Smallest Oscillators Supporting Specific Periods

[Macbi]

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:

Code: Select all

x = 1, y = 1, rule = B1c/S
o!

and technically the smallest period 1 oscillator has 0 cells:

Code: Select all

x = 0, y = 0, rule = B/S
!

So we have

Code: Select all

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

[wildmyron]

p214, 2 cells

Code: Select all

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

[wildmyron]

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:

Code: Select all

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:

Code: Select all

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

Code: Select all

x = 5, y = 1, rule = B2-ae3aikny4ckqy5-ain6ek/S1e2i3-ceir4eij5j6i
obobo!

p115, 3 cells

Code: Select all

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

p123, 3 cells

Code: Select all

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

p131, 3 cells

Code: Select all

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

p137, 3 cells

Code: Select all

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

p163, 3 cells

Code: Select all

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

p279, 3 cells

Code: Select all

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

Even periods:
p218, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cen3eiy4centz5jqy6-ek/S01c2en3cjq4-nryz5einry6a7e8
obobo!

p220, 3 cells

Code: Select all

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

p228, 3 cells

Code: Select all

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

p230, 3 cells

Code: Select all

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

p242, 3 cells

Code: Select all

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

p244, 3 cells

Code: Select all

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

p246, 3 cells

Code: Select all

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

p254, 3 cells

Code: Select all

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

p258, 3 cells

Code: Select all

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

p260, 3 cells

Code: Select all

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

p266, 3 cells

Code: Select all

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

p280, 3 cells

Code: Select all

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

p284, 3 cells

Code: Select all

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

p288, 3 cells

Code: Select all

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

p294, 3 cells

Code: Select all

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

p302, 3 cells

Code: Select all

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

p336, 3 cells

Code: Select all

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

p356, 3 cells

Code: Select all

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

p396, 3 cells

Code: Select all

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

p412, 3 cells

Code: Select all

x = 3, y = 2, rule = B2-ai3jk4eiqt5aciq6aek8/S12cen3-einr4ny5ary6aek8
2o$2bo!

[77topaz]

p228, 3 cells

Code: Select all

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:

Code: Select all

x = 4, y = 4, rule = B2-a3ajy4aejkwy5qr6n7/S01c2ce3eik4e5jn6k
o$bo2$3bo!

p279, 3 cells

Code: Select all

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:

Code: Select all

x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!

And a p71 with a minimum of six:

Code: Select all

x = 11, y = 11, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
o4$5bo$4bobo$5bo4$10bo!

p284, 3 cells

Code: Select all

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

This rule, meanwhile, has an impressive class F (?) replicator:

