists one cell which is in the neighbourhood of both regions(even if nothing happens).

Yes, that is the definition of a pseudo-RRO.

[1and0nlycordershippr]

2-loopable P1284 RRO:

Code: Select all

x = 27, y = 13, rule = M0,2,8,12,1,10,9,11,4,6,5,14,3,7,13,15
$3bo21bo2$3bo21bo2$bo2bo18bo2bo$bo21bo$20bo$17bo2bo2$18bo2$18bo!

[1and0nlycordershippr]

2-loopable P1284 RRO:

Code: Select all

x = 27, y = 13, rule = M0,2,8,12,1,10,9,11,4,6,5,14,3,7,13,15
$3bo21bo2$3bo21bo2$bo2bo18bo2bo$bo21bo$20bo$17bo2bo2$18bo2$18bo!

In the same rule, a 1-2-3-4-loopable p7284 RRO:

Code: Select all

x = 113, y = 19, rule = M0,2,8,12,1,10,9,11,4,6,5,14,3,7,13,15
$45bo63bo2$42bo3bo18b3o29b2o7bo3bo$46bo22bo25bo14bo$67bo8bo2bobo19bo$
73bo$44bo23bo9bo18bo4bo5bo$42bo31bo31bo3$5bo31bo31bo31bo$3bo31bo31bo31b
o5bo4bo2$106bo$bo31bo31bo31bo14bo$bo3bo27bo3bo27bo3bo27bo3bo7b2o2$2bo
31bo31bo31bo!

[Docsy]

Recently in the Discord, I had been looking at this old design for an adjustable RRO that should be arbitrarily loopable, and I realized that it could be dramatically simplified (with one caveat) and still function. The design I came up with uses an orthogonal spaceship (red), a diagonal spaceship with half the speed (blue) and a reaction between them that re-emits them at new angles and displacements in a certain way (gray colors)



AforAmpere decided to search for it, and manage to find an example of this pattern in the INT rulespace, and showed various demonstrations of how it can be arranged. Thank you Ampere for discovering that it works in INT.
Here it is with loopability-2:

Code: Select all

x = 51, y = 49, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
41bobo$42b2o$41bobo$42bo4$49b2o2$50bo5$21bobo$20bobo$21b3o16$27b3o$28b
obo$27bobo5$o2$2o4$8bo$7bobo$7b2o$7bobo!

loopability 5 and 6:

Code: Select all

x = 285, y = 119, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
32bobo179bobo$32bo76bobo102bo60bobo$110b2o164b2o$109bobo163bobo$110bo
165bo4$117b2o164b2o$181bobo$118bo61bobo101bo$181b3o8$13b3o$14bobo$13bo
bo4$31bobo$30bobo$31b3o153b3o$166bo21bobo$187bobo$166b2o4$254bo$253bob
o$253b2o$253bobo4$235bobo$80bo155b2o$79bobo153bobo$79b2o155bo$79bobo4$
61bobo157bobo$62b2o156bobo$61bobo157b3o$62bo8$o2$2o5$61b3o163b3o$62bob
o163bobo$61bobo163bobo4$79bobo$78bobo133bo$79b3o131bobo$213b2o$213bobo
4$195bobo$196b2o$195bobo$196bo4$283b2o$261bobo$32bo227bobo21bo$31bobo
227b3o$31b2o$31bobo4$13bobo$14b2o$13bobo$14bo4$117b2o2$118bo$267b3o$
166bo101bobo$267bobo$166b2o4$174bo$109b3o61bobo$110bobo60b2o$38bo70bob
o61bobo60bo$36bobo195bobo!

This pattern appears to be adjustable to fit any loopability, though it's not been formally proven, as there is a risk of it colliding with itself in certain cases (the caveat mentioned earlier). Ampere showed a version of it that ties the previous record loopability, 89:

