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Smallest Oscillators Supporting Specific Periods

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Re: Smallest Oscillators Supporting Specific Periods

Postby BlinkerSpawn » February 4th, 2019, 11:00 am

Macbi wrote:4 cell, period 4N+3 (N>1):
x = 6, y = 4, rule = B2ei3ir4r/S012ce3j
5bo$2bo$o$2bo!
This completes the proof that all periods can be achieved in at most 4 cells.
2718281828 wrote:4 cells for 4N+1 (N>2):
x = 9, y = 22, rule = B2ei3i4r/S012cek3j4t
5bo$2bo$o$2bo3$6bo$2bo$o$2bo3$7bo$2bo$o$2bo3$8bo$2bo$o$2bo!

2718281828's oscillators are p(4n+3), not p(4n+1), unfortunately. :?
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Re: Smallest Oscillators Supporting Specific Periods

Postby Macbi » February 4th, 2019, 11:25 am

:-o

How's this?
x = 15, y = 4, rule = B2ein3aciq4jkny5any6ck/S012ce3ejnr4jknrwy5-aiky6ci7e
14bo$2bo$o2bo$2bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby BlinkerSpawn » February 4th, 2019, 5:13 pm

Macbi wrote::-o

How's this?
x = 15, y = 4, rule = B2ein3aciq4jkny5any6ck/S012ce3ejnr4jknrwy5-aiky6ci7e
14bo$2bo$o2bo$2bo!

Perfectly valid for p13+4k, so now we have all periods > 9 in at most four cells.
Of course, the specific lower bound doesn't matter much, considering the wide range of periods that now have 2-cell solutions.
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Re: Smallest Oscillators Supporting Specific Periods

Postby Macbi » February 4th, 2019, 5:32 pm

Current status:
Period 0, 1 cell
Periods 2 - 104, 2 cells
Even periods 106 - 204, 2 cells
Periods 109, 208, 212, 2 cells
Periods 117, 119, 127, 139, 165, 189, 214, 216, 224, 232, 234, 240, 248, 263, 274, 286, 304, 314, 320, 344, 358, 368, 376, 392, 3 cells
All other periods, 4 cells
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 5th, 2019, 3:51 am

Some more results - the 5x9 search seems to be providing many more high period results than 9x5

p105, 2 cells
x = 3, y = 1, rule = B2-ck3akqy4cijknry5iknqy6ac8/S01e2ik3-cijn4cjnqrty5-jkq6aci7e
obo!

p107, 2 cells
x = 3, y = 1, rule = B2-ck3ak4ijnr5-cjqy6cei8/S01e2ik3-acik4-erwz5-ajkq6-kn7e
obo!

p111, 2 cells
x = 3, y = 1, rule = B2aei3akqy4ijknry5ijnqy6ac8/S01e2eik3-aijn4-eikz5-ajk6-kn7e
obo!

p206, 2 cells
x = 3, y = 1, rule = B2aei3aky4inqr5-ceq6ci8/S01e2ikn3-cikq4cijnqty5-acjk6cik7e
obo!

p210, 2 cells
x = 3, y = 1, rule = B2-ck3akqy4iknqr5ijkny6ci/S01e2eik3aeknr4-eqrw5-aikq6-n7e
obo!

Edit:
p216, 2 cells
x = 3, y = 1, rule = B2aei3-eikr4-acqwz5-aqry6-kn7e/S01e2-ac3enqry4ijknrtz5cer6-an8
obo!

Updated status:
Period 0, 1 cell
Periods 2 - 112, 2 cells
Even periods 114 - 212, 2 cells
Period 216, 2 cells
Periods 117, 119, 127, 139, 165, 189, 214, 224, 232, 234, 240, 248, 263, 274, 286, 304, 314, 320, 344, 358, 368, 376, 392, 3 cells
All other periods, 4 cells
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Re: Smallest Oscillators Supporting Specific Periods

Postby Macbi » February 5th, 2019, 5:16 am

I just noticed that I accidentally wrote "period 0" instead of "period 1" in that status. I guess since a period 0 pattern is any one which never repeats the smallest period 0 oscillator actually does have only one cell:
x = 1, y = 1, rule = B1c/S
o!
and technically the smallest period 1 oscillator has 0 cells:
x = 0, y = 0, rule = B/S
!


So we have
Period 0, 1 cell
Period 1, 0 cells
Periods 2 - 112, 2 cells
Even periods 114 - 212, 2 cells
Period 216, 2 cells
Periods 117, 119, 127, 139, 165, 189, 214, 224, 232, 234, 240, 248, 263, 274, 286, 304, 314, 320, 344, 358, 368, 376, 392, 3 cells
All other periods, 4 cells
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 5th, 2019, 10:37 pm

p214, 2 cells
x = 3, y = 1, rule = B2aei3ajq4-acjkq5-akqr6ci/S01e2eik3-ain4ajkntw5cejny6-en7e8
obo!


The 5x9 search is now complete, p214 being the only new period found after p216. The 9x5 search looks like it will take much longer to complete. It's currently reporting 79.4314% (in the forward direction) and the output file is now larger than 6 GB. I added some filtering of low period oscillators to the code, but I don't want to restart the search so I'm stuck with letting that file grow very big. I've started a 9x5 search in the reverse direction, but considering the current rate of progress I'm not expecting to be able to completely cover that search space.

Edit: Included p214 which I had overlooked somehow.

Edit 2: Removed comments about summary
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 6th, 2019, 11:50 pm

I tried adapting pop2osc for a 3-cell oscillator search using o.o.o as the starting pattern. It seems to work reasonably well, but search progress is much slower. I was able to complete 5x5 (no new record smallest oscillators found) but anything bigger seems like it's going to run for much longer and I didn't get any promising results. [Edit: I just realised I removed the B2a requirement but forgot about the exploding pattern test, so this result is unreliable.] Instead, I dusted off my Golly Python script for random rule search and ran it to find a few more 3-cell oscillators at high periods. Most of the results have o.o.o as the starting pattern but I also included a few other patterns in the search and there are some results with them as well. See below for results. I included B2a in the allowed transitions, but the highest period oscillator which used it was p98.

Patterns included in search:
ooo     oo.o    o.o.o   o.o     oo      o.o
                        .o      ..o     .
                                        o

The first one is the only one not represented in the results below. I'm considering adapting pop2osc.cpp to run this kind of random rule search with the o.o.o pattern - I suspect it would run a good deal faster than my Python script.

