Smallest Oscillators Supporting Specific Periods

For discussion of other cellular automata.
Post Reply
User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Smallest Oscillators Supporting Specific Periods

Post by 77topaz » January 26th, 2018, 10:29 pm

The oscillator counterpart of the 5s Project. Non-trivial oscillators only.

Here's a few periods to start off with:

Period 2, 2 cells

Code: Select all

x = 2, y = 2, rule = B2/S
o$bo!
Period 4, 2 cells

Code: Select all

x = 3, y = 1, rule = B2-a/S1
obo!
Period 6, 4 cells

Code: Select all

x = 7, y = 1, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
obobobo!
Period 14, 4 cells

Code: Select all

x = 4, y = 3, rule = B2-a/S12
2o$3bo$3bo!
Period 16, 3 cells

Code: Select all

x = 7, y = 1, rule = B026/S1
o2bo2bo!
Period 18, 10 cells

Code: Select all

x = 13, y = 6, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
b2o$2bo$o4bobo$12bo$10bo$10b2o!
Period 26, 6 cells

Code: Select all

x = 4, y = 3, rule=B36/S125
2o$b2o$2b2o!
Period 100, 4 cells

Code: Select all

x = 3, y = 2, rule = B2e3-a/S23
b2o$o$bo!
Period 106, 8 cells

Code: Select all

x = 4, y = 5, rule = B2e3aceij5-ijr/S23-a4
3o$bo$3bo$2b2o$3bo!
Last edited by 77topaz on January 28th, 2018, 12:32 am, edited 1 time in total.

User avatar
Majestas32
Posts: 549
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Smallest Oscillators Supporting Specific Periods

Post by Majestas32 » January 26th, 2018, 10:51 pm

p11, 12 cells:

Code: Select all

x = 11, y = 3, rule = B367/S2-i35ek6ek
b2o5b2o$obo5bobo$b2o5b2o!
p17, 18 cells:

Code: Select all

x = 9, y = 5, rule = B367/S2-i35ek6ek
b2obob2o$2o5b2o2$2o5b2o$b2obob2o!
p20, 8 cells:

Code: Select all

x = 10, y = 7, rule = B2-a/S12-i3ij
7bo$2o7bo2$6bobo2$9bo$7bo!
p24, 4 cells:

Code: Select all

x = 4, y = 3, rule = B3-en4t6-c/S123i4i5
2o$3bo$3bo!
p30, 9 cells:

Code: Select all

x = 4, y = 6, rule = B36/S2-i36-ac
o$obo$o2bo$3bo$b2o$bo!
p34, 4 cells:

Code: Select all

x = 2, y = 4, rule = B2-a/S12-i3ij
2o2$o$bo!
p49, 8 cells:

Code: Select all

x = 17, y = 5, rule = B2-a/S12-i3ij
3bo$o3bo$3bo9bo$12bo3bo$13bo!
p92, 9 cells:

Code: Select all

x = 7, y = 10, rule = B2-a/S12-i
4bo$3bobo2$2bo3bo2$4bo2$2o2$o!
p108, 3 cells:

Code: Select all

x = 2, y = 3, rule = B2-a/S12-i3i
bo$o$bo!
p119, 14 cells:

Code: Select all

x = 3, y = 8, rule = B36/S2-i36-ac
bo$3o$obo$bo$bo$obo$3o$bo!
Last edited by Majestas32 on January 26th, 2018, 11:02 pm, edited 1 time in total.
Searching:
b2-a5k6n7cs12-i3ij4k5j8
b2-a3c7cs12-i

Currently looking for help searching these rules.

User avatar
BlinkerSpawn
Posts: 1992
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Smallest Oscillators Supporting Specific Periods

Post by BlinkerSpawn » January 26th, 2018, 10:52 pm

3-cell p3:

Code: Select all

x = 3, y = 3, rule = B3jy/S012c
obo2$bo!
3-cell p5:

Code: Select all

x = 3, y = 3, rule = B2e3jy7e/S012-in3r4i5i
obo2$bo!
3-cell p6:

Code: Select all

x = 3, y = 3, rule = B3ajy5y7e/S012-in3ijr4i5i
obo2$bo!
LLS might be able to do better.
All even periods take at most 13:

Code: Select all

x = 12, y = 32, rule = B2a3ry/S1c2c3y
2bobo$3bo5bo$8bo$2bobo$4bo$bo$o5bo$5bobo5$3bobo$4bo5bo$9bo$2bobo$4bo$b
o$o5bo$5bobo5$4bobo$5bo5bo$10bo$2bobo$4bo$bo$o5bo$5bobo!
Last edited by BlinkerSpawn on January 27th, 2018, 11:12 am, edited 2 times in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Image

User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Re: Smallest Oscillators Supporting Specific Periods

Post by 77topaz » January 26th, 2018, 10:55 pm

Period 15, 8 cells:

Code: Select all

x = 5, y = 5, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
3o$bo2$3bo$2b3o!
Period 28, 14 cells:

Code: Select all

x = 11, y = 3, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
2bobobobo$obobobobobo$2bobobobo!
Period 42, 10 cells:

Code: Select all

x = 11, y = 7, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
5bo$obobobobobo$5bo2$5bo2$5bo!
Last edited by 77topaz on January 26th, 2018, 11:38 pm, edited 3 times in total.

User avatar
Majestas32
Posts: 549
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Smallest Oscillators Supporting Specific Periods

Post by Majestas32 » January 26th, 2018, 10:55 pm

There's this too: https://goo.gl/buUqjQ

There's a 1 cell p1, p2, p4, p6, and p10.
Searching:
b2-a5k6n7cs12-i3ij4k5j8
b2-a3c7cs12-i

Currently looking for help searching these rules.

User avatar
Majestas32
Posts: 549
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Smallest Oscillators Supporting Specific Periods

Post by Majestas32 » January 26th, 2018, 10:56 pm

77topaz wrote:Period 15, 8 cells:

Code: Select all

x = 5, y = 5, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
3o$bo2$3bo$2b30!
This is a 5 cell spark.
Searching:
b2-a5k6n7cs12-i3ij4k5j8
b2-a3c7cs12-i

Currently looking for help searching these rules.

User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Re: Smallest Oscillators Supporting Specific Periods

Post by 77topaz » January 26th, 2018, 10:58 pm

Majestas32 wrote:
77topaz wrote:Period 15, 8 cells:

Code: Select all

x = 5, y = 5, rule = B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i
3o$bo2$3bo$2b30!
This is a 5 cell spark.
I made a typo in the RLE, that "0" should have been an "o".
Majestas32 wrote:There's this too: https://goo.gl/buUqjQ

There's a 1 cell p1, p2, p4, p6, and p10.
Oh, I didn't realise such a thread existed already. Is it possible to combine threads with this forum's software?

User avatar
Majestas32
Posts: 549
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Smallest Oscillators Supporting Specific Periods

Post by Majestas32 » January 26th, 2018, 11:04 pm

No but there's a 3 cell p17, p19, and p79 there, and 2 cell p5, p7, p8, and p21.
Searching:
b2-a5k6n7cs12-i3ij4k5j8
b2-a3c7cs12-i

Currently looking for help searching these rules.

Gamedziner
Posts: 795
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

Re: Smallest Oscillators Supporting Specific Periods

Post by Gamedziner » January 27th, 2018, 8:08 am

77topaz wrote:
Period 4, 2 cells

Code: Select all

x = 3, y = 1, rule = B2-i/S1
obo!
That's p2.

EDIT: Original post has been fixed.
Last edited by Gamedziner on January 28th, 2018, 7:18 am, edited 1 time in total.

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » January 27th, 2018, 8:22 am

All 2 cell populations:

p3

Code: Select all

x = 3, y = 3, rule = B2ein3ekq4567/S012cn34-a5-i6-n7
2bo2$o!
p8

Code: Select all

x = 3, y = 3, rule = B2en3cejq4cjkt5jkny6i8/S01c2in3-knr4acknqry5qry6aik
2bo2$o!
p9

Code: Select all

x = 1, y = 3, rule = B2ain3-eijr4ijkry5-jkq6aik8/S01e2ein3-y4cjkty5-ejk6aei7e8
o2$o!
p10

Code: Select all

x = 1, y = 3, rule = B2ain3aejkn4acentw5ain6-ci78/S01e2-ae3-air4aciktwz5-jkr6a7c8
o2$o!
p11