Code: Select all

x = 804, y = 805, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
793bobo$794b2o$11bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bo
bo33bobo23bobo$11bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35b
o35bo35bo35bo35bo35bo35bo35bo35bo26bo$798b2o2$799bo$12bo$11bobo$12b2o$
3bobo5bobo$3b2o$3bobo$4bo4$788bo$775bobo9bobo$776b2o9b2o$775bobo9bobo$
776bo2$o2$2o28bo$29bobo$30b2o$21bobo5bobo$21b2o$21bobo$22bo4$770bo$
757bobo9bobo$758b2o9b2o$757bobo9bobo$758bo$798b2o2$799bo$48bo$47bobo$
48b2o$39bobo5bobo$39b2o$39bobo$40bo4$752bo$739bobo9bobo$740b2o9b2o$
739bobo9bobo$740bo2$o2$2o64bo$65bobo$66b2o$57bobo5bobo$57b2o$57bobo$
58bo4$734bo$721bobo9bobo$722b2o9b2o$721bobo9bobo$722bo$798b2o2$799bo$
84bo$83bobo$84b2o$75bobo5bobo$75b2o$75bobo$76bo4$716bo$703bobo9bobo$
704b2o9b2o$703bobo9bobo$704bo2$o2$2o100bo$101bobo$102b2o$93bobo5bobo$
93b2o$93bobo$94bo4$698bo$685bobo9bobo$686b2o9b2o$685bobo9bobo$686bo$
798b2o2$799bo$120bo$119bobo$120b2o$111bobo5bobo$111b2o$111bobo$112bo4$
680bo$667bobo9bobo$668b2o9b2o$667bobo9bobo$668bo2$o2$2o136bo$137bobo$
138b2o$129bobo5bobo$129b2o$129bobo$130bo4$662bo$649bobo9bobo$650b2o9b
2o$649bobo9bobo$650bo$798b2o2$799bo$156bo$155bobo$156b2o$147bobo5bobo$
147b2o$147bobo$148bo4$644bo$631bobo9bobo$632b2o9b2o$631bobo9bobo$632bo
2$o2$2o172bo$173bobo$174b2o$165bobo5bobo$165b2o$165bobo$166bo4$626bo$
613bobo9bobo$614b2o9b2o$613bobo9bobo$614bo$798b2o2$799bo$192bo$191bobo
$192b2o$183bobo5bobo$183b2o$183bobo$184bo4$608bo$595bobo9bobo$596b2o9b
2o$595bobo9bobo$596bo2$o2$2o208bo$209bobo$210b2o$201bobo5bobo$201b2o$
201bobo$202bo4$590bo$577bobo9bobo$578b2o9b2o$577bobo9bobo$578bo$798b2o
2$799bo$228bo$227bobo$228b2o$219bobo5bobo$219b2o$219bobo$220bo4$572bo$
559bobo9bobo$560b2o9b2o$559bobo9bobo$560bo2$o2$2o244bo$245bobo$246b2o$
237bobo5bobo$237b2o$237bobo$238bo4$554bo$541bobo9bobo$542b2o9b2o$541bo
bo9bobo$542bo$798b2o2$799bo$264bo$263bobo$264b2o$255bobo5bobo$255b2o$
255bobo$256bo4$536bo$523bobo9bobo$524b2o9b2o$523bobo9bobo$524bo2$o2$2o
280bo$281bobo$282b2o$273bobo5bobo$273b2o$273bobo$274bo4$518bo$505bobo
9bobo$506b2o9b2o$505bobo9bobo$506bo$798b2o2$799bo$300bo$299bobo$300b2o
$291bobo5bobo$291b2o$291bobo$292bo4$500bo$487bobo9bobo$488b2o9b2o$487b
obo9bobo$488bo2$o2$2o316bo$317bobo$318b2o$309bobo5bobo$309b2o$309bobo$
310bo4$482bo$469bobo9bobo$470b2o9b2o$469bobo9bobo$470bo$798b2o2$799bo$
336bo$335bobo$336b2o$327bobo5bobo$327b2o$327bobo$328bo4$464bo$451bobo
9bobo$452b2o9b2o$451bobo9bobo$452bo2$o2$2o352bo$353bobo$354b2o$345bobo
5bobo$345b2o$345bobo$346bo4$446bo$433bobo9bobo$434b2o9b2o$433bobo9bobo
$434bo$798b2o2$799bo$372bo$371bobo$372b2o$363bobo5bobo$363b2o$363bobo$
364bo4$428bo$415bobo9bobo$416b2o9b2o$415bobo9bobo$416bo2$o2$2o388bo$
389bobo$390b2o$381bobo5bobo$381b2o$381bobo$382bo4$410bo$397bobo9bobo$