Code: Select all

x = 188, y = 186, rule = B2-an3aq4c5iy6i/S01c2n3nqy4cejkwy5aeik6aik8
ob2o6bo3bob3o3bob3o5bo9bo4b4o2bobo3b2ob7o2bobob2ob2o5bo5b7o2bob3obo2b
5obobo3b2o5b3o3b3obo2b2obob2obo2b3o3b2o2b4ob2o2bobobob3o3bo3bo$2ob2obo
5b2o4bo2b2o2b3o4bo2b5o2bobobo3b2o2bo2b2o2bob2o3b2obo3bobobobo2b5obo3b
4ob2obo2b2ob2o2bob5ob2o2b5o3b3o2b2o2bo5bo4bob3obobo2bo5b5o2b2o2b2o3bo$
bo5bo4b4ob3o3b2o2b2obo3b4ob3obobo3b5ob3obo2b2ob2ob9obob2o2b5o2bo2bo2b
7obo3bo2bo3b2ob3ob2o3bo2bob3o2bo4bobob2obob3ob5ob3obobobo2bo2bobob2o$b
2ob2ob2obob2o2b2o6bobo2bo2b2ob6o3b2o4b7obo2bo2b5ob2o6bo2bob2obobo3b2ob
3obo3bobob2o3b4obob2ob3o2bob5ob3obob7o3bo2b2o5bo2b5obob3ob2o5b3o$bobo
4bo7b2ob2obobo5b4obo3bo3bo2bobo5b5o2b6obobobob2ob2o3b3ob3o3b2ob3ob2o4b
obo2b2ob2o2bobo3b2o7bobo7b6o5b2obob2obobo3bo4bob3ob2o2bobob2o$bo2b2ob
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4ob3o3bobobo3bobo2bo2b2o2bo3bo$4obo2b4ob3ob2ob5obobobo2bo2b2o2bob2o3b
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4bo2bobobo2b2o2bobo2b2obo2bo3bob2ob2obo2b2o3bo2b5o3b3o2b3o$bo5bo3bo2b
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2b2ob2o4bob2ob4o2b2o6bo2bo3bo2b2o2b4o3bobo8b2ob2o2bo$2bobobobobobo6bob
2o4b2o2b4o2b2o2b3o2bob3o2b3o7b2ob2o3b3o2b2o3b2o3bo6bob2o2bo2b2o4bob2o
3b3ob5ob2ob2obobo2bobob2ob3ob2o2b2o2bob3ob2o3b3ob5o4b5obobo$obo5bob2o
2bob2o7b2obo2b2ob5o2b4o2bo2b3o2bo2bo2bobob3o4bo2b2o2b4ob2obobo3b7o2bob
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4obo2bo3b2ob3ob3o4bob2ob3o2bo5b2obob4ob2obobo2bo2b3o7bo2b7obo$2b3o2bob
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3bo2b4ob2ob7o2b2obo2bob2o2b4ob2ob5obobo3b2obobo3bo2b2o2bo4bobo5b2o$3bo
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bob2obo2bo2b4ob3ob3ob6o2b2ob2obobobob2obo2bo7bobo2b3o2bob2o2b3ob2obo$
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2b2o2b3o2b4o3b2ob3ob2o3bobob2obo10b4o2bo3bob2o2bob2obo3bob2ob2o6b2o2b
3o$b2obob2ob5ob3obobobobo4bo8b2o3bobob2o4bobo2bo3b4ob4o3b2o2b2ob3o2bo
6b4o4bo2bobo2bobo3bo5b3o8bobobo4b2o2bob4obob2obob2ob2o5bo3bob2o5bo2b2o
$obob2o2bobob5ob2ob4o2b2obo2b3o4bob2ob7ob5o2bo2b3obo3bo2b2obo2bobob4ob
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3bo2bo$bobobo3bo2b3o2bobob4o2bob4o2bo2b10obobobobob2o2bo2b2o2bo4bobobo
2bobo3b2o3b2o3b2o3bobobo4bo4bobo2b2o2bobo3b3o2bo11bob2o2bobo2bo2bo4bob
2ob3o3b3o3b5o$2o2b2ob3o3b3o4bo2bobo3bo2bob2o2b4obobo2b2o3bo2b4obobobo
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2b2obobobobo2bo2bob5o2b2o$o2bobob2o3bo4b4obo2b5o2b2obobobo2b2o2bo3bo3b
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2o3bo2bob2ob2o3bo4bobo2b2ob2obo5b2o2bob10obo3b2o3bob2obob3o2bobo2bo3bo
b4o2b2o2bo5b3o2b3obo5b3o$2bobo5bobo6b2ob2ob4o3bob2obobo4b5obob2o2b2o3b
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4b4obo3bo3b3o2bo4bobo2b2o4bob2o$3b3ob2obobob2o2bo2b2ob3o2bo3b2ob4o5b2o
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4bo2b2ob2o2bo2b3obob3o2b3obo3bobo2bob2o3bo4b2ob2obo$2ob2o4bob2o4bo2bob
ob3obo2b2o2bo3bob3obob7ob5ob3ob3obo2bobo2b2o4b2ob2o2b2o3bo2b2o2bobobo
5bo2b2ob3o2bo2b2ob3ob3o4bo3bob2ob2o2bobob2ob3ob2ob4o2bo5bo2bob4o$b4ob
2o2bobob2o6b2o3bobo3b3o4bo4bo2bob2ob3obobo2bo2b3ob5o2bob3o4b3obob2ob2o
b2o2bob3o2b4ob2o2bo2bob3ob5ob4ob3o4b2ob2o4bo2b2ob3obo4bo3b2ob2ob2o2bob
3o$o5b2o6b7obo3bobobo2bob2o2b7o2b4o4b3ob2obob2o2bo3b2o2b2obobobo3bob5o
2bo3bobo2b2o3b2obo3bobo3b4o5b3o3bob3o3bobo7b2o4bob4ob2o3bobob2o2b2ob2o
$o3bobo2b7o4b10obobo2b4o2bo3b5ob4o4bo2bobobo4bobobob2o4b2o3b3obo2bo3bo
b2obo2b2o2bob4o2bobo2b2ob6o3bo4b4o6b3obobo2b3obo3bobo2bob10o$o3bobo2bo
2bobo3bo6b2o3bo2bo2bo2b4o2bo4bob3o2b2o2b2ob2o3b4o3bob2ob2o2b2o3b2obob
2o2bob2o2bo2b3o4bo4bo2b3ob3o4bo2b6obob2ob3o4b2o2bob3o2b3obob5o4bo$4ob
4o2b2o3b3o7b2ob4ob3o5b4o2b2o2bob2obo3bob3ob3o7b3ob2o2bo4bo2b2ob3o3bob
5ob2o4bo2bobob4obob4ob3o2bo2b2ob5o4b2o2b7ob5o3b2o2bobo4bo$o4b2o3bobo2b
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2o3bo3bobob3o3b2o3b2o2bobobobobo3bo2b3o2b2obobob2o2bob2obo3bo$4ob5o2b
3o2bobo2bo2b3o2b6o3bob4o2bobob5o3b12ob2obo4b2o3b3ob2ob2obob4o2b2o3b3ob
2o3bo3b2o3b2o2b4o2b3o3bo3b3o2bo2b2obob6ob4o2b2o8bo$2o3b6obob3o2b4o4bob
2o2bo3bo4bo3b3o2bo8b3o7bob2o3b3ob2ob2o3bo3b2obob3o3b4o6b3ob4ob2o2bo2b
3o2b3ob2o2bobo5b3ob2ob3obobob4o4bo5bo4b3o$2ob6obo4b2ob2obobo2bo4bo2bo
2b2o2bobob2o2bobob2ob4o2bob3ob2obo2bob4ob2o7bo2bo8b3ob2o4b3o3bo2b3obob
2o3b4ob2o2bob2ob2obo2bob3o4b2o2bobob2obo3b4o3b2obo$2bobo2bo2bobo2b4ob
7ob7obob3o3bob3obob3obo3b3ob2obo3bob2o2bo2b2o3b2obob3ob2ob2o2bo3bo4bob
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3b2ob4o2b3ob3obob3o2b2ob2obo2bo3b4ob3obob3o2bo2bobob2obo2b2o4b6ob5obob
3obobobo2bo3bob2obo2bob5o2bo2b2obobobo3bobo3bo2bo2b3o2bo2bo2bobo3bobo
2bo2b4o$3o6b3o3b2o2b3obo2b5ob5o3bo2b5o5b3o2b9ob2ob3o3bob2ob2ob2ob2o2b
4o5b5o2bo3b4ob2ob2obo3b2ob4obobob2obo3b4o2bob2o4b3o2bobob3o2b4o4bo$o2b
3obo2b4ob2ob2obo2bo3bo3b2o2bob2o4b6o2bob2obob2o3bobo2bo3b2o4b3ob2ob4o
2bob2o2bobob3obo2b3o4b2o2bobo2b3ob2o2b5obo5b2obo2b2o4bobo2bobob2ob2o2b
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2o2bobobo4bob2obo2b2o4b2obo5b2o3b3o2b2obo2b4ob3o2bob3obo3b2obobob2o2b
4obob2o4bob3o2b3o3b3o2bo$2b3ob2ob3o3b5o3b2ob4ob3obob2o7bob2obo2b4o2b3o
bobob6o5b3o5bobo2bo3b2o2b2ob3ob2ob2ob2ob2o2bobo2bo3b9ob3o2bo2b4o4b2o2b
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2o2b3o3b2ob2o2b3obo2b5obob4o3bo2b2obob2o2b2o6bo2b2obob2o2b2o3bo2b2o2b
4o2bobo7bobobob4o3bobobobo2bo2bo2b3obob2o$o2b3ob5ob3o2b6ob2obo2b2o4bo
2bo2b2obob2ob4o2b5obo4bobob4o2bobobob2obob2obo2bobobobobo3bo2b3o7b2ob
5o3bo2bo4b3obo8b4obobo3b4ob3o3bob2obo6b2o$o3b7ob2o3b2o2bo2b2obo2bob2ob
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3o6b8obo4bo2b2o2bob2obob3o2bo5bobo3b4obo2b4obo3bobobo4bo2b4obo3bob2o3b
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3o2bo2bo3b3o2bobo4bobo7b4o2b2ob3o4b3obobobo3bobobobob2ob2obo3bo2b3obo
3b2o2bo4bo2bo4b2o3bob2obobo3b4ob4obo4bo$ob2obobo5bo6bob2obobo2bo4b2o3b
5o3bo3bobo3b5o2bo3b3o9bob3o2b4ob5o2bo2bo3bob2o3b2o2bob2o4b3ob2o3b2o3bo
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2b2o2bob2ob8obo5b4obobo4bob2ob3ob3o3bobob7obobo2b2ob4o4bobo3b2o3b5o2b
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2bobob4ob2o3b2obo2bob3o6b2obo3b2o2bo$4b3o2b2o3b2o2b6o7b3o5bobo2b3obob
3ob2o2bo2bobo3b2obo2bo2bob5obo2b2ob2o2bo2b2ob2obo3b2obob3obo2bob2ob3ob
2ob2ob4ob4o3b3obob2ob2ob5ob3ob3ob2o3bob2ob3o$6o2b3o2b3obo2b3obo3bo4b3o
2b3o2bo7bo7b2ob2o3b3ob2obo3b3o2bo2b2o2bob4o2bob4o3bob2ob2o2b3o2bobo2bo
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2b2o3b2ob2o2b2o5bobo4b2ob4o2bo3b7ob4o3b8obob9o2bo$b3o3b3obo4b6o4bobo4b
2obob2obob2o3bo2b2o2bob3o2b3ob2ob2ob4obo2bob3o2bo7b3obo2bob2o2b3o3b2ob
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3b2ob4o3bob2obob3ob7o2bob2o2b3obob2obo3b2obo3bo4bob2o2b3o2b3o3bo2bobob
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3obob5o2b2o4bo2b3ob5ob3o4b3obob2o3b2o3bobobo2bo6b2ob3o3b3ob2o12b4o5bob
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2o2bo2bo3bo2bo2bo3b3o4b2ob6ob3obobobo2b4o4bo2b2ob2o2bobobo2bob2ob2o8b
3obobobob2o2bob3obo2bob3o3b2ob7o6bo4b6ob3obob2ob2o$2bobo2bob6ob2o3b2ob
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3ob2o3b2o8b2o3b5obo3b2ob2o4b5o3b2o2b2ob2obobob6obo4bo2bobobob2ob4o2bo
2bob2ob2obo3bo2bo3bob2ob2o2b4o2bo2b2o3bo$bo3bob2o2b3obobob2o2b3ob2ob
10o3b2ob2o3b2o2b5ob2ob2o2bob2obo2b2obo3bo2bob2o2b2o4bobo3bob2obob2obo
2b2o6b2obobob7o4b2o2bo3bob4o2bobo2b2o2b3obo4bobo2bo2b3o$4ob3obob2o3b3o
7b7o2b3o3b2o4b3o2b2o3bobo2bob2ob3o2b3obob4ob2o4b2o6b2o2bob2o4bo3b3obob
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4bob2o3b2ob2ob2obo3bo2b7o2bo12bobobo4bobob3o2b2ob5obo2b3o$o2bob4obo2bo
9bo5b4ob4ob2o5b3o5b2obo2bob2obob2o3bobob2obo3bo2bob5ob3o10bo2b2obob3o
2b4o2b2obo3bobobo3bo2b6obob4o2bobob2o3bo2bo3bo3bo5b2o$2o2b3o2bo4b4o3b
3obo2bobobobo3b2ob2obobob2o2bob3o2bob7o2bob2ob2o3bo5b2ob2o2b4obob2ob2o
bo2b2ob2ob2o3bo5b4ob2o2b4o2b5o5bob2obo2b2ob2o4b3obo2b3ob3o5bo$3b2o3bo
2bo2bob4o2bobo2bo3b6ob2ob4ob7obo3b2o3b2obo3bobo3bo3b4o2b2o4bo5b3o3b4o
3bo2bo3b3obob3o2bob4o2bo2bobobob4obob3o5bo4b5o3bo2b3o2bo3bo$2bob2obob
2o2b7ob4o2b2o3b4o4bobo2bo2b2obob3obo2bob4o2bo2bob6ob2ob4o2bob2ob3obo5b
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3o$5ob2obobo2bobobobo2bobob2ob7o3b2o3bo3b2o4b2obo4bo2b3ob3o4b2o4b2o3b
2o8b2ob2o3bo3b2ob4obob3ob2o2bo2bob2obo4b2ob2o4bo3b4o2b4ob2obob4o2bo2bo
2b2o2bo$3ob2o2bo3bo2b2o2bo3b3o2bo2bo3b7o5bob5o2bo2bobobo2b2o3b2o5bo2bo
3b9ob4o3bob2o3b3o2b4obob3obobob3o2bobo4b2ob4obobo2b2o2b2obob3ob4o3b3ob
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b2o3b6o5bo2bo4b2obo4bob7obob4ob4ob2o4b2o2bobo4b3ob3obo4b2ob3o5b2obob2o
$b2o2bo3bo2bobobo3b3ob2ob2o2b4o4b2o2bo3bobo2bo2b3ob4obo3b2o2bobob2ob4o
2bo4bobo3bo2b2ob2o2b2o4b5obob2o6b3o2bobo4b2o2bo2b2obo2bob4o3bobo4bob2o
b2o3b5o2bo$3o2bo2b2o2bo3b3o6bo3bob2o2bo2b3o6b2obo3b3ob2ob4ob3o2b4o2b2o
b3o2b2obob2o5b2o3b2obo3b3o3bo6bob2o4b2ob2ob4o2bob4o2b2obo2bobobob4obo
5b2o5b2ob2o2bo$2ob2o2b3o7bo2bo2bo2b2o3b3ob3o2bo6b4ob4obob3obo2b3ob2obo
2b5o4b5o4bobob4o2bo2b4obobo3bo2bo3bob2ob3o2bo2b2obob2obo3b2ob2o4bo3bob
2obo2bo2b3o2bo5bo$ob2o3b2o4bob3ob8o2bo2b2obob2ob8o4bobobob2o2b6o6b2o2b
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3b3o5b2obo$b2o3b6o4bobobo2bob2o4b2o2bo5bo3bo2b5o3b3obo2b6ob3o5bo4bobo
3b4obobo7bo2b3ob3o5bob8ob3o2b3obobo3b2ob4o2bo5b7o2bob5obo4bobob2o$obo
4b4o2bob2o2b2o4b5o2bobo8bobobob2o3bobo2b4o4bo8bo2b2o2bobo2bo2bob2obo4b
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bobo2bo2b2obobob7obobob3o2b2o2bo5b2ob2o2b2obobob3o3bo3b2o3bob7o2b2obo
4b2o$o7b2o4bo3b9o2bobob2o2b8ob3obob2o2b4ob3obob2o3b5ob5o4b4o2bobob3o3b
2ob2o3b2obo2b7ob2o2b2o3b4ob2o3bo2b2obob5o2b7o2b3ob6obobobo2bo$2ob3obo
2bo5b3obo2bob2ob7obob3obo4b2o2b6o4bob6ob2o2b2o2bobo3bobob2ob3obo2bo2b
2o2b4o3bobobo3b3obob2o2bob3ob3obo3b8ob6ob3o3b3obobob5o3b3o2bo$ob3o9bo
5bo2b3o2bob2o2b3ob3ob2obo3bob2obo2b2ob3ob3obo2b2o4b7o4bobo4b2o2bo5b3ob
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2b3o6b3obo3b2ob2o2b2obo2b3o2bobo2b4ob2o3b7ob3obob3o5b2o3b3obob5obobob
4o2bo6b5o2bob3o6bobobob5o2b2obobo4bo4b2o3b2o2b2obobo2b2o$2b2obo3b3obo
3bob2obobobo2bobob7ob3ob2ob2obob2ob3o3b2ob3obob4ob2ob4o2bo2b3ob3o8b2ob
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6ob2o2bobo2b3o6bo5bo3b2o2bobob5o4b7o2bobob3ob4o2bobobob2ob3o2b2ob2obo
3bob2o2b2ob2o2bo2b2o2bob2ob2obo2b3ob4o6bob2ob6o2b2obobo2bo3bo2b5obo$4b
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2bob2ob2o3bobob3obob2obob2o2b5o4bo5b2ob6ob11o2bo5bo4bo3b5o3bobo3bobob
2o2bo$obo2bo3b4ob4ob2o2bo4b3o3b3obob4o2b2o3b2o2b9o6b2o2bo4b4o4b2o2bob
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3bo3bo2bobobo2bo2bobob2ob2ob4o2b2ob2obo2b7obo3bobob4obo3b5o5b2ob3o2b4o
3bob3obo4b7o2bo$bobobob3obo3b3o10bo3b2o2b5o3bobo2b2ob4o2bo2bo2b5obo2b
3ob2o3bobo5b4obobobob7o2b2o2bob4o5b7o3b2o2bob2o2b2o2bo2b2o2bobo2b5o2bo
bo2bo4bob3o4bo$o2bob2o3b4o9b2obo2bo2b7o2b2o4b3obo2bob2o4bob4o2bo3b4o4b
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3ob2obo3bo3bob2o4b2ob2obo2bob3ob2ob4o2bob2ob2ob2o3bobo2bo3bo4bobob4obo