Code: Select all

x = 3, y = 1, rule = B2-ce3ekn4ntwy5-cek6cei7e8/S01e2in3-q4-cinw5-eqry6aik7e
obo!
p12

Code: Select all

x = 1, y = 3, rule = B2ain3cejkq4cknry5aceir6ckn8/S01e2cei3-ikq4eijnrt5ijny6ak78
o2$o!
p13

Code: Select all

x = 1, y = 3, rule = B2-ck3-aikr4aknrwyz5aeinq6-a7e8/S01e2-a3-ir4cikntwz5-acen78
o2$o!
p14

Code: Select all

x = 3, y = 1, rule = B2ai3ae4intyz5-ajr6eik7e/S01e2-ak3aekqr4-cekwz5aikqr6aek7e
obo!
p15

Code: Select all

x = 3, y = 1, rule = B2ain3-ainr4cjknrt5-enq6cek7/S01e2-an3ejnqy4-cjrwy5-ceny67e
obo!
p16

Code: Select all

x = 3, y = 1, rule = B2ain3cky4-acjqt56ikn78/S01e2in3aeiq4ijny5aijn6i7
obo!
p17

Code: Select all

x = 1, y = 3, rule = B2ai3ajkqy4ijkqrwz5-q6cek7c/S01e2ci3-cir4inqrz5acekn6cei8
o2$o!
p18

Code: Select all

x = 1, y = 3, rule = B2-cn3ejkqy4cjkntyz5-eqr6-ik7e8/S01e2-a3-cikr4acinrt5-ajr6e7e8
o2$o!
p19

Code: Select all

x = 3, y = 1, rule = B2ain3-einr4-acewy56-i78/S01e2cin3-aij4-cejtw5-cjkq6ein7c
obo!
p20

Code: Select all

x = 1, y = 3, rule = B2ain3-aiy4jnqyz5-cjy6ack78/S01e2-ak3-iny4-cz5-eiq6-i7e
o2$o!
p22

Code: Select all

x = 1, y = 3, rule = B2ain3cejqy4cinrwz5-aqy6ein78/S01e2in3-cjny4ijwyz5eknqy6-ac7e8
o2$o!
p23

Code: Select all

x = 1, y = 3, rule = B2ai3cejnq4-aeijy5cikqr6n7c8/S01e2cei3ceq4ceinqrz5ary6ce7
o2$o!
p24

Code: Select all

x = 1, y = 3, rule = B2-ce3-ainr4jknqry5-eiy6ace7c8/S01e2-ak3ace4ckqr5-ck6ci7e8
o2$o!
p25

Code: Select all

x = 1, y = 3, rule = B2ai3ceknq4-cejnz5-enqy6ack/S01e2ikn3-cjy4-cknqr5cenq6-n7e8
o2$o!
p26

Code: Select all

x = 1, y = 3, rule = B2-ek3ejkry4-acjkr5ace6k7e8/S1e2-k3acjnq4eiktyz5aijky6-ci7e
o2$o!
That does everything up to p26, minimally if we don't allow B0. I'm stuck on p27 though, best I can do is population 3:

Code: Select all

x = 3, y = 4, rule = B2ikn3akqry4-ajw5knr6akn7c/S012-k3ik4ciknqtz5ijky6-ai7
o$o2$2bo!

User avatar
Rhombic
Posts: 1072
Joined: June 1st, 2013, 5:41 pm

Re: Smallest Oscillators Supporting Specific Periods

Post by Rhombic » January 27th, 2018, 9:10 am

2-cell p6

Code: Select all

x = 3, y = 1, rule = B2ai4i6i7e/S01e3ery4r6i8
obo!
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » January 27th, 2018, 1:17 pm

p27

Code: Select all

x = 3, y = 1, rule = B2-ce3-ijr4-aejrw5ijqry6ein7c/S01e2cik3-ceiy4-ciy5-jkr6ein7e
obo!
p28

Code: Select all

x = 3, y = 1, rule = B2ain3cejny4-aceiw5-ejkr6-ci7c/S01e2-a3aejqr4-nr5-eky6-ae7
obo!
p29

Code: Select all

x = 3, y = 1, rule = B2ai3jknqr4aeinqwz5-aejn6aik7e/S01e2n3-iknq4ajrty5aeijn6ak
obo!
p30

Code: Select all

x = 1, y = 3, rule = B2ai3acjkq4-ceqwy5-qr6ek7e8/S01e2-ae3-ainr4aijnrtz5-jky6-ce
o2$o!
EDIT:
p31, 3 cells:

Code: Select all

x = 3, y = 5, rule = B2-ac3-cein4aejntw5akr6e78/S012ce3-ceik4eijnqz5iknry6ak7c8
o2$2bo2$o!
p32, 2 cells:

Code: Select all

x = 3, y = 1, rule = B2ain3cjnq4-acenz5-ery6-ck7c8/S01e2cik3-iqr4jknyz5-kr67e
obo!

