ConwayLife.com - A community for Conway's Game of Life and related cellular automata
Home  •  LifeWiki  •  Forums  •  Download Golly

Reflectorless Rotating Oscillators (RRO)

For discussion of other cellular automata.

Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » June 21st, 2018, 7:45 am

I found some reflectorless rotating oscillators (RRO) with small periods, I think record breaking (in terms of cells, periods and bounding box).
They are all 2-fold (but 4-cyclic). They have all 3 cells, except the first p32 has 4 cells:

p32
x = 16, y = 5, rule = B2ce3aejk4aqrtw5-acr6cen78/S12an3cjqy4-ey5akqry6ekn7e8
2o7b2o$obo6bobo2$13bobo$14b2o!
x = 18, y = 5, rule = B2cei3aj4aintwy5ikqy6-ai7e/S012i3-ajn4-eirwy5-ejkq6-a7c
o10bo$obo8bobo2$15bobo$17bo!
x = 18, y = 5, rule = B2e3aikr4kny5cejkn6-kn7c8/S012-n3-acjk4ciwy5aceir6ck7c8
o10bo$obo8bobo2$15bobo$17bo!


p36
x = 16, y = 5, rule = B2cek3aery4aejqrwy5ceqy6cen7c8/S012ikn3-air4centy5-jkry6-kn7c8
2bo8bo$obo6bobo2$13bobo$13bo!
x = 16, y = 5, rule = B2cek3aj4aiknty5-enqr6ek7c/S012ik3cny4akrtwy5cejky6-an78
o8bo$obo6bobo2$13bobo$15bo!

p40
x = 16, y = 5, rule = B2e3-cjnr4ak5-cinq67/S12ack3cjr4cjknz5acnqy6-i7e
o8bo$b2o7b2o2$13b2o$15bo!
x = 18, y = 6, rule = B2cen3acq4-aejnz5-nqy6-c78/S012ik3jnq4-jkntz5-cinq6aek7
2bo9bo$obo7bobo3$15bobo$15bo!

p44
x = 16, y = 5, rule = B2cek3ajkq4aeiqt5-jkr6ce7e/S012ikn3k4aeijrz5cinry6-ai78
o8bo$obo6bobo2$13bobo$15bo!
x = 16, y = 8, rule = B2ci3-iqry4-ajwz5-jnry6-ac78/S12-ck3ejkry4-kqrwz5ejknq6en7e8
2o8b2o2$o9bo3$15bo2$14b2o!

p48
x = 16, y = 5, rule = B2ce3aejqy4ijrt5aknr6-ei7e/S12-ek3jkq4ceinqwz5ejkry6-i8
2bo8bo$2o7b2o2$14b2o$13bo!
x = 18, y = 8, rule = B2cei3aeky4ceiknrw5ejk6-cn7e8/S012-ac3-aeik4-cewy5-aejy6-an7e
2bo9bo$obo7bobo5$15bobo$15bo!

p52
x = 20, y = 5, rule = B2cek3-ein4ikqrtwy5-enr6ack78/S012aci3nqy4ejknqwy5-ciqr6-ck7e8
2bo10bo$obo8bobo2$17bobo$17bo!

p56
x = 20, y = 5, rule = B2ce3jkqy4-cnrwz5aeny6-in78/S1e2-c3-ajn4iqry5aekqy6-ci
3bo10bo$obo8bobo2$17bobo$16bo!

p60
x = 20, y = 9, rule = B2k3acijn4aqty5cejnq6-ck7e/S01e2-a3acikr4ei5-aekr67c
3bo10bo$o10bo$2bo10bo4$17bo$19bo$16bo!

p64
x = 20, y = 9, rule = B2ci3aejqr4aeinqty5jkq6e8/S01e2-en3cjknr4-akwz5jkqr6-ac7
o10bo$obo8bobo6$17bobo$19bo!
My script did not show anything for p28. Larger periods mod 4 very likely exists as well. Maybe we even find an adjustable RRO.