398b2o9b2o$397bobo9bobo$398bo$798b2o2$799bo$408bo$407bobo$408b2o$399bo
bo5bobo$399b2o$399bobo$400bo4$392bo$379bobo9bobo$380b2o9b2o$379bobo9bo
bo$380bo2$o2$2o424bo$425bobo$426b2o$417bobo5bobo$417b2o$417bobo$418bo
4$374bo$361bobo9bobo$362b2o9b2o$361bobo9bobo$362bo$798b2o2$799bo$444bo
$443bobo$444b2o$435bobo5bobo$435b2o$435bobo$436bo4$356bo$343bobo9bobo$
344b2o9b2o$343bobo9bobo$344bo2$o2$2o460bo$461bobo$462b2o$453bobo5bobo$
453b2o$453bobo$454bo4$338bo$325bobo9bobo$326b2o9b2o$325bobo9bobo$326bo
$798b2o2$799bo$480bo$479bobo$480b2o$471bobo5bobo$471b2o$471bobo$472bo
4$320bo$307bobo9bobo$308b2o9b2o$307bobo9bobo$308bo2$o2$2o496bo$497bobo
$498b2o$489bobo5bobo$489b2o$489bobo$490bo4$302bo$289bobo9bobo$290b2o9b
2o$289bobo9bobo$290bo$798b2o2$799bo$516bo$515bobo$516b2o$507bobo5bobo$
507b2o$507bobo$508bo4$284bo$271bobo9bobo$272b2o9b2o$271bobo9bobo$272bo
2$o2$2o532bo$533bobo$534b2o$525bobo5bobo$525b2o$525bobo$526bo4$266bo$
253bobo9bobo$254b2o9b2o$253bobo9bobo$254bo$798b2o2$799bo$552bo$551bobo
$552b2o$543bobo5bobo$543b2o$543bobo$544bo4$248bo$235bobo9bobo$236b2o9b
2o$235bobo9bobo$236bo2$o2$2o568bo$569bobo$570b2o$561bobo5bobo$561b2o$
561bobo$562bo4$230bo$217bobo9bobo$218b2o9b2o$217bobo9bobo$218bo$798b2o
2$799bo$588bo$587bobo$588b2o$579bobo5bobo$579b2o$579bobo$580bo4$212bo$
199bobo9bobo$200b2o9b2o$199bobo9bobo$200bo2$o2$2o604bo$605bobo$606b2o$
597bobo5bobo$597b2o$597bobo$598bo4$194bo$181bobo9bobo$182b2o9b2o$181bo
bo9bobo$182bo$798b2o2$799bo$624bo$623bobo$624b2o$615bobo5bobo$615b2o$
615bobo$616bo4$176bo$163bobo9bobo$164b2o9b2o$163bobo9bobo$164bo2$o2$2o
640bo$641bobo$642b2o$633bobo5bobo$633b2o$633bobo$634bo4$158bo$145bobo
9bobo$146b2o9b2o$145bobo9bobo$146bo$798b2o2$799bo$660bo$659bobo$660b2o
$651bobo5bobo$651b2o$651bobo$652bo4$140bo$127bobo9bobo$128b2o9b2o$127b
obo9bobo$128bo2$o2$2o676bo$677bobo$678b2o$669bobo5bobo$669b2o$669bobo$
670bo4$122bo$109bobo9bobo$110b2o9b2o$109bobo9bobo$110bo$798b2o2$799bo$
696bo$695bobo$696b2o$687bobo5bobo$687b2o$687bobo$688bo4$104bo$91bobo9b
obo$92b2o9b2o$91bobo9bobo$92bo2$o2$2o712bo$713bobo$714b2o$705bobo5bobo
$705b2o$705bobo$706bo4$86bo$73bobo9bobo$74b2o9b2o$73bobo9bobo$74bo$
798b2o2$799bo$732bo$731bobo$732b2o$723bobo5bobo$723b2o$723bobo$724bo4$
68bo$55bobo9bobo$56b2o9b2o$55bobo9bobo$56bo2$o2$2o748bo$749bobo$750b2o
$741bobo5bobo$741b2o$741bobo$742bo4$50bo$37bobo9bobo$38b2o9b2o$37bobo
9bobo$38bo$798b2o2$799bo$768bo$767bobo$768b2o$759bobo5bobo$759b2o$759b
obo$760bo4$32bo$19bobo9bobo$20b2o9b2o$19bobo9bobo$20bo2$o2$2o784bo$
785bobo$786b2o$777bobo5bobo$777b2o$777bobo$778bo4$14bo$bobo9bobo$2b2o
9b2o$bobo9bobo$2bo$798b2o2$799bo$798bo$14bo35bo35bo35bo35bo35bo35bo35b
o35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo32bo$12bobo
33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bo
bo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo25bo$795b3o$
795bo2bo$795bobo!