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » January 27th, 2018, 2:22 pm

Just skipping the hard ones now. All 2 cells:

p34

Code: Select all

x = 1, y = 3, rule = B2ain3cejkq4-aijtz5-jny6-ai7e/S01e2-ak3-ijqr4aeijnqz5cijry6-ac7e
o2$o!
p36

Code: Select all

x = 1, y = 3, rule = B2ain3-eiry4ijknrtz5-ay6aek/S01e2-a3-aijn4-acewy5ejqr678
o2$o!
p38

Code: Select all

x = 1, y = 3, rule = B2ain3-einr4-aent5-kqry6-ci7c/S01e2-a3-iknr4inqt5ceq6-e78
o2$o!
p40

Code: Select all

x = 1, y = 3, rule = B2ain3acjkq4-acewz5aeiny6ck7e/S01e2-ak3cejqy4ijqtwz5aenr6ci8
o2$o!
p42

Code: Select all

x = 3, y = 1, rule = B2ain3acjkq4-aey5-y6k7c/S01e2-an3-in4ijnqtwz5-ciny6-ek7e8
obo!
I guess even periods are easier because they can just rotate 90 degrees after half the period.

EDIT: Now that I've exhausted the brute-force approach, I stopped to figure a few things out. If you want a 2-cell high-period oscillator the two cells have to be one cell apart orthogonally. Then you have to have B2i, S0, B2a, S1e. You can't have B0, B1c, B1e, B2c, B3i.

EDIT2: This lets me fill in some missing periods:

p31

Code: Select all

x = 3, y = 1, rule = B2ai3-eikr4ijnqwy5acenq6-e7/S01e2ce3cekr4-aknz5-aijk6ce7e
obo!
p33

Code: Select all

x = 3, y = 1, rule = B2ain3cenqr4-aejqt5-cijr6-ce8/S01e2en3-ceij4aijknr5aekqy6-e7c8
obo!
p35

Code: Select all

x = 3, y = 1, rule = B2ai3acqr4-crt5anqr6-n7c/S01e2k3-cein4-cknq5acej6-ak7e8
obo!
p37

Code: Select all

x = 3, y = 1, rule = B2ain3-eir4inqr5-cen6-cn/S01e2-a3ck4eijnyz5-cnqr6aei78
obo!
p41

Code: Select all

x = 3, y = 1, rule = B2-ck3aky4-ejrw5ceir6-cn7/S01e2en3eikry4cekrz5-k6ack7c
obo!
p44

Code: Select all

x = 3, y = 1, rule = B2ai3-einr4iknqty5aikry6ik7/S01e3cejry4-ejkqr5inry6a7c
obo!
p46

Code: Select all

x = 3, y = 1, rule = B2ai3cekry4aejknrz5aejqy6-en7e/S01e2-a3-inqy4-ijntw5-ijn6-in8
obo!
p48

Code: Select all

x = 3, y = 1, rule = B2ain3-eiy4aqrwyz5-cij6cen7e8/S01e2in3-eknq4ijnryz5aceqr6-ce
obo!
p50

Code: Select all

x = 3, y = 1, rule = B2ain3-aijr4cijkw5anqry6-kn7c8/S012ekn3-ejny4aiz5ceqy6-n8
obo!