Updated summary:
Periods 2 - 112, 2 cells
Even periods 114 - 216, 2 cells
Odd periods 113-119, 123, 127, 131, 137, 139, 163, 165, 189, 263, 279, 3 cells
Even periods 218, 220, 224, 228, 230-234, 240-248, 254, 258, 260, 266, 274, 280, 284-288, 294, 302, 304, 314, 320, 336, 344, 356, 358, 368, 376, 392, 396, 412, 3 cells
All other periods, 4 cells


Results from 3-cell random rule search:
Odd periods:
p113, 3 cells
x = 5, y = 1, rule = B2-ae3aikny4ckqy5-ain6ek/S1e2i3-ceir4eij5j6i
obobo!

p115, 3 cells
x = 3, y = 2, rule = B2-an3r4-cikw5-cinq8/S12k3aekr4act5aceny6k7c
obo$bo!

p123, 3 cells
x = 5, y = 1, rule = B2-ai3r4ijnqwyz5jnr6i/S012aik3acq4inqryz5jn6ei
obobo!

p131, 3 cells
x = 5, y = 1, rule = B2cik3acj4ceiyz5-cijr/S02-cn3eqy4aitw5eky6ai8
obobo!

p137, 3 cells
x = 5, y = 1, rule = B2cn3aeijk4jnwz5ajny6cik7e8/S01e2i3acknq4-ijkwz5c6k7e
obobo!

p163, 3 cells
x = 5, y = 1, rule = B2-a3acky4cjnwyz5cnq6ci7/S1e3ejkqy4aez5an6cei7e
obobo!

p279, 3 cells
x = 5, y = 1, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
obobo!


Even periods:
p218, 3 cells
x = 5, y = 1, rule = B2cen3eiy4centz5jqy6-ek/S01c2en3cjq4-nryz5einry6a7e8
obobo!

p220, 3 cells
x = 5, y = 1, rule = B2cik3-ikn4-jrtyz5aiy6-ai7e8/S02in3anq4a5cei6ik8
obobo!

p228, 3 cells
x = 3, y = 2, rule = B2-a3ajy4aejkwy5qr6n7/S01c2ce3eik4e5jn6k
obo$bo!

p230, 3 cells
x = 5, y = 1, rule = B2-a3acer4cinr5acery6aik7e/S1e3acry4ejr5-aeq6ein7e8
obobo!

p242, 3 cells
x = 5, y = 1, rule = B2c3aijry4eiktyz5ejkr6ck8/S02ckn3inr4acent5-aeir6aik8
obobo!

p244, 3 cells
x = 3, y = 2, rule = B2-ak3aq4ajw5ary6aik8/S13enqy4-irtw5aijr6ci7e
obo$bo!

p246, 3 cells
x = 3, y = 2, rule = B2-a3jr4acjrz5aejq6ai7/S12in3qy4acenry5knqr6ci7c8
obo$bo!

p254, 3 cells
x = 5, y = 1, rule = B2-an3ky4aejnrw5qry6cen7c/S1e2e3kny4aceknrt5i6i8
obobo!

p258, 3 cells
x = 5, y = 1, rule = B2-ak3-anr4eijkqw5nq6ai7/S12n3kry4jqrtwyz5-ikq6ci7e
obobo!

p260, 3 cells
x = 5, y = 1, rule = B2-a3aky4ijnqrtz5ikr6-ai7e8/S1e2-ai3acek4eiyz5-cjq6-kn
obobo!

p266, 3 cells
x = 5, y = 1, rule = B2cek3aknq4ciz5ajky6cn8/S01c2ekn3ckr4iy5iy6ain7c
obobo!

p280, 3 cells
x = 5, y = 1, rule = B2-ae3acekq4jnqtyz5jn6ac7/S12ek3kry4iqy5ij6-kn7e8
obobo!

p284, 3 cells
x = 3, y = 2, rule = B2-an3aq4c5iy6i/S01c2n3nqy4cejkwy5aeik6aik8
obo$bo!

p288, 3 cells
x = 5, y = 1, rule = B2-an3eikq4cn5eikqy6ik8/S2-n3ry4iy5aejkn6aen8
obobo!

p294, 3 cells
x = 5, y = 1, rule = B2-an3acqr4eqtz5-jknr6ik7/S01c2ac3aei4cnqrtz5kry6ik8
obobo!

p302, 3 cells
x = 5, y = 1, rule = B2-a3iry5-acey6e7/S1e2ein3-ijkr4aceiknz5-eknq6ei7c
obobo!

p336, 3 cells
x = 5, y = 1, rule = B2-an3cikr4ekrtw5cinry6kn8/S1e2ein3ac4eijnrwy5ijk6ek7c
obobo!

p356, 3 cells
x = 4, y = 1, rule = B2ce3-ackn4kntz5j6ae/S12i3ij4ijnqz5j6ei7c
2obo!

p396, 3 cells
x = 3, y = 3, rule = B2eik3-eknq4ainqwyz5i6-in7c/S02k3acjqy4aj
obo2$o!

p412, 3 cells
x = 3, y = 2, rule = B2-ai3jk4eiqt5aciq6aek8/S12cen3-einr4ny5ary6aek8
2o$2bo!
The latest version of the 5S Project contains over 47,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
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Re: Smallest Oscillators Supporting Specific Periods

Postby 77topaz » February 7th, 2019, 3:11 am

wildmyron wrote:p228, 3 cells
x = 3, y = 2, rule = B2-a3ajy4aejkwy5qr6n7/S01c2ce3eik4e5jn6k
obo$bo!


A bit off-topic, but this rule somehow also manages to have a three-cell spaceship, of the somewhat unusual speed of 4c/28 diagonal to boot:
x = 4, y = 4, rule = B2-a3ajy4aejkwy5qr6n7/S01c2ce3eik4e5jn6k
o$bo2$3bo!


wildmyron wrote:p279, 3 cells
x = 5, y = 1, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
obobo!


And this rule has a similarly sparky p49 that has a minimum of five cells:
x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!


And a p71 with a minimum of six:
x = 11, y = 11, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
o4$5bo$4bobo$5bo4$10bo!


wildmyron wrote:p284, 3 cells
x = 3, y = 2, rule = B2-an3aq4c5iy6i/S01c2n3nqy4cejkwy5aeik6aik8
obo$bo!