Edit1:
A 2-fold 3 cell p38 oscillator, not sure if it counts as a RRO:
x = 16, y = 5, rule = B2ce3cej4nrty5ajkry6ae7c/S012ikn3-ik4acey5-aeny6ek7
o8bo$obo6bobo2$13bobo$15bo!
similarly these p30:
x = 18, y = 7, rule = B2cek3eijkq4eikqry5-cejk6e7c/S12cek3aik4eijy5ajr6cei8
bo10bo$o10bo$b2o9b2o2$15b2o$17bo$16bo!
x = 18, y = 5, rule = B2cek3ejkq4aenqrwy5aknry6ack7/S012k3-einq4cekry5knq6ei7e8
o10bo$obo8bobo2$15bobo$17bo!


Edit2:
A 3 cell p32 naturally:
x = 18, y = 5, rule = B2c3air4aijr5j6k/S01e2ack3jkr4aky5aijy
o10bo$obo8bobo2$15bobo$17bo!

https://catagolue.appspot.com/object/xp ... r4aky5aijy
https://catagolue.appspot.com/object/xp ... r4aky5aijy
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby dvgrn » June 21st, 2018, 5:52 pm

2718281828 wrote:I found some reflectorless rotating oscillators (RRO) with small periods, I think record breaking (in terms of cells, periods and bounding box).
They are all 2-fold (but 4-cyclic)...

All except your p60, I think. That one is actually a rare 3-fold RRO, with a period 20 variant:

x = 31, y = 10, rule = B2k3acijn4aqty5cejnq6-ck7e/S01e2-a3acikr4ei5-aekr67c
3bo10bo10bo$o10bo10bo$2bo10bo10bo$28b3o$28b3o$29bo$17bo4bobo3b2o$19bo
2bob2o2bobo$16bo7bo!
User avatar
dvgrn
Moderator
 
Posts: 5213
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » June 25th, 2018, 3:56 pm

A small 4-fold RRO: (p108, p54, p27)
x = 55, y = 16, rule = B2-an3cey4-ikrw5eijkn6ekn7c/S012ei3-eiqy4kqrw5ajkry6-e7c
32b2o18b2o$39bo$32bo6bobo10bo11$bo19bo19bo10bobo$54bo$2o18b2o18b2o!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby AforAmpere » June 25th, 2018, 4:11 pm

2718281828 wrote:A small 4-fold RRO: (p108, p54, p27)
x = 55, y = 16, rule = B2-an3cey4-ikrw5eijkn6ekn7c/S012ei3-eiqy4kqrw5ajkry6-e7c
32b2o18b2o$39bo$32bo6bobo10bo11$bo19bo19bo10bobo$54bo$2o18b2o18b2o!


Amazing! It is also a 3-fold (p36):
x = 18, y = 18, rule = B2-an3cey4-ikrw5eijkn6ekn7c/S012ei3-eiqy4kqrw5ajkry6-e7c
7b2o$6b3ob2o$5bob4o$6b4o7$14bobo$14bo$14b2o2$3bo2$2b2o!


I don't think I've ever seen one where it can function as a 3-fold and a 4-fold. What kind of script are you using? LLS?
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere
 
Posts: 849
Joined: July 1st, 2016, 3:58 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby dvgrn » June 25th, 2018, 5:18 pm

2718281828 wrote:A small 4-fold RRO: (p108, p54, p27)
x = 55, y = 16, rule = B2-an3cey4-ikrw5eijkn6ekn7c/S012ei3-eiqy4kqrw5ajkry6-e7c
32b2o18b2o$39bo$32bo6bobo10bo11$bo19bo19bo10bobo$54bo$2o18b2o18b2o!

AforAmpere wrote:Amazing! It is also a 3-fold (p36)... I don't think I've ever seen one where it can function as a 3-fold and a 4-fold.

Not in regular Moore-neighborhood isotropic CAs, anyway. If you count Larger than Life, the record holder still seems to be the SoldierBugs in Golly's pattern collection, with 1, 2, 3, 4, 6, 8, and 12-fold options.

Seems like it's going to take some luck to get to 5-fold or above outside of Larger than Life, just because the period will have to be divisible by 5 _and_ the RRO has to move unusually quickly while remaining fairly small.
User avatar
dvgrn
Moderator
 
Posts: 5213
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » June 26th, 2018, 1:34 am

AforAmpere wrote:I don't think I've ever seen one where it can function as a 3-fold and a 4-fold. What kind of script are you using? LLS?