User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Re: Smallest Oscillators Supporting Specific Periods

Post by 77topaz » January 28th, 2018, 12:32 am

Gamedziner wrote:
77topaz wrote:
Period 4, 2 cells

Code: Select all

x = 3, y = 1, rule = B2-i/S1
obo!
That's p2.
It was a typo (supposed to be B2-a/S1). I've edited the post and fixed it now.

wildmyron
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Smallest Oscillators Supporting Specific Periods

Post by wildmyron » January 28th, 2018, 12:50 am

p54

Code: Select all

x = 3, y = 1, rule = B2ain3ry4iy5jn6in/S01e3-cjky4ijktwy5-ciy6k8
obo!
Edit:
p62

Code: Select all

x = 3, y = 1, rule = B2ai3eqr4cejnw5cenry6aen/S01e2ei3-anqy4aijnq5ciqr6ce8
obo!
2-cell oscillators are a bit too sparse for random rule search, but 3-cell ones can be found fairly readily (for even periods in any case). I'm compiling a collection of them now - how would you like them posted?

btw, there are also a few high period 3-cell oscillators in this thread
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » January 28th, 2018, 3:17 am

p100

Code: Select all

x = 3, y = 1, rule = B2ain3-eijy4aeinqy5ceq6-ak7c/S01e2i3cijkn4-anq5any6-ak7
obo!

User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Re: Smallest Oscillators Supporting Specific Periods

Post by 77topaz » January 28th, 2018, 3:49 am

Macbi wrote:p100

Code: Select all

RLE
Hm, I wasn't expecting there to be one smaller than the four-cell one I posted in the first post. Granted, the four-cell one would still be the smallest p100 in a non-explosive rule.

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » January 28th, 2018, 6:12 am

77topaz wrote:Granted, the four-cell one would still be the smallest p100 in a non-explosive rule.
I feel bad about interpreting this as a challenge, but I'm still trying to find out what LLS is capable of.

Code: Select all

x = 3, y = 4, rule = B2c3ajq4ejnr5cjr6n/S01c2ci3cijny4aeknrtz5aijr6ace
obo3$o!

User avatar
Majestas32
Posts: 549
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Smallest Oscillators Supporting Specific Periods

Post by Majestas32 » February 3rd, 2018, 1:47 pm

p88, 6 cells:

Code: Select all

x = 7, y = 11, rule = B2-a3c/S12-i
o$o6$6bo$3bo2bo2$4bo!
p136, 8 cells:

Code: Select all

x = 11, y = 3, rule = B2-a4jnr/S12-i
b2o$o7b3o$b2o!
p170, 8 cells:

Code: Select all

x = 25, y = 3, rule = b2i3-ck4e6/s2-i35n
o23bo$2o21b2o$o23bo!
Searching:
b2-a5k6n7cs12-i3ij4k5j8
b2-a3c7cs12-i

Currently looking for help searching these rules.

googleplex
Posts: 308
Joined: January 24th, 2018, 4:36 pm
Location: The hertzsprung gap

Re: Smallest Oscillators Supporting Specific Periods

Post by googleplex » February 7th, 2018, 4:26 pm

p4, smaller bounding box:

Code: Select all

x = 2, y = 3, rule = B2-a3/S0
o2$bo!

wildmyron
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Smallest Oscillators Supporting Specific Periods

Post by wildmyron » February 15th, 2018, 6:22 am

Here is a my collection of odd period 3 cell oscillators. Unfortunately I missed p39 due to a logic error when running the search script.

p43, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3aek4acnq5an6c/S01e3jny4ce5e6i
obobo!
p45, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-an3-iknr4ainryz5-cknq6ak/S02i3jn4nz
obobo!
p47, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3ar4aikntwz5y6a7e/S1e2n3cny4centw5anq6i
obobo!
p51, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3aky4ciqwy5y/S1e2cei3j4ek5i6a8
obobo!
p53, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3aj4cikt5an6ci/S12i3qy4cei5aein7e
obobo!
p55, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3ay4jr5ein6a7e/S01c3er4cnr5cy
obobo!
p57, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3aqry4q5jkr6c7e/S01c2-ac3ejkqr4eijknz5eikny6i
obobo!
p61, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cek3c4cijkrw5aciy6e8/S01c2in3kqy4ceky5n6ci
obobo!
p63, 3 cells

Code: Select all

x = 5, y = 1, rule = B2eik3cin4ainr5cy6ck/S01c2cn3ein4cer5iy7e
obobo!
p65, 3 cells

Code: Select all

x = 3, y = 3, rule = B2ikn3acijy4aceikt5ackr6ak/S012n3ciny4ekqrty5-acnr6ce
obo2$o!
p67, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cen3akqy4eirty5ainy8/S01c2i3a4kt
obobo!
p69, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3eikqr4eintwy5inq6c/S1e2en4eikwz5e6kn
obobo!
p73, 3 cells