This rule, meanwhile, has an impressive class F (?) replicator:
x = 188, y = 186, rule = B2-an3aq4c5iy6i/S01c2n3nqy4cejkwy5aeik6aik8
ob2o6bo3bob3o3bob3o5bo9bo4b4o2bobo3b2ob7o2bobob2ob2o5bo5b7o2bob3obo2b
5obobo3b2o5b3o3b3obo2b2obob2obo2b3o3b2o2b4ob2o2bobobob3o3bo3bo$2ob2obo
5b2o4bo2b2o2b3o4bo2b5o2bobobo3b2o2bo2b2o2bob2o3b2obo3bobobobo2b5obo3b
4ob2obo2b2ob2o2bob5ob2o2b5o3b3o2b2o2bo5bo4bob3obobo2bo5b5o2b2o2b2o3bo$
bo5bo4b4ob3o3b2o2b2obo3b4ob3obobo3b5ob3obo2b2ob2ob9obob2o2b5o2bo2bo2b
7obo3bo2bo3b2ob3ob2o3bo2bob3o2bo4bobob2obob3ob5ob3obobobo2bo2bobob2o$b
2ob2ob2obob2o2b2o6bobo2bo2b2ob6o3b2o4b7obo2bo2b5ob2o6bo2bob2obobo3b2ob
3obo3bobob2o3b4obob2ob3o2bob5ob3obob7o3bo2b2o5bo2b5obob3ob2o5b3o$bobo
4bo7b2ob2obobo5b4obo3bo3bo2bobo5b5o2b6obobobob2ob2o3b3ob3o3b2ob3ob2o4b
obo2b2ob2o2bobo3b2o7bobo7b6o5b2obob2obobo3bo4bob3ob2o2bobob2o$bo2b2ob
2o4bo3b3o2bo2bobob2ob2obo2bo4bobo3b3ob2o6b4obob3o2bobo2b2o4bob2o4bo2bo
bo2b2o2bobob3ob5obob3o5b2o3b2obobobo3b2o2b4o4bo3bobobobo2b3o3b3obo2bo
2bobo$ob2o2bo2bob2o2bob2obo2b5ob3ob2ob4obo2b3o3b6o2bo4b3o2bob2o2bobo2b
2ob4o2bob2obo3b2o2bo2bobobob4ob2obo2b2o4bob3obo3bo4bob3ob2o2bo2b2o2bob
obo2b6ob2obo3b2obob3o$2bob3o2b2ob2o6bo2bo2bob2ob2ob4obo4bobo2bo2bo4b2o
bo7bo2b2ob3o4bo2bobobobo4b2obo2bobo2bobob2o3bob2ob6o2b2o2b7o2b2o6b2ob
4ob3o3bobobo3bobo2bo2b2o2bo3bo$4obo2b4ob3ob2ob5obobobo2bo2b2o2bob2o3b
4ob2ob3obo2bobobo3b2o2b2obob2obo2bob3o3b6obo8bob5o2b2o3bo3bo6b2obobo2b
2o8bobob3o3bob2o7b3o2b3o4b3o$bo3bob6o5bo2b9o2b2o3bo4b5o4b3obobob2obo2b
2o2b2o4bobobob2obo2b3o2bob2ob2o2bob4obobo2b2obo2bobo4bobobo5b2o4b3obob
6o2bo2bo2bo2b2obo2b3ob2o2b2o4b2o$bob2o2bo2bobob2o3bo2bob5obob2o2b2o5b
2o4bo4b2o2b3o5b2ob6ob2obob4ob2obo3b3o2bob2obo3bobobo2b3o2b4o2b2obob3o
2bob4o2bo2b2o2b2obobobo2b2ob10ob2obo3b4ob2o$4b2o3bo3b5o2bo3bo5bo2bob5o
bob5ob3o2bob5o6bo2bo2bob5o5b2o2b4o5bob2ob2obobob6obo2bo3bob3obobobo2b
2o3b5obo2b2o2b3o2bob3obobo2b2obobo3bob2o$bo5b5obobo2b2ob2obo3bob5o2bo
2b2o2bobo3bo3b4o2bobobo2bo2bo2bobo2bo3bo5bob3o2bo2b3o3bo3bo2bob3o6b2o
3bob4ob2obobobobo2bobo3bob5obobobo2b2o2b5o2b2obob2o$bo2b2o2b2ob3o2bo2b
4obo2bo4b3o2bob2ob3o6bo2b3o2bobo3bob3ob2o4b4o2bob2o3b4o2bobo3bob2o3b9o
4bo2bobobo2b2o2bobo2b2obo2bo3bob2ob2obo2b2o3bo2b5o3b3o2b3o$bo5bo3bo2b
2o2bobobobob5o2b2o3bo4b3o3bo3b8ob2ob5o2bo3b2obo5bo8b7ob2obo3b2o3bobo2b
2o4bob3obobobobo3bo9b2o4b2ob3ob4o3bob2ob2ob2ob2obo$2bo2b6o4bo4b3o2bobo
b2o2bob9o4b2o4b2o2bobob3o3bo3bo3bo2b2obob5o2b2ob2obo2bob2o4bo2b3o2bo5b
o9bobo2b2o2bo3b2ob2obob4o2b2obobo2b2o2bo3bo2b6obo$2o4bo4b4obo2bobo7bo
3b4o4b4o2bob2obo2bobob3o2bobo3b2o2b3obo4b2ob4o5b5ob2o2b2obo2b2o6bobo2b
4o3b6obob2ob2obo2bobo2bo2b2o2b2ob2ob2o5b5o7bo$4ob2obo3b2ob3o2bob3ob4ob
obobobobo2bo2bob2obobobobo2bo4bob3o4bo2bo3b6o4b4obob2ob2o3bobo2b3o4bo
2b2ob2o4bob2ob4o2b2o6bo2bo3bo2b2o2b4o3bobo8b2ob2o2bo$2bobobobobobo6bob
2o4b2o2b4o2b2o2b3o2bob3o2b3o7b2ob2o3b3o2b2o3b2o3bo6bob2o2bo2b2o4bob2o
3b3ob5ob2ob2obobo2bobob2ob3ob2o2b2o2bob3ob2o3b3ob5o4b5obobo$obo5bob2o
2bob2o7b2obo2b2ob5o2b4o2bo2b3o2bo2bo2bobob3o4bo2b2o2b4ob2obobo3b7o2bob
o4b2obo2b2o3b2ob2o2bobob3o3b6o2b3obo2bo2b2ob2o3bobob4o4bobo2bobob2obo$
b2ob2ob6o2b2o6bob3obo2bobo3b3o4bob2obo7b2ob4o2b2ob3o5bob6o5bo3bo3b2o2b
4obo2bo3b2ob3ob3o4bob2ob3o2bo5b2obob4ob2obobo2bo2b3o7bo2b7obo$2b3o2bob
o2b3o5b5o2bo3b2o2b3o9bobobob2o5bo2b3o2b2o2bo2b2o4b2obo2b2o2bobobo3b2o
3bo2b4ob2ob7o2b2obo2bob2o2b4ob2ob5obobo3b2obobo3bo2b2o2bo4bobo5b2o$3bo
bob5obo2b5ob3ob4o5bo2bo2b2o2b8ob2obo3bo3bob6obo4bob2ob2obob2o3b5obob2o
bob2obo2bo2b4ob3ob3ob6o2b2ob2obobobob2obo2bo7bobo2b3o2bob2o2b3ob2obo$
3b2ob2ob3ob6obo2bo3b2ob2ob2o2bob2obob4o3b3o2b2ob3ob3o8bo2bo5b2ob4o3bo
2b2o2b3o2b4o3b2ob3ob2o3bobob2obo10b4o2bo3bob2o2bob2obo3bob2ob2o6b2o2b
3o$b2obob2ob5ob3obobobobo4bo8b2o3bobob2o4bobo2bo3b4ob4o3b2o2b2ob3o2bo
6b4o4bo2bobo2bobo3bo5b3o8bobobo4b2o2bob4obob2obob2ob2o5bo3bob2o5bo2b2o
$obob2o2bobob5ob2ob4o2b2obo2b3o4bob2ob7ob5o2bo2b3obo3bo2b2obo2bobob4ob
o5b2o3b2o4b4o2b2o5b2o3b3o8bo5bo2b2obo2bob2ob2o6bobo2bobob3o3b4o4b2o$2b
3ob2o2bobobob2obobob3obob2ob6obo5b2ob2o3b2o4b2obo2bob2o3bob2o3b7ob2ob
3ob3ob6ob2o2bo2b4obobo2b4o2bob4ob2obob2o4bobo3bo3b8ob4ob2o2bobo2bob3o$
o2b2ob2o2b3o3bo3b2o3b2obo2bo2bob2ob3o2b6o2b5ob2o2b2o2bo2bob2obobob3ob
3ob2o5bob2o2b3obob2ob3o5b4obo3b3o2b5ob2obo3bo2b3o2b2o2bobob2ob3obo7b3o
3bo2bo$bobobo3bo2b3o2bobob4o2bob4o2bo2b10obobobobob2o2bo2b2o2bo4bobobo
2bobo3b2o3b2o3b2o3bobobo4bo4bobo2b2o2bobo3b3o2bo11bob2o2bobo2bo2bo4bob
2ob3o3b3o3b5o$2o2b2ob3o3b3o4bo2bobo3bo2bob2o2b4obobo2b2o3bo2b4obobobo
3bob2obo2bob2obo4b4o3b3o2bo2b2ob3ob5ob2o3bob2ob4obo5bo5b3o3b2o4b3ob2o
2b2obobobobo2bo2bob5o2b2o$o2bobob2o3bo4b4obo2b5o2b2obobobo2b2o2bo3bo3b
4ob2obobo3bobob4ob3o2bo2bo2b2o10b3o2b5obo3b8ob5o4bo6b2obo2b3o2bob3obob
ob2o5bob4obo5bob4o$5o2b2o3b7ob2o3bo2b3obo3b5obob6obobo2b3o3b4ob3o2bob
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ob7ob5o3b3obo4b4o4b3obobo3bob2o2bobob2o$2bo7bo6bobo2bo4b4o2b2obob4o3bo
2b3ob2obob4obo2b2obo5bo2b2obob4ob3o6bo2b2o2b4obo2bob3ob3o3b3o2b5o2b2ob
3o2bo3b2o3b2o4bobob2obobobob2ob7obob2o$2o2bo2bo3b3obob2obobobob2obob2o
3b3ob2ob2o2b2obobobo2bo2bo3b2ob2obobo2b2o2b6ob6o3b2obo3bob2obo2b2obobo
3b2o2b2ob2o2bo3bobob2ob4obobob2ob4o2b2ob3ob2o4b6o9bo$o5b4o2b2obo3b2o3b
o4b7ob2o2b5o4b2o2b2o2bo2b2o2b4o3b2ob4o3bo2bo2bo3b2obo2bobo4bo4bo9b2o2b
obo2b3o2bo4bob2o5b2o3b2obo2b2o4b8o2b2obo2bo3b3o$ob2obob6o4b4ob2ob4obob
obo2b2o4b2ob5o2bo2bo5b2o3b2ob2o3bobo2bo3bo2bob2ob2o3b8o3b4o3b6o3b4ob2o
bo2bo2b3ob2o5b4obo3b2o6b3ob3obobobob3ob4o!
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 7th, 2019, 5:40 am