Finally, here's loopability-4 with colorcoding to show each individual copy of the pattern:

Code: Select all

x = 51, y = 51, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7eSuper
15.U.U$15.U4$38.3Q$37.Q.Q$38.Q.Q3$5.U.U$5.2U11.S$5.U.U9.S.S$6.U11.2S$
17.S.S$49.2Q2$36.U.U11.Q$37.U.U$36.3U12$12.3pA$11.pA.pA$S11.pA.pA2$2S
$31.Q.Q$31.2Q11.pA$31.Q.Q9.pA.pA$32.Q11.2pA$43.pA.pA3$10.S.S$11.S.S$10.
3S4$35.pA$33.pA.pA!

I'm fairly certain this can be adjusted to fit any loopability, but at the very least it should be apparent that it can create arbitrarily large loopabilities. I'd also like to note that the use of c/1o and c/2d was for convenience of searching, and versions of this that use slower spaceships, in potentially less explosive rules, are likely to exist.

Edit: Also, for hexagonal rule enjoyers: If you look at the loopability-89 pattern, you can see that its composed of an outer loop, and two inner loops crossing over each other. In some isotropic hexagonal rule (maybe with a higher state count or range if the space is too small), there is likely an adjustable RRO where high loopability versions look like a hexagon with two triangle loops inside, looking like a hexagram inside a hexagon sharing the same corners. you just need to find a collision between an orthogonal spaceship and a diagonal spaceship of the right speeds that re-emits them both in the right way.

[1and0nlycordershippr]

Period is 32+8n.
Smallest:

Code: Select all

x = 10, y = 13, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
8bo$7bobo$8b2o$7bobo$3o$bob3o$5obo$b3obobo2$4bo$3bo$7bo$2bobo!

Unfortunately, the rule itself is explosive.
Using this design, we have a new record for loopability: 101.