Code: Select all

x = 2, y = 3, rule = B2ce3cry4cejkwy6e7c8/S123acnq4kqr5inqy
o$bo$o!
p87, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ce3ekqy4iq5aeijk6ai7c8/S01c2aek3anry4aekqrty5j67e
obobo!
p89, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-an3eijq4cjkqrz5ej6c7c/S1e2-ac3aery4einry5aj6ak7e
obobo!
p119, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3ikq4eikqw5ejn6eik/S1e2n3i4n5cry6i
obobo!
p139, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3acijn4cin6ci/S01e3iqy4ikny5n
obobo!
p165, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cen3y4einqrty5-kqr6ace7e/S012-ae3acer4acejkry5-cikq67e8
obobo!
p189, 3 cells

Code: Select all

x = 5, y = 1, rule = B2in3aeij4eikq5ejknq6aek7e/S01e2ein3aejk4-aijn5ijq6ei7c8
obobo!
p263, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cen3aey4aejt5cny6e7c/S01c2ikn3jry4-aknw5acn6eik78
obobo!
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

googleplex
Posts: 308
Joined: January 24th, 2018, 4:36 pm
Location: The hertzsprung gap

Re: Smallest Oscillators Supporting Specific Periods

Post by googleplex » February 15th, 2018, 8:24 am

p2, 1 cell:

Code: Select all

x=1, y=1, rule=b02/s
o!
Look at me! I make patterns in golly and go on the forums! I wanna be Famous!

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » February 15th, 2018, 8:43 am

wildmyron wrote:Here is a my collection of odd period 3 cell oscillators. Unfortunately I missed p39 due to a logic error when running the search script.

Code: Select all

x = 5, y = 1, rule = B2cik3-eir4cijrt5-ejkq6-cn7c8/S1e2-an3eijqy4ajqw5-cein6ein7c8
obobo!
p52, 2 cells:

Code: Select all

x = 1, y = 3, rule = B2ai3knq4-cekrt5-ijkr67c/S012cen3-ijnq4ajntyz5ikqr6-c7
o2$o!
p56, 2 cells:

Code: Select all

x = 3, y = 1, rule = B2ain3anq4inqtw5-ckq6-n78/S012kn3eqr4acijknz5ejk6i8
obo!
p58, 2 cells:

Code: Select all

x = 1, y = 3, rule = B2ain3acejn4ijnqwyz5ijkr6-ak7e8/S01e2ei3anr4aiqyz5-cer6kn7
o2$o!
I believe that makes p59 our first gap.

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Smallest Oscillators Supporting Specific Periods

Post by Macbi » February 15th, 2018, 3:28 pm

2 cells:

p39

Code: Select all

x = 3, y = 1, rule = B2aei3ackq4aeintwy5-ajqy6-in7e8/S01e2eik3cky4ajtw5-jk6ak7e
obo!
p43

Code: Select all

x = 3, y = 1, rule = B2-ck3ceq4cikwz5-k6ak8/S01e2ein3ejkny4-jqtw5-eijr6ci7e
obo!
p45

Code: Select all

x = 3, y = 1, rule = B2ai3-in4aknrt5cny6ci8/S01e2-ac3aekn4ciknt5-akqr6cek7e8
obo!
EDIT: p47 (3 hours in LLS)

Code: Select all

x = 3, y = 1, rule = B2ain3-aij4ijknqty5cjk6-in/S01e2ik3-cry4-actw56ei8
obo!

wildmyron
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Smallest Oscillators Supporting Specific Periods

Post by wildmyron » February 16th, 2018, 1:39 am

Here is my collection of even period 3 cell oscillators. It includes almost all even periods from p60 through to p128 (only missing p114) and a fair number of higher periods. I've left out periods for which a 2 or 3 cell oscillator has already been posted (although I may have missed some redundant ones).

p60, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cei3inq4jt5i6ci/S012ein3qry4q5an6i
o$bo$o!
p64, 3 cells

Code: Select all

x = 4, y = 2, rule = B2eik3-kqy4jnw5y6c/S02ak3aj4i5i
o2bo$bo!
p66, 3 cells

Code: Select all

x = 3, y = 3, rule = B2en3ceijr4kqrwy5ikq6n7c/S012i3ij4ci5ery6n
obo2$o!
p68, 3 cells

