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!