Neat! There are so many of these things I often don't look at the rules themselves so it's nice to see some of the other interesting things that exist in them.

77topaz wrote:
wildmyron wrote:p279, 3 cells
x = 5, y = 1, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
obobo!


And this rule has a similarly sparky p49 that has a minimum of five cells:
x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!


And a p71 with a minimum of six:
x = 11, y = 11, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
o4$5bo$4bobo$5bo4$10bo!

Hah, and you even apgsearched it. I'm surprised that this little c/3 didn't show up, though there were perhaps not enough soups for that.
x = 7, y = 7, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
4bo$2o3bo$2b2o$2bo3bo$2b2o$2o3bo$4bo!

There's also a 2c/5.
x = 16, y = 15, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
o$3o10bo$bo2b2o7b2o$o4bo8b2o$2bo6b2o2b2o$5bo3b3obo$bo3b4ob2o$b3o2bo3bo
$bo3b4ob2o$5bo3b3obo$2bo6b2o2b2o$o4bo8b2o$bo2b2o7b2o$3o10bo$o!

c/2 seems viable, but I haven't been able to find one.

OK, that was a little diversion, apologies for extending it.
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Re: Smallest Oscillators Supporting Specific Periods

Postby 77topaz » February 7th, 2019, 5:44 am

Nice! The rules with three-cell oscillators do seem to be generally more interesting than the previously posted two-cell ones - because all of those two-cell rules had B2a, and so were explosive.
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Re: Smallest Oscillators Supporting Specific Periods

Postby Hunting » February 7th, 2019, 7:02 am

77topaz wrote:And this rule has a similarly sparky p49 that has a minimum of five cells:
x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!


It has a phase with only four cells...
x = 3, y = 3, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo!

EDIT: Wow.
x = 23, y = 6, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo$21bo$20bobo$21bo!
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x = 4, y = 6, rule = B2e3i4at/S1c23cijn4a
o2bo$4o3$4o$o2bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby 77topaz » February 7th, 2019, 7:36 am

Hunting wrote:EDIT: Wow.
x = 23, y = 6, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo$21bo$20bobo$21bo!


That's an interesting reaction. Unfortunately, because of the large maximum size of the oscillators, it appears it can't be turned into a wick as the different sections interfere with each other:
x = 23, y = 12, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8:T0,12
6$bo$obo$bo$21bo$20bobo$21bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 8th, 2019, 12:00 am

Another update after running my random rule search with maxGen set to 1000:

Summary:
Periods 2 - 112, 2 cells
Even periods 114 - 216, 2 cells
Odd periods 113-119, 123, 127, 131, 137, 139, 163, 165, 189, 191, 263, 279, 3 cells
Even periods 218, 220, 224, 228, 230-234, 240-250, 254, 258, 260, 266, 274, 278, 280, 284-288, 292, 294, 302, 304, 310, 314, 316, 320, 336, 340-344, 348, 356, 358, 368, 376, 392, 396, 398, 412, 420, 434, 674, 788, 998, 3 cells
All other periods, 4 cells


New oscillators:

Odd periods:
p191, 3 cells
x = 5, y = 1, rule = B2-an3cnqry4etwz5ciny6ckn7c/S1e2ek3cen4aknqz5cy6cek7
obobo!