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2obo2bo3bob2ob2ob2obob4obobob2o2b2o2bo$2bob7ob2o2bo3bo2bo6b2obob2o2bo
5bob2o3bo2b5o2bob3ob2ob3o2b6o4b3o2b3o5bo2b6obobo2bo4bo2b4o4bo2bobob3ob
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5b2ob2obo2b4o2bob3obobo3b2obo3bo2b2o$3obo4bo3bob3ob3o5bobobo3b2ob2ob3o
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4b2ob3ob3obo2bob3obo6b2o$b2obo3bo7bob2o3b3o2b3o2bo2b2o3b2ob4o2bobo2bo
3bob8obo3bo3bobobo4b2obob6o2b3obobo2b3o5bo2bob2ob4obobo3bo6b3o6b2obo2b
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5b2o6b5ob2o6bo4bobo2b7ob2o3bo3bob2obo5bob2ob2obob3ob2ob2ob2o2b3o3bo2bo
2bobo3bob3o2bobob3o8bo2bo$2o2b2obo3b4o2b6ob3ob4obob2o3bobob8o2bob16ob
3obob6ob4o2b3o2bo3b3o5bo2b2o3bobobob2ob2ob2o2b3obob3ob6obob3ob6obo3b2o
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3bob6o4b3obob3o2b4obo4b2o2b2ob2o3bobo3bo2b2o4b4o2bo3bobo4b3ob3obobo6b
4obo4b3o2bobobo$2ob2ob6o2bob4o2bob6o2bo2b2o7bo2b2ob2ob2o6bobob2obobobo
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3b2obo2b3o3b2o2bo3bobo4bo2b3o4bob2obobob2ob2o4b4o3b2o2bo2b6ob2ob8o2b3o
7b3ob7o3bo2b6o$4o3bo4bo2bo2bo2b3ob3obob2ob2obob2ob2o2bo4b2obo4bo2b4o4b
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2ob2ob3o3bob2o5b3o8b3ob2ob4ob2o2bob2ob3obobob2ob2ob2ob4obob2o2b3o2bo3b
5o2bob2o2b4obo$bobo3b4obo2bo2b2o3b2o2bo2bo2bo2bo2b3o3bo3b3o4b2o2bo2bob
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b2o2b2obo5b7obobo2bo2bo11bobo2bo2b3o2b3ob5o5b4o4bobobob4obo2bob4ob2ob
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ob2ob4o2b4ob2o3b2obo2bo2bo$6o2b5obo4bo2b3o4b2obo4b5o2bobo2bo2bo3bobobo
bobo3b2o3b2obob2ob2ob9o4bo4b4o5b8obob2o3b2o7b2o2bob2o3b2obob7ob2o3bo4b
6o3bob2o2b3o$2o2bo2bobo2b4obobobob2ob2o4bo3b4o2bobob2o3bobo4b2o2b4o3bo
b2o3bob6o3b3obobob2o4b2o3b2o2bo3bob3obo2b3obob5o3bob3o2b2o3bo5bo3b3obo
b2o7b4obo4bob2o$o2b2o2bob4ob2obobob3obo3b3obo2bob2obo3bobo2bobo5b5obob
3ob3o2bo2bo3bob2obo3bo5b7o2bo5bo5bobo4bob2o2bo2bo2bo2bo3b3obo3b5obo2b
4obo2bo3b2obob2o2bobobo$3bo3b2o3bob2ob2o5b4o2b5o2b2o2bo2b3o2bo3b3ob4ob
2o2b3obo2bo3b2o2b5o3bobob2o2b2ob3obob2o3bobobo6b9obobob3obo2bo2b5obobo
3b4ob2o2bob2obo2b2obo3bo3b2o$ob2obo2b4ob2o3b2ob2o3b4ob2o3b5o3b6o2bo2bo
4bo3b5ob2ob2o2b2o2bob2obo3bo2bo5b2o3b2o4bo6bob6o6b4o3bo7b2o2b5o2b3o2b
2o2b5ob2obobob2obobo$3o2b6obo4bo3bo2bob5ob4obo2bo2bobo3b4o2b4o2bob2ob
2ob2obo3bo2b2obob3ob2o2bo2b2obob4ob5o7bo6bobobo2bo3bo2b4o2b6ob5o3bob3o
3bo2bob3o3bobob3o$b3o2b3o3b3o4bo2b2obobob2ob4o2bobob4ob2ob4o2b2o7bo2bo
3bobobo4b4obob4obob3o6b4obo2bo2b3o5b2obo2bo2bo2b3ob2obob2ob2o3bob2ob3o
b4obob2obob2o3bobob2obo$2ob3o2b3o4b3o4bobo2b2ob2o2b2ob5o3bobob2ob2o2bo
b2o4b4ob2obo2b2obobob4obob6o4b2obo4b3obo3bo6bo2b5o3bobobobo4b4o3bob3o
2bo4b2obo7b5o2b3o2bo$obob2ob2o2b3o3b3ob3obob8o4b3o4bob8ob2ob3o3bob2o3b
3ob2obo3b3o6b2o2b5o2b3ob3o4b2o2bo2b2obo3b6ob6o3b5obob2ob2obo3b5o2bo4bo
2b2ob3obobo$bobobobo2bob2o3b3o2bo2bo2b3o6b2o2bobob3o2b2ob2o5b5obo3b2ob
o3bo3bob3o3b2o6bo2bobo2bo2bobo3b4obobob3o3bobobobob3ob2o3bo2b3o5b2o2bo
b4obo2bo5b6o2b3o$2bo2bo4bobo2b2o2bob3o2bob2ob4ob2o2b2o5b2o3bobobo2b3o
4bo2b2obo3bobob2obo4bo3b7o5b3o2b2ob3o3b3o2b5ob2obo2b3o5b3o3bo3bob4obo
2bob3o2bob3ob3ob4o2b2o$3o3bob3o2bo2b2o2bobo4bob3obob2obo3bo4bob10ob4ob
2o2b5o2bobobo2b2o2bob2o2bobo4b2ob4obob2o3bo2b2ob2o2b3ob2o2bobob3ob4o3b
o3b4o4b2o3b2ob2ob2o2b2obo2b2obobo$2bo2bo2b8ob3o2bo7bo2bob2o2bo7b2o2b3o
bo2bo3b2o2b4obo2bo2bobobob2obo3b2ob3ob4o2bobobo7b3ob2ob4obo2b6ob2o3b2o
b2o3b3ob2o2b2o5b5obob4ob7obo$bo2bobob4o2b2ob2ob2ob2ob3o3bob2o2bobo3b6o
2b2o5b3o2bo2b4o2bo2b4obo2b2o3b2ob3o2b3ob5ob2o2b4o5bobob4obob2o4b2obobo
b3o3b3obob2ob2o2b5o3b2ob5ob3o2bobo$obobo2b2o2b2obo3bo2b12o4bobo3b3o4b
2o2b8ob3ob3o3b2obo2bob3ob3ob2o2bo4bob2ob2obo4bo2bobo2bobo3bob3obo2b2ob
o3b3o3bobob3o3bob2o2bobo2b4o4bob2o2bo$ob2o4bo2b6o5bobo2b2o3b4ob2o2b2ob
2ob5o2b2o2bo3b8obob2o2b3o3bo3b2o4bo3bob3ob2o4bob3o2b2o3b3o3b2o2b5obo2b
4o2b3o2b4ob6obob2obo5b4o4b2o$o2bobo3bo3bo2b2o5bo2bo3b2o2b2o7b2ob3o3b5o
3bo2b2o4b4obo3b4o2bo3bo4b2o3b3o3b4o2b3o2b2obo2bob2o2bo8bo2bo4bo2bo4bob
6o4bob2obo2bo6b2obo$obo4b2obobobo3b2ob4o5b2obob3ob2ob2o2b2obobo3bobo2b
3o3bob2ob2obob2obo2bo2bobo3b2obo2b4o5bo4b3ob2o2bob2o4b3ob2ob8obo8bo7bo
7b2obob3o2b2o2b5o$3b3o3b3obobob2obobo3b2ob3ob2obob2o2b2ob2ob2obo6bo2b
2o3bo4b3obobobobob3o3bo3b2obob4obo2bo4b2o2bo4bob2obobobob3o2bob2obo2bo
2bo4bob3ob3ob2ob2o5bo2b4obobob4o$3b4o3bobob2ob2obob4obobo2b2o2bo3b9obo
bob2o4b3o3bo2b6o2b2ob6o5bob2ob7o2bo5bo3bo3bob2obobob2o2b2obo6bo2bob2ob
2ob3o2b2obob2obobo2bobo5bobob4o$3bobobo8b3o2b3ob5o5b4o2b2obobob2o3bo2b
o2bobo3b2o9bobo3b2o2b2o2bo4bob2ob2o2b2obo4b5o3b2o2b3o2bo3b3obobo3bobob
ob5o2bobo2bobob4o4b2o4b2o5b2o$2bobo2b6obob2o3b2o3b7o2b6o3bobobob3o2bo
3bob4ob2o4bobobobo9bo2b2o2bo4bo6bobo8bob2o2b2o3bobobob3obo4b2obo2b5obo
b2ob2o5b9o8bobo$ob7o3b2o4bo2b2o3b2obo6b3obo3b2obobobob2o2bo2bobo2b2o2b
2ob3o3b5obo2b4obo2b3obob3obobobo8b5o2bobo2b3obo4bob2obob2o4b2o4bob3o2b
o4b2o2bo2b2ob3o3b2o$4o6bob3ob2obobobob2ob3ob2ob2o3b3o3bobobob3o3bo3b2o
bo4b2ob4o3b2obo3b8ob2ob2o5bobobo3bo2b2obo3b2ob2ob2ob2ob2ob4obob4obo3bo
3b2obo2b2ob2o2bob3o2b4o4bo$obo3b4obobo3b3o2b3o2bo3b2o4bo2b2o2bo2b3o2bo
bo3b4o3bobo5b2obob2o4b2obo2b6o2bobo3b2o4b2o2b2ob2ob2obobobob5o4bobo2bo
3b5o3b3o4bobo2bobob2obo4b2ob4o$b2ob2obob6o2b4o3b2obob2o2bob4o5bo3b2obo
bobobobo2b5obobo2bobo2b2o4b2o2bo2bobobobobo2bo2bo3bob2ob2ob7o3b5o2bobo
b4o4bobob3o4b3ob5obob2obobo3b2o2bob4o$3o3b6o6b2o3b3o2bobobo3bob2ob2o4b
o5b3o5b3obo2bo3b3obob4obo3b3obo2b2o3b3ob2o2b2o2bo2b4ob2ob8ob2o4bobob2o
bob3o4bob2o2bo3b4o2b6o2b2ob2o3b3o$o3b2o2b2obo3b3ob2ob6obobob4o3bo4b4ob
2o2b3ob6o2b3ob4o6b2ob3o2bobo3bobobobobobob3o2b3obob2o3bo5bobob2o3b2o2b
2o3b4o4b2o3b2obo3bobobo8b2obob2o$3bobo4b3o2bo2bo2b4ob4obob2o2b4o3bo2b
5ob2o2bobobo2b3o3b3obob2o7bo2b2ob3ob2obobobo2bob2o2b2o2bob9obo2bo3b5o
2bo2b2o4b3ob2obo3bobob2o3b3obo2b2ob2ob3obo$o4bo5b2o3bob2o2b2ob2o2bobob
5o5bobo3b4obo3b2ob2o2b4ob2obobob2obobob2obobob3ob4o2bo4b2o2bobo2bo6bo
2b3obobob4o2bo2bob10o2b2obo3b2obo2b3ob6ob2ob2o2bo$b2obo5bo5b3obob2obob
o3bob6ob2ob2o2bob2obo2bo2b4o3bo3bo2bo2b3ob4obobo2bo4bob2o3bo3bob4o3b3o
bobob2obobo3b3o2b3o2b3ob3ob5o2b3ob3o2bo2bob2o2b2ob2o6bo$bo2bo3b2obob2o
2bo2bo2bobo5bo5b5o6b2o7bobo3bo2b2obo3bob2o2b2obob3o6b2o2bo3b4ob5ob2obo
2b3o2bob2ob2ob2o2bob2o2bobobo2b2obobo6b2ob4ob4ob2ob10obo$obobo3b3o4b2o
2bo2bob3o4bo3b2o3b3obobo4bo2bobobobo2b2ob2o3b4ob2ob2o2b2o3b5obo2bo2bob
obo2b4o3b4o3bo4bob2o2b2ob2ob2o3bob4o2bob2o3bob8ob2obo2b5obo2b4o$ob4o4b
2o2b2o2bo4b2ob3o2b2o5bob2o2bo2bo5b2o2b2obobo4b3ob2o2b2o3b3o6b5o2bo4bo
2bo2bobob2o3b5o2b2obo2bobobob2o2bobo3b5o5b4o2bo2b2ob3o3b2o3bob2o2bob2o
$2b2obo5bob2o2bo3b3o2b2obo5bo2bo2bob3o2b2obob2ob2obobobo6b3obo2bob3obo
3b5o2b2ob2ob3ob2ob2o2b3ob2o4bo2b5o4bob2o2bobo2bo2bobobo2b3o4bob5ob4obo
b2o3b2o3bo$bob3ob3o2bob6o2bobobo4b4ob2ob2ob2o5b7o2b10o6b2obo3b2ob3ob3o
2b2ob7obo6bo3b2o2bo2b5o3b2ob6o2b2o5bobo5b2o2bobob3o3bo2b2o5b8o$ob2o2b
2ob3ob3ob2o4bobob5o3b2obobob3o7b2ob3ob2o3b2o2bo2b5o3bobobo4bobob5o3bob
o4bo3bo3bob4obobo2b3obobob3o2bobob4ob5ob4o3bo2bo4bob3o2bob2o2b4o$bo3bo
3bo3b3obo2b2obobo2b3ob2o2b2ob2o3bob2obo2b3o2b2obob2obo8bo3b4o7b2obo2b
2o2b4obo3bobo2b3ob2obo5b3obob3obob3o2bob5o2b4o2bob3ob8o2b3obo2b7o$o6b
8o3b3obob5o2bo2b2o2b2ob2ob5o3bobo3b3o2b6o2b2o3b2o3bobo3bo4bob4o5b4obo
3b3ob2o4b2ob2ob3obobo4bobo2b2ob5ob2obob2obob2obobo2bo2bo2bo2b2obo3bo$
2b2obobo3b3o2bobo3b2ob2o2bo7bob3obo3b2o2bo2bob2ob5o2b8o3bob2o2bob4o2b
2ob2o2bo2b5obob7obobobo7b4obob2obo2bobo2bob4o2b2obob8obo2b3ob5obobo2bo
$o2bob4ob4o4b3o2b2o2b2ob3o2b3o2bob2obob2o2bo2b2obo5b2o4b3o2b5o5b4obo2b
o2b2o3bobobo2b3o3b2o4bo2bobob2o6bobobo3b4ob4obo3bob2ob2o2bo2b4o3b2ob3o
2bob3o$2b2obo2bob2o2b3ob5ob5ob8o2bo4bob9o2bo2bob3ob3o2bo2bob2ob2ob2ob
4ob2ob5o2bo2b2o2b2obo6bo2b2o2b2ob2o2b3obob2ob2ob3o3b2obo4bo3b2o6b3o2b
4o5b4o$b3ob2o2b4ob2ob2obo2b5o2bo3b2o2b5obob6o2b4ob3obo5b2ob3o2b3ob10ob
6o4b3o2bobo2bo4b6obobobobobo3bo5b2ob2ob2o4b2o2bo3bo2b4obo4b5obob3obo$b
obo3bobo3b2o3b3o4b3ob2o2b2obo4bo3bob2o3b2o2bo3b2o4b3ob5ob4o2b2ob5o2bob
ob3ob2ob2obo5b2o2b4o2b2o2b2o2bobobobo3b7o3bobo2bo3bo2bo2bo2bo2bo2bo7bo
2bobo$2bobobo8b3ob2ob4o2bobo3bo3bobob4o3b2o2b3o3bob2ob2o2b7obob2obob3o
2bo5bo2b4o2bo6bob2o2b2obo3bo2b2o2bo2bo2b10obob4o3bo2b2obo2bobo4b2o2bo
2b3o5bo$2obobo2b6ob3o2b2ob5ob2ob2o3bob5ob5obobobobobo11b3o3b3o3b3o3b5o
2bo3bob2o4b7ob2o3bo3bob5obob2o2bo2bobo2bob3o2b3o2bobo3bo2bobo3b2ob2o2b
o2bob2o$b3o2b3ob3ob3o2b2o2bo3bobo2b2obo2bo2b8ob3o2bob3ob4ob2obo3b4o3bo
bo2bobob2o6bob2o4b3obo5b3o5bob2obo2bo3b2obobobobob2o2bobobob6o2b3ob2ob
o3b2o3b4o2bo$2bo2b4obobobobobobo3b5o3b2ob2ob3obobobo2bob3o2bobo2b2o2b
5o2b2o3bob4obob6ob4ob4o3bobob2ob5o2b2ob6o2bob2o3b2obo2b3o2b3ob4o2bobo
2b2o2bobob2o2b2o4b4o$3obobo2b2ob2o6b4obo2b2o2bo2bobobob2ob5o4bo2b4o2bo
b4o3bo2b2o4b2o4b4ob3o2bo2bobo3b2o6b2o3b3ob4ob2obo4b3ob2ob3ob3ob2o3b2o
2b2obo2b7o4b3o2b4o$bo2b5ob2ob5o2b2o3bob2o3bobob2o3bo4b3o2b2ob2obob2o5b
2o2b4ob2ob2obo2bob3obo4bob2obo4bobo7bo2b4o4bo4b3ob2o2bo2b4obobo3b4o2bo
bo3b3o3b2o2b5obo2bo2bo$2bo4b2obobo4b4obo3bo2bo2bo2b2obobobob6ob4ob4o2b
ob2ob5o2b5obo3bo3b3obo4bob3o2bob3obobob2obo3b2obo3bo2bob2obo2bo3b5o2bo
3bob3ob4obob4ob2o3bo5b2ob2o$2ob6ob3o2bo2bob2ob4obob2ob2o2bo2b3obo3b2ob
2o2bo3bobobob5ob6obo7b2obo4bobo2b3obob2o4bo2bobo4bo5bobo2b3o5bo2bobo2b
ob4o3bo2b2obobobo3bo3b2ob6obo$bob3obo2b5o2b2ob3ob3ob4obo2b2o2b7o2bo3bo
2b3ob3o3bo2bo2b3o2b4obobobobo3bob3obo4b2o4b5o2bo3bob2obob3obo3b3o7bo3b
ob6obob3o4b2ob2o2b4o4bo2b2o$4o6bob2o2bob4obobo4bo2b3o4b3o2b3o2b2obob4o
b2obo2bo2bob3o2b2ob4obo2b3obo2bobo3bob2o2bo3b3ob3o3b2ob2o4b2o2bo3b3o4b
4obob4ob2o2b4o2bo2b3ob2ob2o2bobo$2bo3bo3b3o2bobo4bobob2ob3obobob3o2bo
2b3o5bo3b2ob3o2bo4b3o4bob3obo2b2ob3ob4ob2o3b2obobo2b5o3b3o4b6o6b2ob3ob
3obo2bo3bo4bo2b3o2b3o2b3ob3o2b3obo$b2obobob2o2bobob2obo3bo4b3o3bo2b3o
2b2o2bob2ob3obobo6bo9bob3o2bob2ob3o2b2ob4obobo2b7o3b2o2b4o2b2o3b3o3bo
3bo3b2ob2obo2b2o2bob2ob3obob2o2b2obobo2b2o2b2o$2bo2b3o2b2o4b2ob9o2bob
4o2bob4obo2b2o4bob7o2bo3bobo2bo2bobobo3b4ob5o2b4obobo3b4obo2bo2bobobo
3bo2bo3b3obob4o3bo4b5ob3o6b3o5bo2b2o2b2obo$bob3obo2bobo2bob3ob3obo2bo
5bob3ob2o2bo3b5obob2ob4ob3ob2obob2obo2bobo3bo2bo2b2ob2ob2ob2o2bobo2bo
3b9ob5o2b3o2b4obob3ob2o2bobobobob2o2b2obo2b2ob2o2b2o3b4o$3b2obo2b3o2bo
3b3obo3bo2b2o4b6ob2obo3bob3ob3o3bob2o3bo9bo4bo2b2obo3bo4b3o2b5o3bo2b2o
b4obo3bo2b5o2bo2bob2o3bobo3bob3obo3b4o2b2o4b5o2b2o$2o2b2o4bo2b3o5b3o2b
4o2bobobobob3obobob3o3b3o3bo3b2ob2o3b5o6bob2o3b2o2bobobob2ob2o2b4o2bo
2b2o3b2ob5ob5o4bob3ob2o9bob2ob2obobo4bo5bo5bob3o$2b2obo2bo2b2obo8bobob
2o4bob2o2bob2ob2obo4b2o2b3o2b3o3bobob7obobo5bo3b2obobo2b3ob9o6bo2b3o3b
ob7ob5o3b3obo4b4o4b3obobo3bob2o2bobob2o$2bo7bo6bobo2bo4b4o2b2obob4o3bo
2b3ob2obob4obo2b2obo5bo2b2obob4ob3o6bo2b2o2b4obo2bob3ob3o3b3o2b5o2b2ob
3o2bo3b2o3b2o4bobob2obobobob2ob7obob2o$2o2bo2bo3b3obob2obobobob2obob2o
3b3ob2ob2o2b2obobobo2bo2bo3b2ob2obobo2b2o2b6ob6o3b2obo3bob2obo2b2obobo
3b2o2b2ob2o2bo3bobob2ob4obobob2ob4o2b2ob3ob2o4b6o9bo$o5b4o2b2obo3b2o3b
o4b7ob2o2b5o4b2o2b2o2bo2b2o2b4o3b2ob4o3bo2bo2bo3b2obo2bobo4bo4bo9b2o2b
obo2b3o2bo4bob2o5b2o3b2obo2b2o4b8o2b2obo2bo3b3o$ob2obob6o4b4ob2ob4obob
obo2b2o4b2ob5o2bo2bo5b2o3b2ob2o3bobo2bo3bo2bob2ob2o3b8o3b4o3b6o3b4ob2o
bo2bo2b3ob2o5b4obo3b2o6b3ob3obobobob3ob4o!