Code: Select all

x = 914, y = 909, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
15bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33b
obo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo19b3o$15bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35b
o35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo20bobo$901bobo2$11bo
bo$10bobo894b2o$11b3o$908bo3$5b3o$6bobo$5bobo2$897bobo$898bobo$897b3o
2$bo881b3o$882bobo$b2o880bobo2$29bobo$28bobo$29b3o4$23b3o$24bobo$23bo
bo2$879bobo$880bobo$879b3o2$865b3o$864bobo$865bobo2$47bobo$46bobo858b
2o$47b3o$908bo3$41b3o$42bobo$41bobo2$861bobo$862bobo$861b3o2$bo845b3o
$846bobo$b2o844bobo2$65bobo$64bobo$65b3o4$59b3o$60bobo$59bobo2$843bob
o$844bobo$843b3o2$829b3o$828bobo$829bobo2$83bobo$82bobo822b2o$83b3o$908b
o3$77b3o$78bobo$77bobo2$825bobo$826bobo$825b3o2$bo809b3o$810bobo$b2o808b
obo2$101bobo$100bobo$101b3o4$95b3o$96bobo$95bobo2$807bobo$808bobo$807b
3o2$793b3o$792bobo$793bobo2$119bobo$118bobo786b2o$119b3o$908bo3$113b3o
$114bobo$113bobo2$789bobo$790bobo$789b3o2$bo773b3o$774bobo$b2o772bobo
2$137bobo$136bobo$137b3o4$131b3o$132bobo$131bobo2$771bobo$772bobo$771b
3o2$757b3o$756bobo$757bobo2$155bobo$154bobo750b2o$155b3o$908bo3$149b3o
$150bobo$149bobo2$753bobo$754bobo$753b3o2$bo737b3o$738bobo$b2o736bobo
2$173bobo$172bobo$173b3o4$167b3o$168bobo$167bobo2$735bobo$736bobo$735b
3o2$721b3o$720bobo$721bobo2$191bobo$190bobo714b2o$191b3o$908bo3$185b3o
$186bobo$185bobo2$717bobo$718bobo$717b3o2$bo701b3o$702bobo$b2o700bobo
2$209bobo$208bobo$209b3o4$203b3o$204bobo$203bobo2$699bobo$700bobo$699b
3o2$685b3o$684bobo$685bobo2$227bobo$226bobo678b2o$227b3o$908bo3$221b3o
$222bobo$221bobo2$681bobo$682bobo$681b3o2$bo665b3o$666bobo$b2o664bobo
2$245bobo$244bobo$245b3o4$239b3o$240bobo$239bobo2$663bobo$664bobo$663b
3o2$649b3o$648bobo$649bobo2$263bobo$262bobo642b2o$263b3o$908bo3$257b3o
$258bobo$257bobo2$645bobo$646bobo$645b3o2$bo629b3o$630bobo$b2o628bobo
2$281bobo$280bobo$281b3o4$275b3o$276bobo$275bobo2$627bobo$628bobo$627b
3o2$613b3o$612bobo$613bobo2$299bobo$298bobo606b2o$299b3o$908bo3$293b3o
$294bobo$293bobo2$609bobo$610bobo$609b3o2$bo593b3o$594bobo$b2o592bobo
2$317bobo$316bobo$317b3o4$311b3o$312bobo$311bobo2$591bobo$592bobo$591b
3o2$577b3o$576bobo$577bobo2$335bobo$334bobo570b2o$335b3o$908bo3$329b3o
$330bobo$329bobo2$573bobo$574bobo$573b3o2$bo557b3o$558bobo$b2o556bobo
2$353bobo$352bobo$353b3o4$347b3o$348bobo$347bobo2$555bobo$556bobo$555b
3o2$541b3o$540bobo$541bobo2$371bobo$370bobo534b2o$371b3o$908bo3$365b3o
$366bobo$365bobo2$537bobo$538bobo$537b3o2$bo521b3o$522bobo$b2o520bobo
2$389bobo$388bobo$389b3o4$383b3o$384bobo$383bobo2$519bobo$520bobo$519b
3o2$505b3o$504bobo$505bobo2$407bobo$406bobo498b2o$407b3o$908bo3$401b3o
$402bobo$401bobo2$501bobo$502bobo$501b3o2$bo485b3o$486bobo$b2o484bobo
2$425bobo$424bobo$425b3o4$419b3o$420bobo$419bobo2$483bobo$484bobo$483b
3o2$469b3o$468bobo$469bobo2$443bobo$442bobo462b2o$443b3o$908bo3$437b3o
$438bobo$437bobo2$465bobo$466bobo$465b3o2$bo449b3o$450bobo$b2o448bobo
2$461bobo$460bobo$461b3o4$455b3o$456bobo$455bobo2$447bobo$448bobo$447b
3o2$433b3o$432bobo$433bobo2$479bobo$478bobo426b2o$479b3o$908bo3$473b3o
$474bobo$473bobo2$429bobo$430bobo$429b3o2$bo413b3o$414bobo$b2o412bobo
2$497bobo$496bobo$497b3o4$491b3o$492bobo$491bobo2$411bobo$412bobo$411b
3o2$397b3o$396bobo$397bobo2$515bobo$514bobo390b2o$515b3o$908bo3$509b3o
$510bobo$509bobo2$393bobo$394bobo$393b3o2$bo377b3o$378bobo$b2o376bobo
2$533bobo$532bobo$533b3o4$527b3o$528bobo$527bobo2$375bobo$376bobo$375b
3o2$361b3o$360bobo$361bobo2$551bobo$550bobo354b2o$551b3o$908bo3$545b3o
$546bobo$545bobo2$357bobo$358bobo$357b3o2$bo341b3o$342bobo$b2o340bobo
2$569bobo$568bobo$569b3o4$563b3o$564bobo$563bobo2$339bobo$340bobo$339b
3o2$325b3o$324bobo$325bobo2$587bobo$586bobo318b2o$587b3o$908bo3$581b3o
$582bobo$581bobo2$321bobo$322bobo$321b3o2$bo305b3o$306bobo$b2o304bobo
2$605bobo$604bobo$605b3o4$599b3o$600bobo$599bobo2$303bobo$304bobo$303b
3o2$289b3o$288bobo$289bobo2$623bobo$622bobo282b2o$623b3o$908bo3$617b3o
$618bobo$617bobo2$285bobo$286bobo$285b3o2$bo269b3o$270bobo$b2o268bobo
2$641bobo$640bobo$641b3o4$635b3o$636bobo$635bobo2$267bobo$268bobo$267b
3o2$253b3o$252bobo$253bobo2$659bobo$658bobo246b2o$659b3o$908bo3$653b3o
$654bobo$653bobo2$249bobo$250bobo$249b3o2$bo233b3o$234bobo$b2o232bobo
2$677bobo$676bobo$677b3o4$671b3o$672bobo$671bobo2$231bobo$232bobo$231b
3o2$217b3o$216bobo$217bobo2$695bobo$694bobo210b2o$695b3o$908bo3$689b3o
$690bobo$689bobo2$213bobo$214bobo$213b3o2$bo197b3o$198bobo$b2o196bobo
2$713bobo$712bobo$713b3o4$707b3o$708bobo$707bobo2$195bobo$196bobo$195b
3o2$181b3o$180bobo$181bobo2$731bobo$730bobo174b2o$731b3o$908bo3$725b3o
$726bobo$725bobo2$177bobo$178bobo$177b3o2$bo161b3o$162bobo$b2o160bobo
2$749bobo$748bobo$749b3o4$743b3o$744bobo$743bobo2$159bobo$160bobo$159b
3o2$145b3o$144bobo$145bobo2$767bobo$766bobo138b2o$767b3o$908bo3$761b3o
$762bobo$761bobo2$141bobo$142bobo$141b3o2$bo125b3o$126bobo$b2o124bobo
2$785bobo$784bobo$785b3o4$779b3o$780bobo$779bobo2$123bobo$124bobo$123b
3o2$109b3o$108bobo$109bobo2$803bobo$802bobo102b2o$803b3o$908bo3$797b3o
$798bobo$797bobo2$105bobo$106bobo$105b3o2$bo89b3o$90bobo$b2o88bobo2$821b
obo$820bobo$821b3o4$815b3o$816bobo$815bobo2$87bobo$88bobo$87b3o2$73b3o
$72bobo$73bobo2$839bobo$838bobo66b2o$839b3o$908bo3$833b3o$834bobo$833b
obo2$69bobo$70bobo$69b3o2$bo53b3o$54bobo$b2o52bobo2$857bobo$856bobo$857b
3o4$851b3o$852bobo$851bobo2$51bobo$52bobo$51b3o2$37b3o$36bobo$37bobo2$
875bobo$874bobo30b2o$875b3o$908bo3$869b3o$870bobo$869bobo2$33bobo$34b
obo$33b3o2$bo17b3o$18bobo$b2o16bobo2$893bobo$892bobo$893b3o4$887b3o$888b
obo$887bobo2$15bobo$16bobo$15b3o2$b3o$obo$bobo$906bob5o$907bo5bo$906b
ob3o$12bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo
35bo35bo35bo35bo35bo35bo35bo35bo35bo28bobo2b4o$10bobo33bobo33bobo33bo
bo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33b
obo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo29bo2bobo$905b
3obo!