Yes, LLS, and it is surprisingly fast for smaller periods up to 20 for a 4-fold, then it becomes slower.

1/2/3/4/5-folds (p120/60/40/30/24)
x = 110, y = 25, rule = B2ck3-ciky4cjkqrtz5-cijy6an7c/S02ekn3cq4cqz5-kny6-ci78
4$103b2o$6b2o19b2o19b2o19b2o12bobo4b2o10b3o$85bo18b2o$6bobo18bobo18bob
o18bobo11bo6bobo9bo3$62bobo$64b2o$63bobo$62bo$63bo40bobo$90b3o13b2o$
89b3o15bo$89b2o14b2o$90bobo12bo$41bobo7bo2bo16bo11bobo11bo2bo$51b2o16b
o28bo$42b2o8b3o14bobo12b2o8b2o3b2o$52b2o40b2o2b2o!
x = 110, y = 22, rule = B2-a3ejkq4nqrtwz5aejkq6ei78/S01e2ikn3jkny4ceijqt5-ciky6-ai7c8
83bo18bob2o$4bo21bo21bo21bo21bo12bo$2bobo19bobo19bobo19bobo12b2o5bobo
9b4o3$61bobo$61bobo26bo$90bo$91bo$62bobo26bo13bobo$61b2o27b3o12bobo$
61bobo25b3o$90b2o$90bobo12bo$90bobo$39bobo8b4o15b2o12bobo12b4o$39bo43b
o12b2o$51b3o16bo24bob5o!

This one is only 1/2/3/4-fold (p120/60/40/30)
x = 89, y = 21, rule = B2-a3cjnq4ack5acein6ak7e/S012aik3-any4jkny5ijqry6-n
2$2bo21bo21bo21bo14bobo$4bo21bo21bo21bo$2bobo19bobo19bobo19bobo12b2o3$
61bobo$61bobo$61bobo$61bobo$61bo$61b2o$63bo4$39bobo8b4o15b2o12bobo$39b
o8b4o31bo$41bo5b5obo14bobo14bo$48b3o!

but it gives me the feeling that there might exists something like adjustable RRO families.
x = 3, y = 16, rule = B2-a3cjnq4ack5acein6ak7e/S012aik3-any4jkny5ijqry6-n
bo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$3o$2o!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 77topaz » June 26th, 2018, 2:45 am

Nice finds! :) It's a bit unfortunate, though, that nearly all of them are in explosive rules. Have you found any more RROs in more stable rules?
User avatar
77topaz
 
Posts: 1199
Joined: January 12th, 2018, 9:19 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » June 26th, 2018, 6:04 am

77topaz wrote:Nice finds! :) It's a bit unfortunate, though, that nearly all of them are in explosive rules. Have you found any more RROs in more stable rules?

I have a couple of other RROs, there exists many... however you are right most of them are explosive (as most rules anyway, in the 5s projects its the same most of them live in explosive rules).

This one is stable (but quite boring):
x = 101, y = 41, rule = B2-ai3cq4aktz5-jkny6i7c/S01e2-ae3ij4ejkqz5ci6a7c8
6$4bo5b3ob2o2b2ob6o2bo4b2o$4bobobo5bobobob3o3b2obobob2o$5bob8o2b2o2bob
ob5o3bobo$5bob2o2b2ob4ob2o3bo3bo2b2ob2o20bo20bo$11bob2o5b7ob2obo3bo21b
obo18bobo$6bo2bo4bobobobo3b6o$4bo4b3obo5bo7bob2ob2o$5bob3o2bo2b3o2bobo
bobo4b2o$4bo3bo2b2o3b2ob2o3b7o4bo$4b5obo2bobo2b2ob3obob2obo2bo$4bob7ob
o3b2ob3o6bo2bo$5bo4b2ob2o3b5obob2o5b3o$4bo12bo2b2o2b2ob2ob2ob2o$12bo6b
2ob2o2b3ob3ob2o$5bob3ob3ob3ob5ob3o3bob2o$11b3ob2obo2b4o4b2obo2bo$7b2ob
7o2b2ob3ob3o2bob2o57bobo$9b6ob4ob2obobo4b2o2bo59bo$4b2ob2o2b2obo2bobo
2bo3b3obobo2bo$5bo2bobob3o2b2o4bobo3bo3bobo$5bo2bobo2bo2b3obob2o3b3obo
2b2o$4bo2bo4bobobo4bo2bo4b2obo2bo$4bo3b3o2bo2bo2b2ob5obob3ob2o$4bobob
2obo2bob2ob4o2b2o2bo3b3o$4bob7o3b2o2bo2bo5b2o$5bo2bo4b6o5bo3bob3o$5b2o
3b5obo2bo2bob3o3bobobo$5bobob2obo2b2ob3obobo4b2ob3o$4bo2bo4bo2bob10o2b
7o$6bobo2b4ob2ob2o2b2ob4ob3o$5bo2b2ob3ob2obo2bo4bo2b3ob3o$4bo3bob2o5bo
2b2o3bo3bob4o!