[wildmyron]

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.

p279, 3 cells

Code: Select all

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:

Code: Select all

x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!

And a p71 with a minimum of six:

Code: Select all

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.

Code: Select all

x = 7, y = 7, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
4bo$2o3bo$2b2o$2bo3bo$2b2o$2o3bo$4bo!

There's also a 2c/5.

Code: Select all

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.

[77topaz]

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.

[Hunting]

And this rule has a similarly sparky p49 that has a minimum of five cells:

Code: Select all

x = 5, y = 5, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
2bo2$obobo2$2bo!

It has a phase with only four cells...

Code: Select all

x = 3, y = 3, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo!

EDIT: Wow.

Code: Select all

x = 23, y = 6, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo$21bo$20bobo$21bo!

[77topaz]

EDIT: Wow.

Code: Select all

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:

Code: Select all

x = 23, y = 12, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8:T0,12
6$bo$obo$bo$21bo$20bobo$21bo!

[wildmyron]

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

Summary:

Code: Select all

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

Code: Select all

x = 5, y = 1, rule = B2-an3cnqry4etwz5ciny6ckn7c/S1e2ek3cen4aknqz5cy6cek7
obobo!

Even periods:
p250, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ae3-jknr4ry5qy6cn7c/S02in3-cn4cejq5-cej6cin
obobo!

p278, 3 cells

Code: Select all

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

p292, 3 cells

Code: Select all

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

p310, 3 cells

Code: Select all

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

p316, 3 cells

Code: Select all

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

p340, 3 cells

Code: Select all

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

p342, 3 cells

Code: Select all

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

p348, 3 cells

Code: Select all

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

p398, 3 cells

Code: Select all

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

p420, 3 cells

Code: Select all

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

p434, 3 cells

Code: Select all

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

p674, 3 cells

Code: Select all

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

p788, 3 cells

Code: Select all

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

p998, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ai3ikry4ceiryz5-cknr6ce8/S01c2i3cik4cejnwz5ejkny6an7e8
obobo!