Code: Select all

x = 2, y = 3, rule = B2ce3nqry4aer5eijy6c7e/S12k3eqr4iqyz5aiy6i7e
o$bo$o!
p70, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cen3cijkr4aeikz5ijq6aci7e8/S01c2-ck3ekqy4ckw5-aikq6ci
obobo!
p72, 3 cells

Code: Select all

x = 4, y = 3, rule = B2cen3ajn4aeijknt5ay6a7c/S023ry4it5aiy6a7e
o2bo2$bo!
p74, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-an3ay4jkrz5jkq6i7e8/S02ae3nqy4aceiqrt5aen6aci7c8
obobo!
p76, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ae3-cikn4aceknty5cy6ck7e/S13n4w5cj6ci8
obobo!
p78, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3a4ac5ai6c8/S02in3jn4ai5enqy7e
obobo!
p80, 3 cells

Code: Select all

x = 4, y = 2, rule = B2-an4eit6k/S1e2aek3ry
o2bo$bo!
p82, 3 cells

Code: Select all

x = 4, y = 1, rule = B2cek3ckny4eiqt5-ikry8/S02en3iqry4inr5cy6c
2obo!
p84, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ae3aejr5jq7c/S01e2-ck3cei4artw5cein6k7c
2o2$bo!
p86, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3ajkn4cejnrt5knq6ik/S02i3inqr4ceik5c6ci
obobo!
p88, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ce3cekr4ckt5ny6i8/S02aen3aciky4jknry5i6i
obobo!
p90, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cn3ainqy4eijkt5ny/S02-ac3jry4cejnt5e6ci8
obobo!
p92, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cei3ijk4ce5i6ai/S1e2ai3jny4e5ey
obobo!
p94, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cek3iy4iq5aci/S01c4a5k6c
o$bo$o!
p96, 3 cells

Code: Select all

x = 4, y = 2, rule = B2-ac3aeijn4n5a/S03ijk4qwz
o2bo$bo!
p98, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-ac3acik4cenqt5ijnqy6e7c8/S02ack3ceky4-iknyz5aejq6c7e
obo2$o!
p102, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cen3-cikn4acijr5cinr6ck/S1e3ai5i
o$bo$o!
p104, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3ajnr4ijqt5ejnry6a8/S02a3-jnry4inrty5eny6ek
obobo!
p106, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-ae3-knqy4ijky5aejnq/S02ei3aein4cijqrw5ai
o$2bo$o!
p110, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3aciky4-ejqz5aq6c/S1e2an3cy4acn5r6k
obobo!
p112, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ak3jqy4wy5acer6i/S01c2en3-cq4jqrtwy5ky
o$bo$o!
p116, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-ae3aejy4knqrz5cek6aik8/S01c2cn3jq4qwy5kn6c
obo2$o!
p118, 3 cells

Code: Select all

x = 3, y = 3, rule = B2ein3cijkr4jknrtyz5-ceir6-ai7c8/S01c2acn3cejy4-cijny5ay6-ce7
obo2$o!
p120, 3 cells

Code: Select all

x = 5, y = 2, rule = B2cin3-jknq4ekrtwy5ainr6ik7e8/S02cen3-aknq4acrw5iqry6e
obo$4bo!
p122, 3 cells

Code: Select all

x = 4, y = 2, rule = B2-ae3acnr4nqr5-ceky6ckn7/S1c2aei3q4ajkqr5-qry6-a
o2bo$bo!
p124, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3ijy4ekyz5ac6an7c8/S1e2in3ceqr4acejqw5acr6ack7e8
obobo!
p126, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3aeqry4kqt5-acir6eik78/S02eik3eijnr4-eikqt5ir6aek8
obobo!
p128, 3 cells

Code: Select all

x = 4, y = 2, rule = B2eik3ijqr4knqrtz5ijkn6-ci7e/S02aei3cijqy4aknq5c6e
o2bo$bo!
p136, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ak3ac4ejkr5airy6ce7c/S12ain3knq4nqr5cijr6i7e
o$bo$o!
p138, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ai4ijnw5aceq6ek/S01c2in3inqr4-erwy5eikqy6c7
obobo!
p140, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ai3cjky4iknrtwz5-nry6ci8/S02kn3iqy4-ijnt6k8
obobo!
p142, 3 cells