Even periods:
p250, 3 cells
x = 5, y = 1, rule = B2-ae3-jknr4ry5qy6cn7c/S02in3-cn4cejq5-cej6cin
obobo!

p278, 3 cells
x = 5, y = 1, rule = B2-an3acy4cijkw5y/S02aik3jqry4aeikr5jy6e
obobo!

p292, 3 cells
x = 3, y = 3, rule = B2-ae3aeikn4-jwy5cekr6k7/S02n3acikr4-anryz5ckr6e7e8
obo2$o!

p310, 3 cells
x = 3, y = 2, rule = B2-a3aeqry4acjkt5ein6ei7e/S1c2a3ejny4ceijrty5jy6ci7c
obo$bo!

p316, 3 cells
x = 4, y = 1, rule = B2-ak3acek4aetyz5cekr6k/S1e2ak3jn4ckn6ai
2obo!

p340, 3 cells
x = 5, y = 1, rule = B2cik3aceiq4-cnrty5-ajqy6ac7/S1e3q4cijz5ir6cn
obobo!

p342, 3 cells
x = 3, y = 2, rule = B2-a3i4eknw5-jn6in7/S02e3cei5aeqr6-an
obo$bo!

p348, 3 cells
x = 5, y = 1, rule = B2cin3-eknr4cijky5iq6acn7e/S02ai3e4irw5jkny6ak
obobo!

p398, 3 cells
x = 3, y = 3, rule = B2cen3eijkq4acejtw5ej6cin/S01c3kny4aikqryz5iq6ci7
obo2$bo!

p420, 3 cells
x = 5, y = 1, rule = B2-ae3acnry4acity5ajny6ce7c/S12ac3acik4en5cj8
obobo!

p434, 3 cells
x = 3, y = 2, rule = B2-ai3cqry4-acerz5ckny6aek7c8/S12n3ejny4ceijtyz5ciny6c
obo$bo!

p674, 3 cells
x = 5, y = 1, rule = B2-ae3aikq4aeinr5jnr6ci/S13iy4ary5in
obobo!

p788, 3 cells
x = 5, y = 1, rule = B2ci3-jkqy4acejtyz5cek6/S1e2i3aciky4er5ijy6-kn
obobo!

p998, 3 cells
x = 5, y = 1, rule = B2-ai3ikry4ceiryz5-cknr6ce8/S01c2i3cik4cejnwz5ejkny6an7e8
obobo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 11th, 2019, 4:47 am

A final update after a run with the maxGen set to 5000 - one oscillator with period > 1000 showed up. I think this will be my final update to this thread for some time. The 2-cell 9x5 search is still running, but both the forward and reverse searches seem to be bogged down in parts of the search space which are unproductive and I'm going to discontinue them. See the end of this post for progress.

Updated Smallest Oscillators summary:
Periods 2 - 112, 2 cells
Even periods 114 - 216, 2 cells
Odd periods 113-119, 123, 127-143, 157, 163-167, 173, 189, 191, 193, 211, 225, 231, 263, 271, 279, 297, 313, 453, 843, 3 cells
Even periods 218-236, 240-250, 254, 258, 260-266, 270-278, 280, 284-288, 292, 294, 298, 302, 306, 310-316, 320, 328, 334-348, 356, 358, 364, 368, 376, 384, 390, 392, 396, 398, 412, 420, 422, 432, 434, 442, 444, 448, 460, 484, 502, 512, 550, 554, 626, 674, 698, 706, 788, 806, 832, 998, 1010, 3 cells
All other periods, 4 cells

Apologies for the very long post, but I'm not sure how else to share all the new 3-cell oscillators:

Odd periods:
p129, 3 cells
x = 5, y = 1, rule = B2-an3-ijnr4ceintz5acknr6ikn78/S03ajy4aiknw5aiqr6aei7e
obobo!

p133, 3 cells
x = 5, y = 1, rule = B2cin3acnr4-ckrwy5aijy6-ci7/S02a3jky4aijknt5cjkq7c
obobo!

p135, 3 cells
x = 5, y = 1, rule = B2ckn3aciky4eijnrwz5-nqr6ae8/S02a3jnq4jnq5cny6cn
obobo!

p141, 3 cells
x = 5, y = 1, rule = B2cik3aenr4eity5c6k7c8/S12ci3ceq4ceknz5ajqy6ek
obobo!

p143, 3 cells
x = 5, y = 1, rule = B2cek3jkqr4cijqtz5cijnr67e8/S01c2ik3-jq4ckrt5-nqry6an78
obobo!

p157, 3 cells
x = 5, y = 1, rule = B2-ae3-ejnq4enqr5cr6ce7c8/S02in3acikr4cijkqrz5ainy6aei78
obobo!

p167, 3 cells
x = 5, y = 1, rule = B2-ai3cei4cqrtz5-cejq6-ei7c/S01c2e3q4kyz5inr
obobo!

p173, 3 cells
x = 5, y = 1, rule = B2cik3aeijq4-jqwyz5-ijny6i7c/S1e3j4jtz5ry6i
obobo!

p193, 3 cells
x = 5, y = 1, rule = B2cik3-eijy4ijrz5eikry6c7/S02ain3ajkqr4cijqry5acjnr6aik7e
obobo!

p211, 3 cells
x = 5, y = 1, rule = B2-a3eikr4eikwyz5ikr6-ai/S02ei3air4ajkq5cenqr6ik8
obobo!

p225, 3 cells
x = 5, y = 1, rule = B2-an3aejr4einqrw5-eknq6ae7/S02-ce4i5eir6ci
obobo!

p231, 3 cells
x = 5, y = 1, rule = B2-ak3eik4cijq5aijq6acn8/S1e2akn3kn4cny5q8
obobo!

p271, 3 cells
x = 5, y = 1, rule = B2-ae3aciqr4-aejy5nqr6ck7c8/S02-ac3eiry4aejqz5aeq6-n7
obobo!

p297, 3 cells
x = 5, y = 1, rule = B2cin3aijq4jknqtw5akry6-kn7/S01e2ai3ijr4nqtwz5ejqr6ekn7
obobo!

p313, 3 cells
x = 5, y = 1, rule = B2-an3a4acertwz5cqy6ei7c8/S1e2k3ceqy4ertwy5-cejq6c78
obobo!

p453, 3 cells
x = 5, y = 1, rule = B2-ae3aeiqr4cinqwyz5ij6-ci/S02kn3acy4ar5ikqy6ein
obobo!

p843, 3 cells
x = 5, y = 1, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
obobo!