[wildmyron]

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:

Code: Select all

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

Code: Select all

x = 5, y = 1, rule = B2-an3-ijnr4ceintz5acknr6ikn78/S03ajy4aiknw5aiqr6aei7e
obobo!

p133, 3 cells

Code: Select all

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

p135, 3 cells

Code: Select all

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

p141, 3 cells

Code: Select all

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

p143, 3 cells

Code: Select all

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

p157, 3 cells

Code: Select all

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

p167, 3 cells

Code: Select all

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

p173, 3 cells

Code: Select all

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

p193, 3 cells

Code: Select all

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

p211, 3 cells

Code: Select all

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

p225, 3 cells

Code: Select all

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

p231, 3 cells

Code: Select all

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

p271, 3 cells

Code: Select all

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

p297, 3 cells

Code: Select all

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

p313, 3 cells

Code: Select all

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

p453, 3 cells

Code: Select all

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

p843, 3 cells

Code: Select all

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

Even periods:
p222, 3 cells

Code: Select all

x = 3, y = 3, rule = B2-a3aek4cenrtyz5-cenq6ak7/S02-ce4jkq5cikn6in7c
obo2$o!

p226, 3 cells

Code: Select all

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

p236, 3 cells

Code: Select all

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

p262, 3 cells

Code: Select all

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

p264, 3 cells

Code: Select all

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

p270, 3 cells

Code: Select all

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

p272, 3 cells

Code: Select all

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

p276, 3 cells

Code: Select all

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

p298, 3 cells

Code: Select all

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

p306, 3 cells

Code: Select all

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

p312, 3 cells

Code: Select all

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

p328, 3 cells

Code: Select all

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

p334, 3 cells

Code: Select all

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

p338, 3 cells

Code: Select all

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

p346, 3 cells

Code: Select all

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

p364, 3 cells

Code: Select all

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

p384, 3 cells

Code: Select all

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

p390, 3 cells

Code: Select all

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

p422, 3 cells

Code: Select all

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

p432, 3 cells

Code: Select all

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

p442, 3 cells

Code: Select all

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

p444, 3 cells

Code: Select all

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

p448, 3 cells

Code: Select all

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

p460, 3 cells

Code: Select all

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

p484, 3 cells

Code: Select all

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

p502, 3 cells

Code: Select all

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

p512, 3 cells

Code: Select all

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

p550, 3 cells

Code: Select all

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

p554, 3 cells

Code: Select all

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

p626, 3 cells

Code: Select all

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

p698, 3 cells

Code: Select all

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

p706, 3 cells

Code: Select all

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

p806, 3 cells

Code: Select all

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

p832, 3 cells

Code: Select all

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

p1010, 3 cells

Code: Select all

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

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

Forward search (no output filtering):

Code: Select all

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 :

Code: Select all

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)

[Macbi]

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:

Code: Select all

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!

[77topaz]

p460, 3 cells

Code: Select all

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

This rule has a natural 4c/30 orthogonal which pushes an octomino:

Code: Select all

x = 7, y = 3, rule = B2cik3aekn4ntw5cjqry6ae7c/S12ek3iqy4cijrw5aj6acn7c8
bob4o$5obo$bob4o!

p843, 3 cells

Code: Select all

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

And this one has a natural c/7 orthogonal:

Code: Select all

x = 4, y = 5, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
3bo$3bo$3o$3bo$3bo!

And a nice p9:

Code: Select all

x = 9, y = 3, rule = B2-an3eijr4eiqt5cey6ek/S1e2cen3jkqr4eiq5in6n7e
bo5bo$obo3bobo$bo5bo!

[Hdjensofjfnen]

Period 20200:

Code: Select all

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.

[muzik]

EDIT: 188 cells, so not that impressive.

Precisely, given that that's quite a lot bigger than 4.

[Moosey]

Period 20200:

Code: Select all

longlife

EDIT: 188 cells, so not that impressive.

Isn’t that a trivial oscillator too? Or does some cell oscillate at that period

[wildmyron]

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

Code: Select all

x = 3, y = 1, rule = B2-cn3ejnq4ejntw5-jky6cek8/S01e2ikn3-in4-tyz5-ajnq6-kn
obo!

p220, 2 cells

Code: Select all

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

p222, 2 cells

Code: Select all

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

p226, 2 cells

Code: Select all

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

p234, 2 cells

Code: Select all

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:

Code: Select all

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

[Hdjensofjfnen]

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.

[wildmyron]

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.

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

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#C p56 oscillator
x = 10, y = 1, rule = B2cei3acr4-jknqy5ceiny7e/S01c2ai3cejqy4eint
2obo5bo!

[muzik]

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:

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x = 3, y = 3, rule = 01c/2n/7
2.A2$A!
[[ THEME Blues ]]

[Sarp]

Here are some new periods

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 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

Code: Select all

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

p330

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

p238

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

p498

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

p185

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

p380

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

p505

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

p145

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

p572

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

p161

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

p149

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

p756

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

p322

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

p199

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

p145

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

p227

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

p988

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

p716

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

p826

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

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

[Sarp]

More unfiltered results, probably a few interesting discoveries here.