EDIT: Doesn’t count because it’s adjustable
EDIT 2: The smallest period for an 8-loopable adjustable RRO is 264.

[B468S02357]

Give me the solitwry form of the l101 arro

[ThePlayzr]

Give me the solitwry form of the l101 arro

Did you mean the singular form? If so, here:

Code: Select all

x = 464, y = 449, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
10bobo$10bo9$3o$bobo$obo434$460bobo$461bobo$460b3o460$920bo!

This is adjustable, so I believe it doesn't count for the record.
Yes, it hasn't been formally proven, but it's quite easy to make an arbitrarily large one.
EDIT: you just have to extend it like this:

Code: Select all

x = 376, y = 199, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
225bobo77bobo$225bo79bo60bobo$367b2o$366bobo$367bo4$374b2o$192bobo$191b
obo181bo$192b3o16$198b3o$177bo21bobo$198bobo$177b2o4$345bo$344bobo$344b
2o$344bobo3$48bobo$48bo60bobo214bobo$110b2o215b2o$109bobo214bobo$110b
o216bo4$117b2o$15bobo214bobo$14bobo101bo112bobo$15b3o214b3o16$21b3o214b
3o$o21bobo214bobo$21bobo214bobo$2o4$88bo216bo$87bobo214bobo$87b2o215b
2o$87bobo214bobo4$69bobo214bobo$70b2o215b2o$69bobo214bobo$70bo216bo4$
374b2o$55bobo214bobo$54bobo214bobo101bo$55b3o214b3o16$61b3o214b3o$62b
obo112bo101bobo$61bobo214bobo$177b2o4$48bo216bo$47bobo214bobo$47b2o215b
2o$47bobo214bobo4$29bobo214bobo$30b2o215b2o$29bobo214bobo$30bo216bo4$
117b2o$95bobo214bobo$94bobo21bo192bobo$95b3o214b3o16$101b3o214b3o$o101b
obo214bobo$101bobo214bobo$2o4$8bo216bo$7bobo214bobo$7b2o215b2o$7bobo60b
o153bobo$68bobo3$206bobo$207b2o$206bobo$207bo4$374b2o$352bobo$351bobo
21bo$352b3o16$358b3o$177bo181bobo$358bobo$177b2o4$185bo$184bobo$184b2o
$184bobo60bo79bo$245bobo77bobo!