Even periods:
p222, 3 cells
x = 3, y = 3, rule = B2-a3aek4cenrtyz5-cenq6ak7/S02-ce4jkq5cikn6in7c
obo2$o!

p226, 3 cells
x = 5, y = 1, rule = B2-ak3cjq4ny5iq6ci7e/S1e2ik3anqr4eijz5r
obobo!

p236, 3 cells
x = 5, y = 1, rule = B2ein3ijkn4ckqrtw5-aejq6-en78/S01e2ei3aknq4-kqrw5ajnqr6aen7c
obobo!

p262, 3 cells
x = 5, y = 1, rule = B2-a3-air4twz5aeknq6-k8/S12i3iq4ey5ackqr6cn
obobo!

p264, 3 cells
x = 5, y = 1, rule = B2cin3aiqy4cry5cijry7e/S01e2k3acjkn4ijnqryz5cnry7
obobo!

p270, 3 cells
x = 3, y = 2, rule = B2-an3ikn4cei5ejnr6aei/S1c2cei3aejnr4ey5cr6a7
obo$bo!

p272, 3 cells
x = 5, y = 1, rule = B2cen3-ajr4eijry5acikq6ci7c/S02k3cir4cj5cjkn6aen
obobo!

p276, 3 cells
x = 5, y = 1, rule = B2cek3aekq4ekqw5aeiqr6eik7c/S02cin3-eikq4jqrtz5jn6ei78
obobo!

p298, 3 cells
x = 5, y = 1, rule = B2-a3ceijr4cjnqyz5acnqr6cin7c/S03a4eknty5ceiqr6ak8
obobo!

p306, 3 cells
x = 5, y = 1, rule = B2cin3aiq4-jqr5aeikr6kn7e8/S1e2ekn3ijkq4-acnwz5eiqy6ack8
obobo!

p312, 3 cells
x = 3, y = 3, rule = B2-ak3akn4ciwy5aceny6k7e/S12acn3-aijn4aiknz5jknqy6ci
obo2$o!

p328, 3 cells
x = 5, y = 1, rule = B2-a3cnqry4-cijtw5ckqry6cek8/S1e2in3ci4ijq5cy8
obobo!

p334, 3 cells
x = 5, y = 1, rule = B2-a3cn4ejqtwyz5ciny6acn7e/S1e2n3aeikq4kqtyz5acjy6ace7e
obobo!

p338, 3 cells
x = 5, y = 1, rule = B2-ai3-acij4jkrtz5-cj6in7c8/S01c2aen3-aijq4ceijtw5ikny6-ci7c
obobo!

p346, 3 cells
x = 5, y = 1, rule = B2cei3-ajkq4eqtz5-acek6eik7c8/S1e2ikn3anq4cenqty5ajry6ai8
obobo!

p364, 3 cells
x = 3, y = 2, rule = B2-a3y4-ciknt5eqry6cn/S01c2akn3-akr4-aknq5-einr6-ik
obo$bo!

p384, 3 cells
x = 3, y = 2, rule = B2-ak3aq4etz5cejy6a7c/S12aen3cj4ajqtyz5-ciky6ci7c
obo$bo!

p390, 3 cells
x = 3, y = 3, rule = B2cei3ajry4rz5acikn6ae/S01c2-c3iqy4eiz5-eknr6-i78
obo2$o!

p422, 3 cells
x = 5, y = 1, rule = B2-ae3aeik4-aijrw5cikry6ein78/S1e2ein3ackny4cew5enq7e8
obobo!

p432, 3 cells
x = 5, y = 1, rule = B2-ae3aenqr4-jknwz5ckn6akn/S02i3ajk4ijnq5ciny6eik
obobo!

p442, 3 cells
x = 5, y = 1, rule = B2cen3er4acwz5-jqr/S01c2kn3ajnry4-ajnqt5kq6cin7
obobo!

p444, 3 cells
x = 5, y = 1, rule = B2-an3acej4cekqrz5-q6ack/S1e2ci3jkny4aeqr5ackr6-ei7e
obobo!

p448, 3 cells
x = 3, y = 2, rule = B2-a3iq4jnryz5ceiky6-en7c8/S1c2e3aenr4qtw5en6k7c8
obo$bo!

p460, 3 cells
x = 3, y = 3, rule = B2cik3aekn4ntw5cjqry6ae7c/S12ek3iqy4cijrw5aj6acn7c8
obo2$bo!

p484, 3 cells
x = 3, y = 2, rule = B2-ak3ijk4cijkq5eijy6aen7c8/S01c3aijy4cqr5ijqr6ck8
obo$bo!

p502, 3 cells
x = 5, y = 1, rule = B2eik3ik4-a5-ceky6a8/S01c2ack3-acny4cty5ceknq6k
obobo!

p512, 3 cells
x = 3, y = 2, rule = B2-ac3-jnry4eityz5aknqy6n7c8/S2-k3inqr4cqrz5-ikny6in7c
obo$bo!

p550, 3 cells
x = 3, y = 2, rule = B2cei3ajny4eijnqwy5cr6ac7e8/S1c2-kn3ek4jnw5-ejry6cek8
obo$bo!

p554, 3 cells
x = 5, y = 1, rule = B2-ak3ceiry4acekrwz5cer6ik/S12i3cej4-aqtw5-jkqr6cn7c8
obobo!

p626, 3 cells
x = 5, y = 1, rule = B2-ai3ae4-aeijt5-acen6-ek78/S02ek3-aeqy4kq5anr6e
obobo!

p698, 3 cells
x = 3, y = 2, rule = B2-ac3aeiq4krtwz5r6i7e8/S1c2ae3eijy4airt5k6-k7e
obo$bo!

p706, 3 cells
x = 5, y = 1, rule = B2-a3aqr4-aejqt5-anqr6aik7/S1e2i3aeq4ejny5e6ai
obobo!

p806, 3 cells
x = 5, y = 1, rule = B2cen3-aik4ceqrz5-inr6i7c/S02c3ejk4-ajy5ackqy6ai7e8
obobo!

p832, 3 cells
x = 5, y = 1, rule = B2cei3iqry4kntwyz5cijk6acn7e/S12ein3-aijn4ejkrwy5ijnry6acn7e8
obobo!

p1010, 3 cells
x = 5, y = 1, rule = B2-ai3eqry4knqtz5ackn6cik7e/S01c2c3-ckn4cnrt5ajry6ae7e8
obobo!


==========
Edit: Update on 9x5 2-cell oscillator search progress:

Forward search (no output filtering):
Number of iterations = 614335 million
Number of oscillators = 117248244
Progress = 79.4404% (6/8, 2/8, 3/4, 5/16, 28/32, 1/16, 111/128, 26/32, 0/16, 3/4, 1/2, 29/32, 7/16, 1/2, 0/4, 1/4, 1/2, 0/4, 5/8, 0/2, 28/32, 0/2)

Number of iterations = 614340 million
Number of oscillators = 117248244
Progress = 79.4404% (6/8, 2/8, 3/4, 5/16, 28/32, 1/16, 111/128, 26/32, 2/16, 4/8, 1/4, 3/8, 4/8, 0/1, 0/1, 1/4, 5/8, 1/2, 1/2, 3/4, 2/4, 2/8, 0/1, 1/4, 0/4, 0/1, 0/1, 1/4, 3/4, 1/4, 0/1, 0/2, 1/2, 0/2)

Reverse search (results filtered to only include odd period >= 81 and even period >= 160 :
Number of iterations = 919540 million
Number of oscillators = 3
Progress = 14.2759% (1/8, 1/8, 2/16, 11/64, 3/4, 1/4, 2/4, 4/8, 5/16, 0/8, 8/16, 2/8, 1/16, 1/2, 2/4, 1/4, 0/2, 8/16, 2/4, 1/2, 2/4, 0/8, 6/16, 1/4, 1/2, 0/2, 0/2, 1/2, 3/4, 0/4, 0/4)