Code: Select all

3, B2cei3-acek4-acrty5acenq6aci7e/S02ck3cnq4eikrwy5ijkn6ik, 0, 0, 102, obobo!
3, B2-a3y4acetw5-jkq6i7e8/S02en3-nry4aknqry6aci, 0, 0, 116, obobo!
3, B2-an3-aknq4ajnwy5acijy6ack/S02ci3r4cekqrtw5-cr6ikn, 0, 0, 102, obobo!
3, B2cei3cnqry4ktw5jy7e/S02-ac3iq4er5cekqy6ai8, 0, 0, 104, obobo!
3, B2cik3akr4-ektz5aenqy7e8/S02ei3-jkqr4nqrwz5-jy6i, 0, 0, 104, obobo!
3, B2cik3-eir4jkr5nqy6c8/S01c2cin3-aery4ejqr5ace6aci7c, 0, 0, 128, obobo!
3, B2-ae3-inry4ekqrtwy5ejny6ikn7c/S02cik3-qy4ejqryz5ejkq6k7e8, 0, 0, 112, obobo!
3, B2-a3acekr4c5ejknr6eik7e/S01c2cin3eknr4cenqz5acnqr6ikn7, 0, 0, 152, obobo!
3, B2ci3-iknr4ejn5-cein6a8/S02-ce3-ajn4-aejnw5acinr6ekn7c8, 0, 0, 204, obobo!
3, B2cei3enqy4eknw5ejy6aci7e/S01c2cin3-ry4eny5aenqr78, 0, 0, 102, obobo!
3, B2-a3acekq4ejnrtyz5-jr6ikn7c/S01c2an3ceinq4-iknqr5acq6k7c8, 0, 0, 100, obobo!
3, B2cin3acei4acjtw5aijnq6cei7c8/S02a3-jny4-inqr5akqr6aci7e, 0, 0, 804, obobo!
3, B2ci3aekr4-acqw5-ceky6ce7c/S01c23-ajq4acjnyz5ikny6cek78, 0, 0, 124, obobo!
3, B2cei3-ajkq4-ckry5iny6k8/S012n3ceq4-aekty5-ciny6k7e8, 0, 0, 114, obobo!
3, B2-ak3aejy4-aetz5-ck6-e7c/S01c2cik3-aeik4-ceiy5-ijry6aen, 0, 0, 324, obobo!
3, B2cei3ry4-ektwz5eijkq6-an7/S02-e3-aery4cikty5cejnq6-cn7c8, 0, 0, 510, obobo!
3, B2ci3ajky4ainwz5acy6ci7c/S01c2-k3aijny4jkqr5qry7e8, 0, 0, 102, obobo!
3, B2cei3ejnqr4cijkryz5cknr6ace7e/S02ei3-iky4-nrt5cenq6aei7c8, 0, 0, 185, obobo!
3, B2-an3aej4cjkz5ejnq6cen7e/S02i3-er4-eiktz5aijn6ac7, 0, 0, 102, obobo!
3, B2cin3acy4aeity5jry67/S02cei3ckqy4-nz5eijnq6aci7c8, 0, 0, 180, obobo!
3, B2cik3-ik4w5j6-ek/S01c2c3air4ejnt5acjqy6ik, 0, 0, 154, obobo!
3, B2cin3aeir4-acjr5eiknq6-k7/S02ik3aijq4-aijrt5-aky6akn, 0, 0, 202, obobo!
3, B2-ae3aen4aeijrtw5enqy6ce7e/S02ik3cjkq4-aceiw5-knqy6a7e8, 0, 0, 226, obobo!
3, B2-a3aceqr4ceijkt5aenqr6aik8/S01c2aei3-aky4cjktwz5cjnqy6cik8, 0, 0, 192, obobo!
3, B2cin3aeikn4eiqtw5ceir6-i7e/S02ae3jnr4-aijnt5-ajnq6aen, 0, 0, 174, obobo!
3, B2cik3-cein4aer5-aijk6-en78/S02ack3-knry4cijy5ekqry6eik7c8, 0, 0, 126, obobo!
3, B2cei3akqry4-eknwz5ce6ikn8/S02en3-ejk4ekqrtwz5acnr6eik7e8, 0, 0, 115, obobo!
3, B2-a3-acjn4cejrwz5ciny6ack7c/S02i3cir4aknr5cjq6aek7e8, 0, 0, 108, obobo!
3, B2cik3aek4ceikqwz5-eny6aei7e/S02ei3aejkq4jktz5-ejqr6cen7, 0, 0, 114, obobo!
3, B2ci3acei4acekt5kqr6aci78/S02i3-aky4y5aenry6c7c, 0, 0, 170, obobo!
3, B2cin3aijy4aceiknr5-ceir6aei8/S02i3ae4ckntwy5ay6ei8, 0, 0, 152, obobo!
3, B2-a3aeqr4kqry5cjy6ac7e/S02aei3cekny4cejnt5ciry6ekn8, 0, 0, 246, obobo!
3, B2ci3-i4ceiknyz5enqy6ik7c/S02ikn3eknqy4-acjty5cejq6ck7, 0, 0, 1086, obobo!
3, B2cin3acq4aikqwy5cry6ck7c/S02en3ajnqr4-ckt5jr6ci7e, 0, 0, 180, obobo!
3, B2-ak3akry4-cejty5aein6ai8/S02k3cknr4acnrwy5-cjy6ae7e, 0, 0, 124, obobo!
3, B2-ae3aey4aijrwy5kq6k7e/S02-en3cejkr4inrz5r8, 0, 0, 134, obobo!
3, B2-ak3ay4acikny5-einq67c/S01c2aci3-jqy4aent5ejy7e8, 0, 0, 112, obobo!
3, B2cin3aceq4aeijt5aceir6ac7c8/S012i3-eqy4ejnw5ijkr6aei7c8, 0, 0, 128, obobo!
3, B2cik3ar4eijkz5ceikq6cin7c8/S01c2-ac3-ceiy4-ceknr5aej6-e78, 0, 0, 219, obobo!
3, B2-ae3aq4einqrw5jnqry6cek7c/S02ain3aeiqr4cekrtw5eijnr8, 0, 0, 110, obobo!
3, B2-a3enqry4-eqrtz5-air6-an7/S02ci3aeknr4eky5ejqr6-ek8, 0, 0, 165, obobo!
3, B2-ak3aeik4ijqw5ace6ai/S01c2cei3eiq4et5eky6-in7e, 0, 0, 130, obobo!
3, B2-an3cekny4aeinrtz5aiy6aci/S02cei3-acjy4cjknrwz5n6ae78, 0, 0, 104, obobo!
3, B2-a3e4cenqwz5eq6-ik78/S02ein3-cjqr4-ntz5ijnry6ek, 0, 0, 220, obobo!
3, B2cei3-eikn4ikqrz5ijnry6cik7e8/S01c2ci3ajny4anrt5ajnry6ikn78, 0, 0, 142, obobo!
3, B2cik3aceiq4cjnrw5ceqy6-an7c8/S02cin3aejr4cejqyz5-aeij6ek8, 0, 0, 1344, obobo!
3, B2cin3-cin4iqrtz5acr6-k78/S02-ak3ainry4-ceikr5-ary6-ek, 0, 0, 298, obobo!
3, B2-ae3-cinr4-aknwz5-acqy7/S01c2-ck3cejkn4-qry5-nry6ekn7, 0, 0, 190, obobo!
3, B2cik3acej4aekrty5cnqry6ace8/S02ikn3acy4ceijk5nqry6-c7e, 0, 0, 154, obobo!
3, B2cin3aiqr4ckny5eiry6eik/S02k3-aciq4aekt5-cik6aci78, 0, 0, 108, obobo!
3, B2cin3acejn4cenqrt5-acjn6-ce7e/S02a3aikn4-nrwy5cenr6-en78, 0, 0, 132, obobo!
3, B2-ae3ai4jwyz5jknry6ace7c/S01c2ei3ceiny4cikrtwy5cijy6eik7e8, 0, 0, 104, obobo!
3, B2cin3acekn4aejknw5-cejq6cik7e8/S01e2e3cikr4-cjqtw5-cinr6-i7c, 0, 0, 626, obobo!
3, B2cik3acn4acjrtwy5cijnr7e8/S01e2ei3-ceqy4ikyz5eknry6cek7c8, 0, 0, 107, obobo!
3, B2cik3-in4acinqrt5ek6ack/S02in3ckr4-ikqt5aeijy6eik7e, 0, 0, 118, obobo!
3, B2cin3acqr4aeijkw5cer6ik7e8/S01c2aei3-aekq4acjz5qr6-en7c, 0, 0, 124, obobo!
3, B2cei3acqry4jnqrwyz5an6ai7c8/S02ekn3-acek4acnqw5-aik6-ae8, 0, 0, 118, obobo!
3, B2cik3ai4ejntwz5-ikqy6ein7/S012en3-cinq4eikny5cinq6ace7c, 0, 0, 106, obobo!
3, B2cik3aekqy4cntz5-cknr6aci7e8/S01c2aei3ejqry4-cnqtz5-ajny6aei7c8, 0, 0, 132, obobo!
3, B2ci3-cjny4kqwyz5cekn6ack7e8/S02ci3-jknr4aq5cjkr6ci, 0, 0, 338, obobo!
3, B2-ae3-iknq4aceiktw5-aciq6cei7c/S02in3jky4-aeijz5-ny6-an78, 0, 0, 100, obobo!
3, B2cei3-inqr4eikqy5acin6a7e8/S02ik3acnry4crtwyz5jnry8, 0, 0, 144, obobo!
3, B2-ae3aq4cejkryz5-ciqr6-n7c8/S01c2cin3-ackq4ceijtz5eijy6aei7e, 0, 0, 161, obobo!
3, B2-ak3-eijn4cejnqw5ajny6aen8/S023jnr4aeqrtz5cn6i7e, 0, 0, 112, obobo!
3, B2-an3aery4ciqr5-cjkn6ci7e/S02-kn3ijnqr4-ceqry5jkqry6-e8, 0, 0, 100, obobo!
3, B2cik3-nqry4-ent5-cein78/S02ein3eiy4-aijwz5kn6an7e, 0, 0, 106, obobo!
3, B2cik3aer4aciqr5-aenr6-n/S02cik3jr4ijwy5ijnqr6ek78, 0, 0, 168, obobo!
3, B2-a3acer4ijqrtz5cky6in78/S02ik3-aeq4-enrt5aciq6eik7e8, 0, 0, 112, obobo!
3, B2cik3acir4ijnz5eij6ak78/S01c2ein3-ejqr4ejknrwz5enqy6c7e, 0, 0, 112, obobo!
3, B2-ak3ek4-ijrtz5eij6-an7/S02eik3-jqr4acjkqrt5cijr6k7e, 0, 0, 168, obobo!
3, B2cik3acei4acijqr5ejry6c7e8/S02ein3-aijr4eknrwy5ciq6cin8, 0, 0, 116, obobo!
3, B2ci3aceiq4cenrtwz5-eiqr6c7e/S01e2a3jkn4cent5inr6i7e, 0, 0, 200, obobo!
3, B2cik3-cnqy4ceiqrw5cknr6aen7c/S02ik3-ijq4ceqyz5cqry6ack7e, 0, 0, 100, obobo!
3, B2cin3acny4cinwz5-ajry6c7/S01c2ek3jknry4acejkqy5enqy6i7c8, 0, 0, 114, obobo!
3, B2cik3aeik4ert5ny7/S02ik3aceiq4ejnqry5aekqy6k8, 0, 0, 102, obobo!
3, B2-ae3ay4ciz5ciky6-ei7/S01c2-ck3anqry4acenr5nry6eik7, 0, 0, 122, obobo!
3, B2ci3aeiqr4ceijy5aceiy6ai7c8/S02ikn3acey4aintwy5akqry6ikn7e8, 0, 0, 142, obobo!
3, B2-ae3aceiy4enwyz5cijy6-kn7c8/S02i3aery4ajkr5acinr6ikn7e, 0, 0, 190, obobo!
3, B2cik3aeqr4acikn5inq6k7e8/S02-a3einy4atw5iry6ik, 0, 0, 106, obobo!
3, B2-an3-ijny4iqrtyz5-ejn6-n7c/S01c2-an3ekq4acety5cjknr6-n7e8, 0, 0, 170, obobo!
3, B2-a3ik4-kntwz5acjk6ci8/S02cik3-ckqy4cejqwz5acijk6-ei7e8, 0, 0, 152, obobo!
3, B2-ak3acnr4ceijkn5-cjqr6ei7e8/S023iq4cy5enry6ai78, 0, 0, 182, obobo!
3, B2-a3-aejn4ikrz5-ikq6cin/S01c2cik3-jkny4eijry5cjknr6-ei78, 0, 0, 968, obobo!
3, B2-ak3nr4jkqrtwy5enqry6in/S01c2ekn3-cnq4aceijnr5ej6ce, 0, 0, 112, obobo!
3, B2-an3-cijn4eintz5j6-en8/S02-ce3j4cjkqrty5ejnr6en7c, 0, 0, 132, obobo!
3, B2-a3ae4aeijk5nqry6ci7e8/S02ci3ejnr4aiz5ajkq6i7c, 0, 0, 112, obobo!
3, B2ci3aejkr4aceiqtw5ckny6cek7e/S02aci3aijky4-cjtz5ackqr6ek7e8, 0, 0, 158, obobo!
3, B2-an3akqy4-acjqy5-airy6n8/S02ckn3jknqr4-aciqz5-jqy6-e7e8, 0, 0, 201, obobo!
3, B2cei3cejny4-ijrwz5acknq6-en7e/S01c2n3ain4ceknqw5-ekn6cin, 0, 0, 230, obobo!
3, B2ci3-nqry4ceinqr5-ky6e/S02n3-ijky4cnrtyz5ciqry6-en, 0, 0, 116, obobo!
3, B2cin3aejkq4ejrwyz5aekqy6ai/S02aei3nr4ce5ey, 0, 0, 100, obobo!
3, B2ci3-cjkn4ejkqrtz5cn6cin78/S02cek3-anr4-cnqtz5cik6aci7, 0, 0, 894, obobo!
3, B2-ak3ceiqr4-nqwyz5-ekry6-a7c8/S03-kq4ijkz5aeikq6aen7e, 0, 0, 129, obobo!
3, B2-an3enry4aeijrwy5e6ce78/S02ai3eijry4-akqw5kqry6ai7e8, 0, 0, 130, obobo!
3, B2-ak3aq4aejkqrz5-akqr6-n7e/S01c2ikn3-ekqr4ajnrt5-nq6a7c8, 0, 0, 190, obobo!
3, B2ci3aeikn4eirtwyz5ce6cik7e8/S02ae3-acin4acjnqry5aejy6ack7c, 0, 0, 268, obobo!
3, B2cei3ajqry4ijryz5eijnr6aei7e8/S02cik3-ikqr4anqtz5-cjq6-ei7c, 0, 0, 116, obobo!
3, B2-an3ejkr4-kqtwz5-acin6ace7e8/S012i3enqr4aeijkrt5aejq6-in, 0, 0, 138, obobo!
3, B2-ae3acy4aceijnw5r6an/S02ein3-aeij4-ijnqr5eij6-ac7e8, 0, 0, 140, obobo!
3, B2cin3aeky4-cityz5cejnq6cik7e/S02-en3-ejn4ceinq5cjkqy6ack7c, 0, 0, 224, obobo!
3, B2cin3aeiq4eit5aenqy6i7e/S02-ce3ain4ceqz5iqr6ac7e, 0, 0, 104, obobo!
3, B2-an3-ijqy4cijnwz5-akq6cik7e8/S01c2ci3ackny4cejn5aijqy6eik7e, 0, 0, 112, obobo!
3, B2cik3anqr4cknq5cjqry6acn78/S02e3-cej4aekqrwy5aeny6ain7, 0, 0, 222, obobo!
3, B2ci3aqy4aceinr5-aiqy6ai8/S01c2-ek3-jny4cenry5jr6-in7e, 0, 0, 100, obobo!
