## Smallest oscillators with a certain period

For general discussion about Conway's Game of Life.

### Smallest oscillators with a certain period

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/S232o\$2o!`

`x = 1, y = 3, rule = B3/S23o\$o\$o!`

P3(Caterer, cell count)
`x = 8, y = 6, rule = B3/S232bo\$o3b4o\$o3bo\$o\$3bo\$b2o!`

P4(Mold, cell count)
`x = 6, y = 6, rule = B3/S23b2o\$o2bo\$obo2bo\$bo\$2b2obo\$4bo!`

P5(Psuedo-barberpole, cell count)
`x = 12, y = 12, rule = B3/S232o\$o\$2bo\$2bobo2\$4bobo2\$6bobo2\$8b2o\$11bo\$10b2o!`

P5(Octagon 2, bounding box)
`x = 6, y = 6, rule = B3/S23bo2bo\$ob2obo\$bo2bo\$bo2bo\$ob2obo\$bo2bo!`

P6(Unix, cell count and bounding box?)
`x = 8, y = 8, rule = B3/S232b2o\$4bob2o\$o2bo2b2o\$obo\$bo2\$b2o\$b2o!`

P7(Burloaferimeter, cell count and bounding box, two phases)
`x = 22, y = 11, rule = B3/S234b2o10b2o\$4b2o10b2o2\$4b4o8b4o\$2obo4bo3b2obo4bo\$2obo3bobo2b2obo2b2obo\$3bobo2bo6bo4bo\$3bob3o7bob3o\$4bo11bo\$5bo11bo\$4b2o10b2o!`

P8(Figure 8, cell count and bounding box)
`x = 6, y = 6, rule = B3/S232o\$2obo\$4bo\$bo\$2bob2o\$4b2o!`

P17(Honey thieves, cell count)
`x = 15, y = 15, rule = B3/S232o\$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/S235bo9b\$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/S234b2o6bo\$2bob2o4bo3b4o\$bo8bo3bo\$4bo5bo\$2obo9bo\$2o9b2o!`

By the way, I have a search program for Life and other totalistic cellular automata here:
Last edited by wwei23 on July 4th, 2017, 10:36 am, edited 6 times in total.

wwei23

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### Re: Smallest oscillators with a certain period

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.

dvgrn
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### Re: Smallest oscillators with a certain period

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.

wwei23

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### Re: Smallest oscillators with a certain period

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.
waiting for apgsearch to support one-dimensional rules
muzik

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### Re: Smallest oscillators with a certain period

But is there an undiscovered smaller oscillator?

wwei23

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### Re: Smallest oscillators with a certain period

That's what we all like to believe, but searching for such a thing would take ages and probably wouldnt be worth our time.
waiting for apgsearch to support one-dimensional rules
muzik

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Location: Scotland

### Re: Smallest oscillators with a certain period

Just checked with WLS, found no solutions for an 11-cell or less p3 oscillator within an 8 by 8 bounding box.
Gamedziner

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### Re: Smallest oscillators with a certain period

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?).

wwei23

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### Re: Smallest oscillators with a certain period

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

wwei23

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