Number of iterations = 919560 million
Number of oscillators = 3
Progress = 14.2759% (1/8, 1/8, 2/16, 11/64, 3/4, 1/4, 2/4, 4/8, 5/16, 0/8, 8/16, 2/8, 3/16, 1/2, 1/2, 0/2, 0/4, 21/32, 1/2, 0/2, 0/8, 1/8, 0/1, 0/1, 0/4, 0/2, 1/2, 0/1, 0/1, 0/2, 1/2, 0/1, 0/1, 0/4, 0/2, 0/1, 1/2, 0/1, 0/1, 0/1, 0/1, 0/1, 0/1, 0/1, 1/4, 3/4, 0/2, 1/2, 2/4, 0/2)
The latest version of the 5S Project contains over 47,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
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Re: Smallest Oscillators Supporting Specific Periods

Postby Macbi » February 11th, 2019, 7:39 am

Wow! The first period over 1000! Congratulations!

The p1010 has the same minrule and maxrule, so it completely specifies the rule. It's quite a nice rule too, there's a nice 4 cell spaceship and some small oscillators:
x = 34, y = 80, rule = B2-ai3eqry4knqtz5ackn6cik7e/S01c2c3-ckn4cnrt5ajry6ae7e8
o7bo6bo$2bo3bo6bo$b3o4b2o5b2o$2b2o4b3o4b3o$8b2o6bo$18bo5$2bo$b3o2$b3o$
2bo5$6bo$bo3bo$4bo$3bo$2bo$bo3bo$o5$2bo3bo5bo7bo2bo$bo3b4o2bob2o6b2o8b
obo$o4b4o3bobo5b4o6b3o$7bo5bobo3b2o2b2o4bob2o$13b2obo11b3o$15bo13b2o$
28bo6$2bobo$b2o$ob4o$b2obo5$o$2bo2$2bo$o25$obobo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby 77topaz » February 11th, 2019, 4:39 pm

wildmyron wrote:p460, 3 cells
x = 3, y = 3, rule = B2cik3aekn4ntw5cjqry6ae7c/S12ek3iqy4cijrw5aj6acn7c8
obo2$bo!


This rule has a natural 4c/30 orthogonal which pushes an octomino:
x = 7, y = 3, rule = B2cik3aekn4ntw5cjqry6ae7c/S12ek3iqy4cijrw5aj6acn7c8
bob4o$5obo$bob4o!


wildmyron wrote:p843, 3 cells
x = 5, y = 1, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
obobo!


And this one has a natural c/7 orthogonal:
x = 4, y = 5, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
3bo$3bo$3o$3bo$3bo!


And a nice p9:
x = 9, y = 3, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
bo5bo$obo3bobo$bo5bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby Hdjensofjfnen » February 11th, 2019, 6:18 pm

Period 20200:
x = 66, y = 8, rule = B345/S5
4bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$2bobo3bo
bo3bobo3bobo3bobobo5bobo3bobo3bobo3bobobo3bo$2bobo3bobo3bobo3bobo3bobo
7bobo3bobo3bobo3bobo7bo$obobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobo$bo3bobo3bobo3bobobobo3bobo3bobo3bobo3bobo3bobo7bobo$
3bobobobobobobobobobobo3bobo3bobo3bobo3bobo3bobo3bobobobo$3bobo3bobobo
bo3bobobobobobobobobobobobobobobobobobobobo3bo!

EDIT: 188 cells, so not that impressive.
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby muzik » February 11th, 2019, 6:21 pm

Hdjensofjfnen wrote:EDIT: 188 cells, so not that impressive.

Precisely, given that that's quite a lot bigger than 4.
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Re: Smallest Oscillators Supporting Specific Periods

Postby Moosey » February 11th, 2019, 6:22 pm

Hdjensofjfnen wrote:Period 20200:
longlife

EDIT: 188 cells, so not that impressive.

Isn’t that a trivial oscillator too? Or does some cell oscillate at that period
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 14th, 2019, 11:43 pm

wildmyron wrote:A final update after a run with the maxGen set to 5000 - one oscillator with period > 1000 showed up. I think this will be my final update to this thread for some time. The 2-cell 9x5 search is still running, but both the forward and reverse searches seem to be bogged down in parts of the search space which are unproductive and I'm going to discontinue them. See the end of this post for progress.

Well, I couldn't bring myself to kill that search off completely, so I left the reverse search running. 4 days later and it has progressed from 14.2759% to 14.2806%, but this morning it finally reached an interesting part of the search space and the number of oscillators found has jumped from 3 to > 18000.

Here are some new periods for 2-cell oscillators:
p218, 2 cells
x = 3, y = 1, rule = B2-cn3ejnq4ejntw5-jky6cek8/S01e2ikn3-in4-tyz5-ajnq6-kn
obo!

p220, 2 cells
x = 3, y = 1, rule = B2-ck3acek4ijktwy5-akq6ace/S01e2in3-ci4aejwy5-jqr6cei7e
obo!

p222, 2 cells
x = 3, y = 1, rule = B2-cn3-aci4ejkny5cijn6c7e8/S01e2ein3-aikn4-tyz5-nq6cik
obo!

p226, 2 cells
x = 3, y = 1, rule = B2aei3aceqy4cjknw5-ak6-cn7e/S01e2ikn3acejq4aeijnqy5-y6-an7e
obo!

p234, 2 cells
x = 3, y = 1, rule = B2-ck3aceqy4ijktwy5-qr6cei/S01e2i3-cijy4-inqtw5ekny6-kn7e
obo!


I'm quite surprised by the jump from p226 to p234. Those two oscillators are the only 2 found with period greater than 222 and nearly all the other searches I've done have had only small gaps between the highest periods found as well as a large number of results at slightly lower periods before the new record high period was found. The 3-cell random rule search behaves quite differently, which I suspect is because it doesn't have the same bounding box restriction.