3, B2-a3-cein4ceijknw5-nry6c7c/S02-en3nq4acjknq5ejkqr6-in7e, 0, 0, 146, obobo!
3, B2-ae3-inq4acjnrt5cjry6-a7e8/S01c2a3ir4-qrtz5ceqy6i78, 0, 0, 108, obobo!
3, B2-ae3acek4-etyz5kr6-ak7c/S02ci3cekqy4aikqyz5-aenq6-c7e, 0, 0, 314, obobo!
3, B2cik3aejnq4ijtz5-cqy6-ae7c8/S02k3acr4aceknqt5ciqy6ci, 0, 0, 112, obobo!
3, B2cik3-cnqy4ceirw5cejqy6-n7e8/S02cik3cejk4-ijnyz5ijky6n7, 0, 0, 228, obobo!
3, B2-a3jkn4cjrtz5aekqr6kn7c/S02ck3ejkqr4ceknryz5-anqr6ckn7c8, 0, 0, 256, obobo!
3, B2cik3aiqr4cejkn5aery6ce7e8/S01c2ai3-anr4ckrwz5-ejkq6ci7e8, 0, 0, 108, obobo!
3, B2cin3ajkny4cz5eijry7e8/S01c2in3acq4cijnwy5a6aei7e, 0, 0, 126, obobo!
3, B2-ak3enqry4acjqyz5-aek6ein8/S02n3-cj4acijknr5aejqy6-ek, 0, 0, 177, obobo!
3, B2cei3ckry4-ackt5cenr6cei/S01c2ikn3-ckny4aejwyz5einqy6-ek7c, 0, 0, 168, obobo!
3, B2-an3cky4acjqrty5aijkn6acn7e8/S02-ac3-ckqy4ikwy5einqr6-ae, 0, 0, 110, obobo!
3, B2cin3aen4aeijnwy5aijn6in/S02aei3-eikq4enrtw5eikny6c8, 0, 0, 114, obobo!
3, B2cei3cenr4-ntwyz5aejny6-cn/S01c2en3iknr4-knq5aikny6aik8, 0, 0, 102, obobo!
3, B2cei3-cinr4aijnqty5ijny6acn7c/S01c2eik3jkqry4ijktz5jknry68, 0, 0, 120, obobo!
3, B2-ae3aekry4-cnyz5-ikq6cik/S02in3acjkn4ceiqwz5-ciqr6ik7c, 0, 0, 188, obobo!
3, B2-ae3airy4ceknqrw5-cy6-ce7e/S02ce3acejq4cejnz5iqy6cek, 0, 0, 168, obobo!
3, B2cin3-cikn4acqz5-aeqy6ak7e8/S02cik3ejky4-aejnr5aejry6-kn, 0, 0, 730, obobo!
3, B2cei3-acn4iknrtw5kr6aen/S012cn3acnqr4ekry5ackr6-kn78, 0, 0, 240, obobo!
3, B2-ak3aceqy4akrw5acjnr6-ak7c/S02ce3-cijy4ijktwz5-knry6c7c, 0, 0, 324, obobo!
3, B2cin3-inqy4-ckny5cejkn6ci7e/S01c2ei3-any4aijw5ckr6acn7, 0, 0, 318, obobo!
3, B2-an3cenry4knqtwyz5ary6ain/S01e3-ik4cejnqy5cijqy6aei, 0, 0, 148, obobo!
3, B2-ak3ary4cektz5-ekqy6acn7/S01c2-ck3-anq4-actz5aenq6cen, 0, 0, 154, obobo!
3, B2cin3-eiqr4ejknqr5cer6c7e/S01e2a3j4aeqryz5iknq6ai, 0, 0, 100, obobo!
3, B2cei3-any4-twyz5-aejr6ei78/S02cei3c4cekqrwy5ceikq6en7c8, 0, 0, 290, obobo!
3, B2ci3acnr4-eijnw5ejkry6-ek8/S01c2ei3-aejq4acnrtwy5acry6-cn, 0, 0, 126, obobo!
3, B2-an3-iknr4acjknry5ceik6ikn7c/S01c2k3ijy4-inrtz5-ekqr6k, 0, 0, 121, obobo!
3, B2-ak3aek4-ajkw5ejny6-ci7e8/S01c2-ck3einqr4jknrtw5-akny6-an7c8, 0, 0, 136, obobo!
3, B2cei3aqry4ceijtw5nqy6cek78/S02ain3ceny4ceikqyz5enqry6ein78, 0, 0, 148, obobo!
3, B2cin3-cnry4aiknqt5ar6aei7e8/S02-ac3ejqr4knrwz5cejqy6aci7e, 0, 0, 122, obobo!
3, B2-a3aek4eirtyz5ceinq7c8/S01c2-a3ej4cijknt5-aejq6ak8, 0, 0, 346, obobo!
3, B2cin3-einr4-acjr5aeiny6-an7e/S02eik3-nqry4-kt5kr6en7c, 0, 0, 136, obobo!
3, B2cei3acekq4-acrtw5jkny6ai7e8/S02ekn3jnqr4aijn5ekr6-ae8, 0, 0, 134, obobo!
3, B2cei3kq4ijkz5-ckr6i/S01c2i3aeikr4acktwz5ei6ae8, 0, 0, 132, obobo!
3, B2-ak3cqy4jnrtwyz5in6eik7e/S03-y4acijnqt5cijn6k, 0, 0, 138, obobo!
3, B2ci3acjqr4aiqtw5-ijry6-ek8/S02ak3cjnry4ciknqy5aeiq6-i7, 0, 0, 192, obobo!
3, B2cin3acenq4certz5ackq6ci/S02-ai3-ejry4yz5-acjk6ai7e8, 0, 0, 130, obobo!
3, B2cik3-ikn4ceiqryz5einqy6-ac7/S02-ck3cekry4-aejr5aceny67c8, 0, 0, 101, obobo!
3, B2cik3aekq4aceiwz5eijk6ci7e/S02cin3-cein4knrwy5-eiky6-ek7e8, 0, 0, 118, obobo!
3, B2-ae3-i4eijknyz5-cijy6a78/S02in3ikr4cijy5eqry6ai7e8, 0, 0, 206, obobo!
3, B2-ak3acry4aceiqrw5ceij6aek8/S01c2-a3iky4aciknqt5aeikn6aci8, 0, 0, 882, obobo!
3, B2-a3ejqr4ceirtw5ijnqr6-in7e8/S01c2i3ceiqy4aijnrt5ceknr67c8, 0, 0, 124, obobo!
3, B2-a3ae4ciknrz5i6aci/S02-cn3iny4enqtwz5acer6ckn78, 0, 0, 112, obobo!
3, B2-ak3ny4-ey5ceir6ac78/S01e2ik3iqry4anqz5ijk6aci7c, 0, 0, 122, obobo!
3, B2cik3aeqr4-ijk5cjknq6-ak/S02ci3knqy4ekny5cejkn6aci78, 0, 0, 212, obobo!
3, B2-a3-eikn4-ackwy5cjqr6ein7e/S01c2-ae3ejknq4cjknt5-aeir6kn7c8, 0, 0, 123, obobo!
3, B2-an3acjq4-aejnz5cejn6i7e/S02ikn3-enq4ejnz5anqy6-ak7c8, 0, 0, 114, obobo!
3, B2-ae3akn4cijqrw5-ckq6-a78/S02cik3anq4einqtwy5-ikn6ik7c8, 0, 0, 144, obobo!
3, B2-ak3anq4cijqrtz5anqry6e/S02-e3ackny4acjnqrt5-ijkr6-ck, 0, 0, 120, obobo!
3, B2-ak3acjr4aceint5c6-c7e8/S02ckn3-iy4acintw5k6ae7c, 0, 0, 256, obobo!
3, B2-a3kry4ceikqyz5-cjk6-k7e8/S02-ak3-cjk4ajqrtwy5-inqy6c7, 0, 0, 1102, obobo!
3, B2-an3er4acektw5-acjr6ek8/S01c2-an3eikny4-einq5enq7e8, 0, 0, 110, obobo!
3, B2ci3-knqy4ijnqyz5-ai6-k7c8/S02ein3-iqry4-knqty5acjr6ae8, 0, 0, 154, obobo!
3, B2-ae3acqy4jknq5ejy6ack8/S02ai3aknqy4-iktyz5jy6eik7, 0, 0, 172, obobo!
3, B2-a3-acjk4eiknw5ajn6-ce/S01e2ci3eknr4aeikrwy5eijq6i7e8, 0, 0, 100, obobo!
3, B2cin3-cjn4akrw5-acqr6ac7c8/S01c2-ck3iq4ekqr5acnr6aei, 0, 0, 120, obobo!
3, B2ci3-ceiy4krw5cjkn6ci7e8/S01c2i3-ejn4acjkqwz5enq6ci78, 0, 0, 144, obobo!
3, B2cin3aeijq4-jnty5aci6aei7e8/S02i3-eijk4cekt5eijn6ac7e, 0, 0, 132, obobo!
3, B2cik3aejy4jkqryz5cey6i7e/S02in3-eijy4cjknqrz5cjkr6c, 0, 0, 152, obobo!
3, B2cik3aejry4ceik5cj6k8/S02ik3-acik4jkrtwy5in6i7c8, 0, 0, 112, obobo!
3, B2ci3akqry4cijkqw5einqr6acn78/S02aei3acqr4cjnqtz5-jn6ein7e, 0, 0, 134, obobo!
3, B2-ae3aijr4eijrty5kqr6ai8/S01c2en3-aekr4ackq5nry6ac, 0, 0, 142, obobo!
3, B2ci3aejkq4iknwy5cknry6ack/S02ain3aejkn4aijknz5-nqr6-a7e, 0, 0, 159, obobo!
3, B2-ak3aekqy4aikrtw5ek6cen7e/S02ci3anq4ejkqtw5eijky6cin, 0, 0, 176, obobo!
3, B2cin3-knr4ejknqt5cjq6c7c8/S02e3aejny4acikqrz5acer6cik7e8, 0, 0, 128, obobo!
3, B2-ae3ai4ekqtwz5-kry6a8/S02ae3jkr4ceiz5cnr6e78, 0, 0, 118, obobo!
3, B2cin3aceqy4-ckqtz5aceir6ikn7e8/S02cin3jn4cjqwy5ainy6-kn8, 0, 0, 108, obobo!
3, B2cei3iqr4-acekq5ceijn6-k78/S02ikn3ijy4acijkz5ikr6aci7, 0, 0, 480, obobo!
3, B2ci3aeny4-ijknq5kq6cei7e8/S02-a3ikn4cjkrw5ajn6-kn, 0, 0, 182, obobo!
3, B2-a3r4cknqrtw5cjkny6cei7e8/S02ckn3-ekq4eiqy5-aeiq6c8, 0, 0, 116, obobo!
3, B2cin3-nqry4ejnwy5ejnqy6c78/S02ik3ceiy4ijknqwy5acekn6-ek7e8, 0, 0, 656, obobo!
3, B2cin3-cny4-acnqw5ein6eik78/S01e3cer4eikrty5acery6ac7e, 0, 0, 140, obobo!
3, B2cin3-eiqr4-inqyz5aejry6cei7e/S02i3acijy4eijkrwy5eikr6cei7, 0, 0, 212, obobo!
3, B2cin3acir4eijkry5-aekn6k7c/S02ci3-cery4cinqrw5ejn6-ae7e8, 0, 0, 120, obobo!
3, B2cin3aijy4-cktwz5ijkr6cei8/S02ik3ajkr4ektwy5ejr6ci7, 0, 0, 192, obobo!
3, B2-ae3acer4eiz5aejqy6-e7e/S01c2ei3ciknq4ackrw5ek6cik7c8, 0, 0, 110, obobo!
3, B2-ae3-ijn4ijknqty5aek6ain7/S01c2i3cry4aknqtz5ajq6ikn7e, 0, 0, 204, obobo!
3, B2cik3acjqr4aeijkt5ijr6ack78/S02-ae3-aciq4cey5enqr6-en7e8, 0, 0, 120, obobo!
3, B2cik3ajy4-acijz5ny6in7c8/S02akn3ejqr4inrz5-ay6aci7c, 0, 0, 156, obobo!
3, B2cin3aeiy4aeikqr5ceijk6ace7/S02i3-cjr4-acwz5cnr6ci78, 0, 0, 150, obobo!
3, B2ci3aqr4ceijkqt5-acjk6a7/S02aik3acjn4aeknqtz5cjqry6cik8, 0, 0, 136, obobo!
3, B2-an3ckq4aejkqwz5iknry6-ac/S01c2kn3-jqy4cknqz5-air6-ce78, 0, 0, 606, obobo!
3, B2cin3aeij4iny5aijny6cik7c/S02ein3aeir4itwy5ceijn6ack7c8, 0, 0, 118, obobo!
3, B2cik3ackqr4aejqrw5ijkqr6n7c8/S02ik3ijnqr4cekqrt5einq6ae7e, 0, 0, 124, obobo!
3, B2-ae3ajqr4cikqrt5ajnq6c78/S02ei3jnry4cijtwz5-aj6ac7, 0, 0, 116, obobo!
3, B2-ak3einr4cqrt5ejqr6c8/S01c2i3-ajqr4-jqrtz5aciry6c7e, 0, 0, 122, obobo!
3, B2cei3-knqy4einrw5aceky6-ai8/S02cik3ceijr4jnrwy5-enr6acn, 0, 0, 140, obobo!
3, B2-a3-ainy4aekqy5-cinq6-ei7c/S01c2-ak3cenry4-cqty5einqr6ak7c8, 0, 0, 123, obobo!
3, B2-ak3-ceij4nqty5enry6cik7e/S01c2-ek3-jry4aejkqrz5acei6aci7e, 0, 0, 104, obobo!
3, B2cin3ain4ceikty5kry6c78/S02en3-cejn4r5jy6i7e8, 0, 0, 108, obobo!
3, B2cik3akq4cy5aijky6k7e/S01c2aik3ajqr4-nqwyz5aeiy6i7e, 0, 0, 100, obobo!
3, B2-an3-aijn4jqrty5-cenq6c78/S01c2-ac3eiqy4acjrty5jknq6ikn8, 0, 0, 105, obobo!
3, B2ci3-jn4ceijkqz5ejry6cn7e/S02-cn3ceij4aeiqry5aijky6cik78, 0, 0, 238, obobo!
3, B2cin3aeiqr4cjnqwy5eijkr6acn8/S02ai3aei4ajkqwyz5acjn6eik7c, 0, 0, 124, obobo!
3, B2cin3ae4aerz5-jqr6-ak7e/S02-ik3akqy4antwy5eijry6-cn8, 0, 0, 182, obobo!
3, B2-ak3enqy4-ejknt5ajknr6-ik7e8/S02ei3akqr4ejkrt5-ajky6-c7, 0, 0, 146, obobo!
3, B2cik3aijk4eiqr5-cjqr6akn8/S02ei3acnqy4ceryz5acej6ak7e8, 0, 0, 280, obobo!
3, B2-an3akny4eqt5jk6aci8/S01c2-k3knqy4cey5-ceiy6ac7e8, 0, 0, 116, obobo!
3, B2-an3acer4ajkrz5jknq6-en7c8/S01c2-ce3eiy4acjy5akqry6cin7, 0, 0, 142, obobo!
3, B2-ae3-eikq4einrz5ainry6en8/S02cn3enqy4aeknwy5ekn6-n7c8, 0, 0, 122, obobo!
3, B2ci3aeikr4cjz5acj6ci7e/S02-ck3-cer4inry5jkqy6ck7e8, 0, 0, 100, obobo!
3, B2-a3jqy4ceijqwy5i6ac78/S012i3acjk4ejqrz5acei8, 0, 0, 106, obobo!
3, B2cin3ajkqy4aijrtz5ejkqy6-kn/S03cjkny4jrw5-ainy6ik7e8, 0, 0, 162, obobo!
3, B2-an3aknry4ceiqrwz5-akny6acn7e8/S01c2-c3cjknq4ekyz5ekqr6-ae7c8, 0, 0, 160, obobo!