But this one is nicer, here we have a small natural spaceship:
x = 100, y = 33, rule = B2cn3acr4ijnrwyz5inqr6aci/S01e2-k3cn4aeiknrz5acy6ck7c8
$3bobo2b2o5bobobo4b3ob3o2bo$3bob2obobo3b2obobobo5b5obo$2b4obob2ob2o2bo
2bo2b3o2b4ob2o$3bo3b4obob3o4bo2bo2bob5o$2b5ob4ob3obo4b2ob4o2b2o$2bob5o
4b3o3bo9b2o2bo$3b3o4b3ob2o4bobobo2bo2bobo24bo18bo$2bobo2bob3obo4b3ob4o
3b2ob2o23bobo16bobo$4bo2b2o5b2o2b2o2bo4b3obo$3bob3obo2bobobob3obobobo
4bobo$2b4o2bobobo4bob2ob4o4bo$2bobo3b2o2b4o2bob2ob5ob4o$4bo2b2o2bob3ob
obobob2o2b3ob3o$3bo4bo2b5obo3b3o2bo2b2obo$2b6o2bo2bob2obo4b4o3bobo$3bo
b4o5bo3bo4b3obo5bo$3b2obob3o4b3o2b2ob3o4bobo$2b6ob8o6bo2bob6o54bobo$2b
2obo2b2o2bob2o2bo3bo2bo2bo2bo58bo$2bo3bobo2bo4bo4bo3bobob3o$3b2obo2bo
2b2o4bob2o2bo4bo$4b2o2b3obo5bo3bobo2b2o2bobo$2bo4bo5b3obo2bob8obobo$2b
o2bob2o3b2o2b2obo3b3o4b4o$3b3o2b3ob2o3bobo2b5obo2bobo$2bobo2bob6ob3obo
4b2o6bo$7b2o3b2ob3obobob2ob3obo$2bobob2obo2b4ob2ob2obob4o3bo$3b7obob2o
bo3bobo4bobo2bo$2bobo2b3o5b2o3bobo4b3o2bo$2bob2obobo7b2ob2o2b2o5b2o$3b
6o2b3ob2ob3obobobobo2b3o!

It also has this nice natural spaceship (xq20_275se4):
x = 6, y = 5, rule = B2cn3acr4ijnrwyz5inqr6aci/S01e2-k3cn4aeiknrz5acy6ck7c8
b2o$2o2bo$b5o$3b2o$3bo!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » June 29th, 2018, 7:54 pm

An interesting natural p256 (https://catagolue.appspot.com/object/xp ... t5-aky67c8), 1,2,4-fold:
x = 184, y = 53, rule = B2kn3aijnr4aciky/S2n3-cek4aijnt5-aky67c8
6$107b3o35bo28b3o$106b5o32b3o2b4o21b5o$105bob4o29b6o2b3o21bob4o$104b2o
bo2bo28b3obobobo2b2o19b2obo2bo$104b8o27b3ob4obobo20b8o$104b5ob2o27b9ob
obo19b5ob2o$105b8o27bo2b4o2b2o21b8o$106b3o32b5o27b3o$107bobo32b3o29bob
o$108bob2o63bob2o$106b2o2b2o61b2o2b2o$106bob4o61bob4o$107bobobo62bobob
o16$6bobobo62bobobo62bobobo$6b4obo61b4obo61b4obo$6b2o2b2o61b2o2b2o61b
2o2b2o$6b2obo63b2obo63b2obo$8bobo64bobo64bobo29b3o$9b3o64b3o64b3o27b5o
$5b8o59b8o59b8o21b2o2b4o2bo$6b2ob5o59b2ob5o59b2ob5o19bobob9o$6b8o59b8o
59b8o20bobob4ob3o$7bo2bob2o60bo2bob2o60bo2bob2o19b2o2bobobob3o$7b4obo
61b4obo61b4obo21b3o2b6o$7b5o62b5o62b5o21b4o2b3o$8b3o64b3o64b3o28bo!