Updated Smallest Oscillators summary:
Periods 2 - 112, 2 cells
Even periods 114 - 222, 226, 234, 2 cells
Odd periods 113-119, 123, 127-143, 157, 163-167, 173, 189, 191, 193, 211, 225, 231, 263, 271, 279, 297, 313, 453, 843, 3 cells
Even periods 224, 228-232, 236, 240-250, 254, 258, 260-266, 270-278, 280, 284-288, 292, 294, 298, 302, 306, 310-316, 320, 328, 334-348, 356, 358, 364, 368, 376, 384, 390, 392, 396, 398, 412, 420, 422, 432, 434, 442, 444, 448, 460, 484, 502, 512, 550, 554, 626, 674, 698, 706, 788, 806, 832, 998, 1010, 3 cells
All other periods, 4 cells
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Re: Smallest Oscillators Supporting Specific Periods

Postby Hdjensofjfnen » February 15th, 2019, 12:10 am

wildmyron wrote:Periods 2 - 112, 2 cells
Even periods 114 - 222, 226, 234, 2 cells
Odd periods 113-119, 123, 127-143, 157, 163-167, 173, 189, 191, 193, 211, 225, 231, 263, 271, 279, 297, 313, 453, 843, 3 cells
Even periods 224, 228-232, 236, 240-250, 254, 258, 260-266, 270-278, 280, 284-288, 292, 294, 298, 302, 306, 310-316, 320, 328, 334-348, 356, 358, 364, 368, 376, 384, 390, 392, 396, 398, 412, 420, 422, 432, 434, 442, 444, 448, 460, 484, 502, 512, 550, 554, 626, 674, 698, 706, 788, 806, 832, 998, 1010, 3 cells
All other periods, 4 cells

Hmm... so I propose a conjecture. Can someone prove or disprove it?
Every period of oscillator can be achieved in three cells or fewer.
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My favorite oscillator of all time:
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4b3o$6bo$o3b3o$2o$bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby wildmyron » February 15th, 2019, 6:26 am

Hdjensofjfnen wrote:Hmm... so I propose a conjecture. Can someone prove or disprove it?
Every period of oscillator can be achieved in three cells or fewer.

I'm fairly certain this conjecture is true, certain enough that I'm sure it couldn't be disproved. Proving that it is true requires showing that there are rules which contain 3 cell oscillators with adjustable period. I think the easiest proof would be to actually construct/discover said adjustable oscillators. The earlier posts by Macbi speculating on this topic, and A for Awesome showing a failed version of this idea are enough to convince me that it is possible to find such oscillators. It is worth noting that the quad wickstretcher and its interaction with the dot work in 2^61 rules. And there are many other possibilities for growing patterns plus interaction with a single dot which broaden the rulespace which could be used. Here are a few (non-adjustable) oscillators which show a dot hassling the quad wick-stretcher. They come from a brief random rule search I ran to explore this possibility. Neither of them actually has a 3-cell phase but that's mainly because of the way I set up the search.

#C p37 oscillator
x = 8, y = 3, rule = B2cei3aq4-cjknq5q6i/S01c2ain3jkry4ejt5ceq
bo$obo4bo$bo!

#C p56 oscillator
x = 10, y = 1, rule = B2cei3acr4-jknqy5ceiny7e/S01c2ai3cejqy4eint
2obo5bo!
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Re: Smallest Oscillators Supporting Specific Periods

Postby muzik » February 15th, 2019, 8:12 am

There's on obvious way to get 2-cell for every period, but we're only counting 2-state I'm assuming, so this wouldn't count:
x = 3, y = 3, rule = 01c/2n/7
2.A2$A!
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Re: Smallest Oscillators Supporting Specific Periods

Postby Sarp » February 16th, 2019, 3:20 pm

Here are some new periods
B2-a3acjkq4cijqrz5aik6-n7c/S01c2ekn3-aeik4ijqtwy5acejy6ai7c8, obobo!, Period 181
B2cei3-aeq4eiq5aejnr6ain7c8/S02cn3acery4aejknty5-cjky6-ek7e, obobo!, Period 365
B2-an3-anqy4acnrtwy5enqy6-kn7/S02n3ekqy4cekn5-jnqr6c7c, obobo!, Period 229


Edit:
p282
x = 5, y = 1, rule = B2-a3ei4aikrtwy5acq6-ce8/S02ikn3aeiqy4ceijqy5-jky6-ai8
obobo!


p330
x = 5, y = 1, rule = B2ci3-einq4ceiqtw5-ciqy6ikn7/S01c2ekn3iqry4-ejkqr5-cjny6-e7
obobo!


p238
x = 5, y = 1, rule = B2-an3cjry4ajknry5ijkry6-cn7c8/S02ikn3-aekn4ciknr5ciqy6-k7c
obobo!


p498
x = 5, y = 1, rule = B2cin3ajk4-cnrtz5ejkny6-k8/S02-n3ei4ejqrw5aekqr6-an7c8
obobo!


p185
x = 5, y = 1, rule = B2ci3-nqry4aerz5ikr6aik7c8/S02cin3cij4cery5-akqr6ain7e8
obobo!


p380
x = 5, y = 1, rule = B2-a3-aejn4cnwy5-einy6-n8/S01e2e3acery4ejkqrty5ceiy6aei7e8
obobo!


p505
x = 5, y = 1, rule = B2cik3aeikq4aenr5-acn6cen7e8/S02ci3eijkr4acinwy5cij6a7e
obobo!


p145
x = 5, y = 1, rule = B2ci3acqr4eijqr5-acjk6c7e8/S02-ck3-ckqr4cikntz5cknqr6-n7e
obobo!


p572
x = 5, y = 1, rule = B2cin3aceir4aeijnwz5-ir6-ek78/S02ei3acek4aceqrtz5aer6ce8
obobo!


p161
x = 5, y = 1, rule = B2ci3acky4cinry5-einr6a/S02eik3aijry4crz5-nry6-cn7c
obobo!


p149
x = 5, y = 1, rule = B2-an3-aeiq4ceknryz5knqry6c8/S02ikn3-eikq4-aintw5ajnq6eik7c8
obobo!


p756
x = 5, y = 1, rule = B2-ae3aekry4aeit5-cek6k/S01c2ein3-cnqy4ajnrwy5eky6aei
obobo!


p322
x = 5, y = 1, rule = B2-a3-aiy4ckt5aeqr6cei7c8/S01c2ac3kq4-crtz5-cqry6ae7e
obobo!


p199
x = 5, y = 1, rule = B2cin3aeijq4aceqwz5ckr6-kn78/S02ik3-aeky4jtw5cjkn6cek7c8
obobo!


p145
x = 5, y = 1, rule = B2cin3-cjnq4-acny5acijr6ckn8/S02aek3ckqy4ejknwz5enqr6aik
obobo!


p227
x = 5, y = 1, rule = B2cin3aikq4aciqtw5jny6-en8/S01e2kn3eiq4aceijz5jnqry6-i78
obobo!


p988
x = 5, y = 1, rule = B2cin3aikry4-anyz5jknqr6cn7e8/S02akn3aejr4einqw5aejnq6cek78
obobo!


p716
x = 5, y = 1, rule = B2cik3ajqr4ceinq5jkr6-ce7e/S02eik3-akn4aekny5-ekny6-ac8
obobo!


p826
x = 5, y = 1, rule = B2cik3aeknr4enqrty5-ikqr6-c7c8/S02ae3aceny4aceiqtz5-aeiq6ck
obobo!


B2cik3aeikr4ijw5-nqr6ckn8/S02ain3-jkny4cjnqy5-aiqy6ck7c, obobo! Period 606
B2cik3-ikny4aijknrz5-aejn8/S02-ae3cejky4ijqtw5knr6ae8, obobo! Period 678
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