Here it goes from loopability 6 to loopability 10, and the center and corners are the exact same, meaning it can be extended infinitely.

[1and0nlycordershippr]

Give me the solitwry form of the l101 arro

Did you mean the singular form? If so, here:

Code: Select all

x = 464, y = 449, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
10bobo$10bo9$3o$bobo$obo434$460bobo$461bobo$460b3o460$920bo!

This is adjustable, so I believe it doesn't count for the record.
Yes, it hasn't been formally proven, but it's quite easy to make an arbitrarily large one.
EDIT: you just have to extend it like this:

Code: Select all

x = 376, y = 199, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
225bobo77bobo$225bo79bo60bobo$367b2o$366bobo$367bo4$374b2o$192bobo$191b
obo181bo$192b3o16$198b3o$177bo21bobo$198bobo$177b2o4$345bo$344bobo$344b
2o$344bobo3$48bobo$48bo60bobo214bobo$110b2o215b2o$109bobo214bobo$110b
o216bo4$117b2o$15bobo214bobo$14bobo101bo112bobo$15b3o214b3o16$21b3o214b
3o$o21bobo214bobo$21bobo214bobo$2o4$88bo216bo$87bobo214bobo$87b2o215b
2o$87bobo214bobo4$69bobo214bobo$70b2o215b2o$69bobo214bobo$70bo216bo4$
374b2o$55bobo214bobo$54bobo214bobo101bo$55b3o214b3o16$61b3o214b3o$62b
obo112bo101bobo$61bobo214bobo$177b2o4$48bo216bo$47bobo214bobo$47b2o215b
2o$47bobo214bobo4$29bobo214bobo$30b2o215b2o$29bobo214bobo$30bo216bo4$
117b2o$95bobo214bobo$94bobo21bo192bobo$95b3o214b3o16$101b3o214b3o$o101b
obo214bobo$101bobo214bobo$2o4$8bo216bo$7bobo214bobo$7b2o215b2o$7bobo60b
o153bobo$68bobo3$206bobo$207b2o$206bobo$207bo4$374b2o$352bobo$351bobo
21bo$352b3o16$358b3o$177bo181bobo$358bobo$177b2o4$185bo$184bobo$184b2o
$184bobo60bo79bo$245bobo77bobo!

Here it goes from loopability 6 to loopability 10, and the center and corners are the exact same, meaning it can be extended infinitely.

The caveat can be avoided by “expanding” the RRO.

[ThePlayzr]

Give me the solitwry form of the l101 arro

Did you mean the singular form? If so, here:

Code: Select all

x = 464, y = 449, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
10bobo$10bo9$3o$bobo$obo434$460bobo$461bobo$460b3o460$920bo!

This is adjustable, so I believe it doesn't count for the record.
Yes, it hasn't been formally proven, but it's quite easy to make an arbitrarily large one.
EDIT: you just have to extend it like this:

Code: Select all

x = 376, y = 199, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
225bobo77bobo$225bo79bo60bobo$367b2o$366bobo$367bo4$374b2o$192bobo$191b
obo181bo$192b3o16$198b3o$177bo21bobo$198bobo$177b2o4$345bo$344bobo$344b
2o$344bobo3$48bobo$48bo60bobo214bobo$110b2o215b2o$109bobo214bobo$110b
o216bo4$117b2o$15bobo214bobo$14bobo101bo112bobo$15b3o214b3o16$21b3o214b
3o$o21bobo214bobo$21bobo214bobo$2o4$88bo216bo$87bobo214bobo$87b2o215b
2o$87bobo214bobo4$69bobo214bobo$70b2o215b2o$69bobo214bobo$70bo216bo4$
374b2o$55bobo214bobo$54bobo214bobo101bo$55b3o214b3o16$61b3o214b3o$62b
obo112bo101bobo$61bobo214bobo$177b2o4$48bo216bo$47bobo214bobo$47b2o215b
2o$47bobo214bobo4$29bobo214bobo$30b2o215b2o$29bobo214bobo$30bo216bo4$
117b2o$95bobo214bobo$94bobo21bo192bobo$95b3o214b3o16$101b3o214b3o$o101b
obo214bobo$101bobo214bobo$2o4$8bo216bo$7bobo214bobo$7b2o215b2o$7bobo60b
o153bobo$68bobo3$206bobo$207b2o$206bobo$207bo4$374b2o$352bobo$351bobo
21bo$352b3o16$358b3o$177bo181bobo$358bobo$177b2o4$185bo$184bobo$184b2o
$184bobo60bo79bo$245bobo77bobo!