But I am not sure if it is an RRO due to the interactions in the centre.
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 77topaz » June 30th, 2018, 7:42 pm

Slightly off-topic, but that last rule also has possibly the smokiest spaceship I've ever seen:
x = 12, y = 30, rule = B2kn3aijnr4aciky/S2n3-cek4aijnt5-aky67c8
3bo$b5o$7o$2obob3o$bo3bo$o3bo$3o$2bo2$3bo$bo2$bo12$8bo$6b5o$6b2obobo$6b2ob3o$
6bo4bo$8bobo!


It's c/2 orthogonal, but with period 920.
User avatar
77topaz
 
Posts: 1199
Joined: January 12th, 2018, 9:19 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » July 20th, 2018, 1:03 am

A 1/2/3/4/5/6 fold RRO:
x = 132, y = 26, rule = B2-an3-eiky4aiqw5ijnr6ak/S012ik3-acir4kqw5acq6ack7c8
3$3bo21bo21bo21bo21bo21bo$2bo21bo21bo21bo21bo11b2o8bo9bo$82bobo19bo18b
2o$2bo21bo21bo21bo16bo4bo11bo9bo9bo2bo4$60bobo63bobo$61bo26bo22b2o14bo
$63bo25b3o37bo$89b2o19bo$61b2o26bo14bobo5bo14b2o$104bobo4bobo$89bobo
13b2o$89bobo13b2o2$39bo8bo2bo14bo16bo14b2o14bo2bo9bo$49b2o16bobo25bobo
17b2o$39bo11bo31bo11b5o17bo9bo$38bo43bo43bo!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » January 8th, 2019, 12:01 pm

two RROs in B2a rules:
p40/p20:
x = 24, y = 8, rule = B2aci3eqr4iqt5jq6a/S02cek3eikqr4jkrwy5aq6a
22bo$22b2o$20bo3$3bo13bo$2o12b2o$bo13bo!

p36/p18:
x = 15, y = 10, rule = B2ai3aek4k5i/S12cik3cery4ajqrz5ae
o12bo$bo12bo$bo12bo$bo12bo3$9bo$9bo$9bo$10bo!

Edit1:
p32/p16:
x = 18, y = 8, rule = B2-en3r4jky5c/S1e2cei3eqy4aknz5jn
2bo14bo$bo14bo$3o12b3o3$10b3o$11bo$10bo!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby 2718281828 » January 8th, 2019, 4:46 pm

A really rare one:
p60/p20 (1/3 fold)
x = 31, y = 21, rule = B2acn3cnqr4jnty5ajkn6ak7e/S01e2n3ceqy4-ceqz5cijr6-ei7c
3$4bo15bo$3bo15bo$2b3o13b3o5$25bo$25b2o$14b5o4b3o$16b3o$16b4o$18bo$14b
o2bo!

It fails for the 2 fold:
x = 3, y = 15, rule = B2acn3cnqr4jnty5ajkn6ak7e/S01e2n3ceqy4-ceqz5cijr6-ei7c
2bo$bo$3o10$3o$bo$o!
User avatar
2718281828
 
Posts: 500
Joined: August 8th, 2017, 5:38 pm

Re: Reflectorless Rotating Oscillators (RRO)

Postby muzik » February 15th, 2019, 8:15 am

Any success on a 7-fold yet?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik
 
Posts: 3216
Joined: January 28th, 2016, 2:47 pm
Location: Scotland


Return to Other Cellular Automata

Who is online

Users browsing this forum: 77topaz, skomick, testitemqlstudop and 2 guests