Edit:
There is a p1102 in the list

Code: Select all

x = 5, y = 1, rule = B2-a3kry4ceikqyz5-cjk6-k7e8/S02-ak3-cjk4ajqrtwy5-inqy6c7
obobo!

[2718281828]

Edit:
There is a p1102 in the list

Code: Select all

x = 5, y = 1, rule = B2-a3kry4ceikqyz5-cjk6-k7e8/S02-ak3-cjk4ajqrtwy5-inqy6c7
obobo!

Even a p1344:

Code: Select all

x = 5, y = 1, rule = B2cik3aceiq4cjnrw5ceqy6-an7c8/S02cin3aejr4cejqyz5-aeij6ek8
obobo!

[testitemqlstudop]

Are b0 rules allowed? Because if so, no one mentioned this 1-cell p2:

Code: Select all

x = 1, y = 1, rule = B01c2ae3an4cinrwz5er6cik7e8/S2c3ajq4intz5jn6cek
o!

EDIT: Heck, there's this: (max pop 9 though)

Code: Select all

x = 1, y = 1, rule = B0/S
o!

[wildmyron]

Are b0 rules allowed?

As for the 5S project, oscillators in rules with B0 are not included in the main project, but there is a separate effort to collect small population oscillators in rules with B0 - its just that no one has picked up the task of maintaining the current status of that separate project. You'll find some B0 oscillators here: http://conwaylife.com/forums/viewtopic.php?f=12&t=3020 . I don't think anyone has been as comprehensive as for small ships in rules with B0. I outlined my thoughts on why patterns in rules with B0 should be considered separately in the 5S thread here: http://conwaylife.com/forums/viewtopic. ... 161#p56161 . There's some further discussion on that topic either side of my post. The same thoughts apply to this thread.

Here are some new periods

More unfiltered results, probably a few interesting discoveries here.

Nice work, and that p1344 certainly blows the previous record holder out of the water. Looks like you've been running the search script for quite a while. You should be able to run the filter-ships.py script on that output to get a list sorted by period and with exact duplicates removed (unless I've made some ships only assumption in there somewhere). I have another script which I use to format the results of the oscillator search with bbcode tags ready to post to the forum. It also picks out a single oscillator of each period. It's not as fully automated as the scripts used to manage the 5S collection, but I'm happy to provide it if anyone wants to run more of these searches. Here is an updated summary followed by the new 3-cell oscillator periods from your unfiltered results. Edit: script appended to the end of this post.

Updated summary of lowest population oscillators

Code: Select all

Periods 2 - 112, 2 cells
Even periods 114 - 222, 226, 234, 2 cells
Odd periods 113-123, 127-145, 149, 157-167, 173, 177, 181, 185, 189, 191, 193, 199, 201, 211, 219, 225-231, 263, 271, 279, 297, 313, 365, 453, 505, 843, 3 cells
Even periods 224, 228-232, 236-250, 254-292, 294, 298, 302, 306, 310-324, 328, 330, 334-348, 356, 358, 364, 368, 376, 380, 384, 390, 392, 396, 398, 412, 420, 422, 432, 434, 442, 444, 448, 460, 480, 484, 502, 510, 512, 550, 554, 572, 606, 626, 656, 674, 678, 698, 706, 716, 730, 756, 788, 804, 806, 826, 832, 882, 988, 998, 1010, 3 cells
All other periods, 4 cells

Odd periods:
p121, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-an3-iknr4acjknry5ceik6ikn7c/S01c2k3ijy4-inrtz5-ekqr6k
obobo!

p159, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3aejkq4iknwy5cknry6ack/S02ain3aejkn4aijknz5-nqr6-a7e
obobo!

p177, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3enqry4acjqyz5-aek6ein8/S02n3-cj4acijknr5aejqy6-ek
obobo!

p201, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-an3akqy4-acjqy5-airy6n8/S02ckn3jknqr4-aciqz5-jqy6-e7e8
obobo!

p219, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3ar4eijkz5ceikq6cin7c8/S01c2-ac3-ceiy4-ceknr5aej6-e78
obobo!

Even periods:
p256, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3jkn4cjrtz5aekqr6kn7c/S02ck3ejkqr4ceknryz5-anqr6ckn7c8
obobo!

p268, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3aeikn4eirtwyz5ce6cik7e8/S02ae3-acin4acjnqry5aejy6ack7c
obobo!

p290, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cei3-any4-twyz5-aejr6ei78/S02cei3c4cekqrwy5ceikq6en7c8
obobo!

p318, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-inqy4-ckny5cejkn6ci7e/S01c2ei3-any4aijw5ckr6acn7
obobo!

p324, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3aejy4-aetz5-ck6-e7c/S01c2cik3-aeik4-ceiy5-ijry6aen
obobo!

p480, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cei3iqr4-acekq5ceijn6-k78/S02ikn3ijy4acijkz5ikr6aci7
obobo!

p510, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cei3ry4-ektwz5eijkq6-an7/S02-e3-aery4cikty5cejnq6-cn7c8
obobo!

p656, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-nqry4ejnwy5ejnqy6c78/S02ik3ceiy4ijknqwy5acekn6-ek7e8
obobo!

p730, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3-cikn4acqz5-aeqy6ak7e8/S02cik3ejky4-aejnr5aejry6-kn
obobo!

p804, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cin3acei4acjtw5aijnq6cei7c8/S02a3-jny4-inqr5akqr6aci7e
obobo!

p882, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-ak3acry4aceiqrw5ceij6aek8/S01c2-a3iky4aciknqt5aeikn6aci8
obobo!

p894, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3-cjkn4ejkqrtz5cn6cin78/S02cek3-anr4-cnqtz5cik6aci7
obobo!

p968, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3-aejn4ikrz5-ikq6cin/S01c2cik3-jkny4eijry5cjknr6-ei78
obobo!

p1086, 3 cells

Code: Select all

x = 5, y = 1, rule = B2ci3-i4ceiknyz5enqy6ik7c/S02ikn3eknqy4-acjty5cejq6ck7
obobo!

p1102, 3 cells

Code: Select all

x = 5, y = 1, rule = B2-a3kry4ceikqyz5-cjk6-k7e8/S02-ak3-cjk4ajqrtwy5-inqy6c7
obobo!

p1344, 3 cells

Code: Select all

x = 5, y = 1, rule = B2cik3aceiq4cjnrw5ceqy6-an7c8/S02cin3aejr4cejqyz5-aeij6ek8
obobo!

Edit: Script to format highP oscillator search results:

Code: Select all

# filter_oscs_forum.py

# Script to process output of oscillator search scripts
# - Reads in high period oscillator search results from a file (in sss format)
# - Selects one osc of each period
# - Writes bbcode formatted results to file
# NOTE: Clobbers the clipboard

import golly as g
import sss

resultFile = 'highPosc.txt'
outFile = 'highPosc-forum.txt' # File with osc collection formatted for forum

foundShips = dict()

# Return the minimum and maximum of the absolute value of a list of numbers
def minmaxofabs(v):
    v = map(abs, v)
    return min(v), max(v)

# Read in the results file and check each ship to see if it is unique
# If it is then add it to the set of known ships
# Adapted from filter_ships.py

g.show('Converting oscillators ...')
g.new('')
N = 0
with open(resultFile) as fIn:
    for shipstr in fIn:
        if not shipstr[0] in '123456789':
            continue
        ship = shipstr.split(', ')
        # ship format: "minPop, rulestr, dx, dy, period, rlestr"
        if not len(ship) == 6:
            g.note('Invalid ship string found:\n\n' + shipstr)
        pop = int(ship[0])
        rulestr = ship[1]
        P = int(ship[4])
        shiprle = ship[5].strip()
        
        if not P in foundShips:
            # Clear the layer
            r = g.getrect()
            if r:
                g.select(r)
                g.clear(0)
            
            g.putcells(g.parse(shiprle))
            g.setrule(rulestr)
            g.select(g.getrect())
            g.copy()
            shipRLEstring = g.getclipstr()
            
            foundShips[P] = shipRLEstring
                
g.show('Writing results to file...')
with open(outFile, 'w') as fOut:
    # Write out odd period ships first (above p100)
    Plist = foundShips.keys()
    Plist.sort()
    for P in Plist:
        if (P>100) and P%2:
            fOut.write('p%d, 3 cells\n[code]%s

\n' % (P, foundShips[P].strip()))
fOut.write('\n')
# Write out even period ships (above p200)
for P in Plist:
if (P>200) and (P+1)%2:
fOut.write('p%d, 3 cells\n

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%s

\n' % (P, foundShips[P].strip()))

g.show('Finished writing bbcode formatted oscillators to file: %s' % outFile)
[/code]

[Macbi]

Nice work Sarp!

Updated summary of lowest population oscillators

You missed the periods 498, 894, 968, 1086, 1102 and 1344. The correct status table is:

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Periods 2 - 112, 2 cells
Even periods 114 - 222, 226, 234, 2 cells
Odd periods 113-123, 127-145, 149, 157-167, 173, 177, 181, 185, 189-193, 199, 201, 211, 219, 225-231, 263, 271, 279, 297, 313, 365, 453, 505, 843, 3 cells
Even periods 224, 228-232, 236-250, 254-294, 298, 302, 306, 310-324, 328, 330, 334-348, 356, 358, 364, 368, 376, 380, 384, 390, 392, 396, 398, 412, 420, 422, 432, 434, 442, 444, 448, 460, 480, 484, 498, 502, 510, 512, 550, 554, 572, 606, 626, 656, 674, 678, 698, 706, 716, 730, 756, 788, 804, 806, 826, 832, 882, 894, 968, 988, 998, 1010, 1086, 1102, 1344, 3 cells
All other periods, 4 cells