Here it goes from loopability 6 to loopability 10, and the center and corners are the exact same, meaning it can be extended infinitely.

The caveat can be avoided by “expanding” the RRO.

As such, these don't really count towards loopability records.
So, what is the real record right now for loopability?

[1and0nlycordershippr]

Did you mean the singular form? If so, here:

Code: Select all

x = 464, y = 449, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
10bobo$10bo9$3o$bobo$obo434$460bobo$461bobo$460b3o460$920bo!

This is adjustable, so I believe it doesn't count for the record.
Yes, it hasn't been formally proven, but it's quite easy to make an arbitrarily large one.
EDIT: you just have to extend it like this:

Code: Select all

x = 376, y = 199, rule = B2aik3acekr4-ajntz5acijy6ck7c/S2an3acejk4ejqtwy5cny6-ac7e
225bobo77bobo$225bo79bo60bobo$367b2o$366bobo$367bo4$374b2o$192bobo$191b
obo181bo$192b3o16$198b3o$177bo21bobo$198bobo$177b2o4$345bo$344bobo$344b
2o$344bobo3$48bobo$48bo60bobo214bobo$110b2o215b2o$109bobo214bobo$110b
o216bo4$117b2o$15bobo214bobo$14bobo101bo112bobo$15b3o214b3o16$21b3o214b
3o$o21bobo214bobo$21bobo214bobo$2o4$88bo216bo$87bobo214bobo$87b2o215b
2o$87bobo214bobo4$69bobo214bobo$70b2o215b2o$69bobo214bobo$70bo216bo4$
374b2o$55bobo214bobo$54bobo214bobo101bo$55b3o214b3o16$61b3o214b3o$62b
obo112bo101bobo$61bobo214bobo$177b2o4$48bo216bo$47bobo214bobo$47b2o215b
2o$47bobo214bobo4$29bobo214bobo$30b2o215b2o$29bobo214bobo$30bo216bo4$
117b2o$95bobo214bobo$94bobo21bo192bobo$95b3o214b3o16$101b3o214b3o$o101b
obo214bobo$101bobo214bobo$2o4$8bo216bo$7bobo214bobo$7b2o215b2o$7bobo60b
o153bobo$68bobo3$206bobo$207b2o$206bobo$207bo4$374b2o$352bobo$351bobo
21bo$352b3o16$358b3o$177bo181bobo$358bobo$177b2o4$185bo$184bobo$184b2o
$184bobo60bo79bo$245bobo77bobo!

Here it goes from loopability 6 to loopability 10, and the center and corners are the exact same, meaning it can be extended infinitely.

The caveat can be avoided by “expanding” the RRO.

As such, these don't really count towards loopability records.
So, what is the real record right now for loopability?

89, I think.

[Docsy]

In terms of trying to find records, I'd agree that maximizing non-adjustable loopability is still of interest, 89 is the largest there. But I would say it is still a rule that contains RROs of arbitrary loopability, making an adjustable RRO that can be looped indefinitely was a nontrivial problem, and it's cool to be able to construct any loopability you want explicitly. It's a bit harder than a regular adjustable spaceship in the realm of INT. To my knowledge silversmith constructed the first adjustable RRO ever not too long ago, and it couldn't be looped infinitely.

As a small clarification by the way, it's trivial to see that you can make arbitrarily large loopabilities, but it's not formally proven that any specific loopability can be constructed, because the diagonal spaceships can collide in the middle. Like that it's easy to see that for any number, you can find a larger loopability, but not necessarily trivial to show you can make a specifically 848-loopable RRO. I gave the following argument on the Discord to suggest it should be fully capable, though:
"Basically, the time offsets that cause collisions in the RRO become a smaller and smaller proportion of the total period as it adjusts, because the number of offsets that fail don't grow the period grows. At the same time those offsets divided by the period asymptotically approach 1/4 and 3/4 as the RRO is made bigger. However it never actually includes p/4 or 3p/4. So as it adjusts the offsets never cover any specific fraction of the period forever as it goes to infinity, cuz they cover less and less of the period and asymptotically approach a value they never equal. As such, some size of adjustable should include any loopability you want "

As a final note, if you can find the specific reaction that powers this RRO with c/2os and c/4ds, you'll likely be able to find it in a non-explosive rule that is more fun to explore. Ampere speculated that you could maybe even find it with LWSSs and gliders!

[B468S02357]

Could i please perhaps see the L89 rro?

[splitterrules]

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?