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Smallest oscillators with a certain period

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Smallest oscillators with a certain period

Postby wwei23 » June 27th, 2017, 10:00 am

There are two ways to do it. One-smallest cell count. Two-smallest bounding box. If a and b are tied in a category but one of them wins in the other, then it will be that one that gets the credit.
P1(Block, both categories)
x = 2, y = 2, rule = B3/S23
2o$2o!

P2(Blinker, both categories)
x = 1, y = 3, rule = B3/S23
o$o$o!

P3(Caterer, cell count)
x = 8, y = 6, rule = B3/S23
2bo$o3b4o$o3bo$o$3bo$b2o!

P4(Mold, cell count)
x = 6, y = 6, rule = B3/S23
b2o$o2bo$obo2bo$bo$2b2obo$4bo!

P5(Psuedo-barberpole, cell count)
x = 12, y = 12, rule = B3/S23
2o$o$2bo$2bobo2$4bobo2$6bobo2$8b2o$11bo$10b2o!

P5(Octagon 2, bounding box)
x = 6, y = 6, rule = B3/S23
bo2bo$ob2obo$bo2bo$bo2bo$ob2obo$bo2bo!

P6(Unix, cell count and bounding box?)
x = 8, y = 8, rule = B3/S23
2b2o$4bob2o$o2bo2b2o$obo$bo2$b2o$b2o!

P7(Burloaferimeter, cell count and bounding box, two phases)
x = 22, y = 11, rule = B3/S23
4b2o10b2o$4b2o10b2o2$4b4o8b4o$2obo4bo3b2obo4bo$2obo3bobo2b2obo2b2obo$
3bobo2bo6bo4bo$3bob3o7bob3o$4bo11bo$5bo11bo$4b2o10b2o!

P8(Figure 8, cell count and bounding box)
x = 6, y = 6, rule = B3/S23
2o$2obo$4bo$bo$2bob2o$4b2o!

P17(Honey thieves, cell count)
x = 15, y = 15, rule = B3/S23
2o$bo$bobo9b2o$2bobo8bo$11bobo$11b2o$5b2o$5b2ob2o$8b2o$2b2o$bobo$bo8bo bo$2o9bobo$13bo$13b2o!

P17(54P17.1, bounding box)
x = 15, y = 13, rule = B3/S23
5bo9b$4bobo8b$4bobo3b2o3b$b2obob2o3bo3b$2bobo6bob2o$o2bobob3obo2bo$2ob obo4bobo2b$3bobo2b2o2b2ob$3bobo3bobo3b$4b2obobobo3b$6bobobo4b$6bobo6b$ 7b2o!

P24(Caterer on figure 8, cell count)
x = 18, y = 6, rule = B3/S23
4b2o6bo$2bob2o4bo3b4o$bo8bo3bo$4bo5bo$2obo9bo$2o9b2o!

By the way, I have a search program for Life and other totalistic cellular automata here:
https://www.khanacademy.org/computer-pr ... 0702893056
Last edited by wwei23 on July 4th, 2017, 10:36 am, edited 6 times in total.
Replicator!
x = 3, y = 3, rule = B3/S234y
2bo$3o$bo!
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Re: Smallest oscillators with a certain period

Postby dvgrn » June 27th, 2017, 10:14 am

wwei23 wrote:There are two ways to do it. One-smallest cell count. Two-smallest bounding box.

I think muzik's collection posted two days ago would be a good place to start. I haven't checked to see if muzik chose smallest population or smallest bounding box for all those samples.

There are a lot of people out there who are somewhat obsessive about these statistics, so the relevant LifeWiki pages usually mention if a small oscillator is a record setter in either category.
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Re: Smallest oscillators with a certain period

Postby wwei23 » June 27th, 2017, 10:31 am

Now all we need to do is search every pattern in a 48-cell bounding box for the P3, and we're done for P3 and bounding box.
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Re: Smallest oscillators with a certain period

Postby muzik » June 27th, 2017, 10:50 am

dvgrn wrote:
wwei23 wrote:There are two ways to do it. One-smallest cell count. Two-smallest bounding box.

I think muzik's collection posted two days ago would be a good place to start. I haven't checked to see if muzik chose smallest population or smallest bounding box for all those samples.


There's an updated version below that post.

I chose minimum population, however due to my laziness some of them might not be in the minimum phase.
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Re: Smallest oscillators with a certain period

Postby wwei23 » June 27th, 2017, 10:58 am

But is there an undiscovered smaller oscillator?
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2bo$3o$bo!
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Re: Smallest oscillators with a certain period

Postby muzik » June 27th, 2017, 3:18 pm

That's what we all like to believe, but searching for such a thing would take ages and probably wouldnt be worth our time.
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Re: Smallest oscillators with a certain period

Postby Gamedziner » June 27th, 2017, 8:14 pm

Just checked with WLS, found no solutions for an 11-cell or less p3 oscillator within an 8 by 8 bounding box.
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Re: Smallest oscillators with a certain period

Postby wwei23 » June 27th, 2017, 8:41 pm

Smallest cell count does not mean smallest bounding box. The big problem is that that while it is trivial to search for a pattern that fits in a bounding box, searching for cell count is much harder, because of long-distance interactions between spaceships(mostly gliders?).
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x = 3, y = 3, rule = B3/S234y
2bo$3o$bo!
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Re: Smallest oscillators with a certain period

Postby wwei23 » June 27th, 2017, 8:42 pm

I'm pretty sure that 12 cells is the limit, though. Now, where can we keep a list without it getting in the way?
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