Code: Select all

x = 3, y = 3, rule = B2cen3aqr4arw5ijknr6cn7c/S01c2ae3-aeiy4cejnqz5ckry6acn
obo2$o!
p144, 3 cells

Code: Select all

x = 4, y = 2, rule = B2-an3ajky4ainqt5-aeny6ck/S02ck3ekry4aijkrz5inr6ak7e
o2bo$bo!
p146, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3cejry4aknwyz5cejkq6e7e8/S12n3jk4ijrz5jr6ei7e8
obobo!
p148, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ak3inqy4acjqrtz5aekry6k7c/S01c3kq5y7e
o$bo$o!
p150, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3cijr4aektz5ci6-in7/S1e2eik3ckq4w5acy6n8
obobo!
p152, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3aekn4jqtz5aen6n7/S02-ce3-in4jkty5-anr6cei
obobo!
p156, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-ae3aejqy4cjwz5-akn6akn7/S02ai3cekry4acjktwy5ceiq6aek78
obo2$o!
p158, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ak3-ckqr4eiknqt5cny6ce7e/S1c2i3e4ej5y6a
o$bo$o!
p160, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3-cnqy4-aejqz5acij6ce/S02n4-qrwyz5qy6-in7c
obobo!
p162, 3 cells

Code: Select all

x = 2, y = 3, rule = B2-ai3nr4jkt5jry/S12ace3cknr4qz5eijry6i
o$bo$o!
p164, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cek3ajkr4ikrwyz5eq6-an8/S02k3kr4eiknw5n6ci8
obobo!
p168, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-ai3enqy4aiqt5iknr6cek7/S02-cn3enqr4iqz5cqr7
obo2$o!
p170, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3-acny4arz5-cijn6-cn7/S1e2ik3jnqry4ceijkt5ay6-ai7e
obobo!
p180, 3 cells

Code: Select all

x = 5, y = 2, rule = B2cek3ciky4anqr5cknr7c/S01c2ckn3eiry4ajryz5ekry6ae
obo$4bo!
p182, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-jr4knry5-cjry6aei/S02ai3ijkqy4acjnr5einr6ik
obobo!
p188, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cei3ir4cekwy5aeq6a/S12k3ij4ejy5ciry6ei
o$bo$o!
p190, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cei3ciq4ajnqz5ejk6ck7e/S01c2-ek3q4rwy5aek6c
o$bo$o!
p214, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3ajqy4cjkqrwz5aceq6ak7c/S12ck3aijqr4cqwyz5-cqry6-c7c
obobo!
p216, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3aeinq4ejqrtz5-ijy6aci/S02en3ceinr4ajny5aeiny78
obobo!
p224, 3 cells

Code: Select all

x = 5, y = 2, rule = B2-ae3aejr4ajkntyz5kq6a7e8/S01c2i3jqr4acijrwz5ceikn6ik7c
obo$4bo!
p232, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-cknr4aejqyz6eik/S01e2a3ijnr4jqr5r6c8
obobo!
p234, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ai3ry4-ajkwz5-aekq6a/S01e3ar4aciwy5cejn6i7c8
obobo!
p274, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3-ejn4-rty5-aejk6-ck8/S1e2n3kn4aw5cny
obobo!
p304, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cek3ekny4aejnwz5-cjqr6k7c8/S12-ac3iqy4z5ein6ce7e
2o2$bo!
p314, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ikn3-jqry4ceitwz5-cej6ikn78/S01e2en3ain4et5eijky6kn7e
obobo!
p344, 3 cells

Code: Select all

x = 5, y = 1, rule = B2eik3ij4ciqtyz5iy6e7e/S01c2ckn3-ikqr4enz5acikr6ci8
obobo!
p358, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-ejry4einrwz5ijk6aci7c/S1e2k3ik4cikryz5i6ci
obobo!
p368, 3 cells

Code: Select all

x = 2, y = 3, rule = B2ce3iny4aeinqw5acr6-ci7c/S12e3knr4acjrt5ai6e
2o2$bo!
p376, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3aqry4ejnry5ceinr6-kn7/S01c2cin3aijky4ajnqz5cknqr6-en7
obobo!
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

Post Reply