Slowest 2-state spaceships of each cell count

[Saka]

This will be a challenge to find the slowest 2-state ship of each cell count in any rule. Because it is 2-state, we can use MAP rules instead of ruletables, but that is optional. A direction is not needed, just a speed. For 1 cell, it's obviously this, c orthogonal or c diagonal:

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x = 1, y = 1, rule = MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

For 2 cells, here is BlinkerSpawn's, a c/11o ship:

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x = 3, y = 1, rule = MAPBTDe/yAA9/8AAP//AAD//yAA/78AAP//AID//wAA//8AAP//AAD/2wAA//8AgP//AAD//4AA//+AAH//AAD//w
obo!

3 cells (Rocknlol), c/313:

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x = 2, y = 3, rule = B2cen3jkq4eiqrz5-jn6eik7e8/S02n3anq4knqr5jy6ein7c
bo$o$bo!

4 cells (wildmyron), c/141:

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x = 3, y = 3, rule = B2cn3-ejqr4aeiknty5einqr6-ac7e/S02ac3anr4nqz5ir8
2bo$obo$2bo!

Provide a ruleTable (Unless you have a MAP generated) and an RLE

[muzik]

Wouldn't c orthogonal for one cell make more sense? If you think about it, c diagonal is sqrt(2) times as fact as c orthogonal...

[Saka]

Wouldn't c orthogonal for one cell make more sense? If you think about it, c diagonal is sqrt(2) times as fact as c orthogonal...

A direction is not needed, just a speed.

So basically it doesnt matter

[Rocknlol]

Three-cell c/313, although this can almost certainly be improved on:

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x = 2, y = 3, rule = B2cen3jkq4eiqrz5-jn6eik7e8/S02n3anq4knqr5jy6ein7c
bo$o$bo!

[wildmyron]

@Saka: nice 2-cell spaceship

@Rocknlol: very nice 3-cell spaceship, current record holder for the slowest 3-cell spaceship challenge in the Find a rule with... thread.

Here is the slowest 4-cell spaceship I have found so far, which pales in comparison to the above at c/141:

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x = 3, y = 3, rule = B2cn3-ejqr4aeiknty5einqr6-ac7e/S02ac3anr4nqz5ir8
2bo$obo$2bo!

[muzik]

Couldn't an evolution sequence like this allow for a slower 2-cell ship?

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x = 26, y = 2, rule = B/S012
2o3b2o3bo4bo4bo3b2o$6bo4bo3bo3bo!

[wildmyron]

Couldn't an evolution sequence like this allow for a slower 2-cell ship?

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x = 26, y = 2, rule = B/S012
2o3b2o3bo4bo4bo3b2o$6bo4bo3bo3bo!

No. Gen 3 to gen 4 requires birth transition which would cause undesired birth after gen 1.

[Saka]

No. Gen 3 to gen 4 requires birth transition which would cause undesired birth after gen 1.

Actually;

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@RULE MuzikThing

@TABLE
n_states:2
neighborhood:Moore
symmetries:none
0,1,0,0,0,0,0,0,1,1

1,0,0,0,0,1,0,1,0,0

0,1,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,0,1,0

0,0,1,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0

1,0,1,0,0,0,0,0,0,0
0,0,0,1,0,1,0,0,0,1

[wildmyron]

No. Gen 3 to gen 4 requires birth transition which would cause undesired birth after gen 1.

Actually;

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@RULE MuzikThing

@TABLE
n_states:2
neighborhood:Moore
symmetries:none
0,1,0,0,0,0,0,0,1,1

1,0,0,0,0,1,0,1,0,0

0,1,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,0,1,0

0,0,1,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0

1,0,1,0,0,0,0,0,0,0
0,0,0,1,0,1,0,0,0,1

Ha, evidently I was looking at it backwards.

[muzik]

So what's its MAP string?

[BlinkerSpawn]

So what's its MAP string?

What's the MAP string for this (c/11)?

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x = 3, y = 1, rule = 2CellSlug
obo!

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@RULE 2CellSlug

@TABLE
n_states:2
neighborhood:Moore
symmetries:none
0010000011

0100000101
0101000001

0110000011

0100000111
1110000010

1011100110

0001101101
1100000000
0000111001

1000111000
1011000000
1101100100
1000010110
0001110001
0000011101

0100010001

[Saka]

So what's its MAP string?

What's the MAP string for this (c/11)?

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x = 3, y = 1, rule = 2CellSlug
obo!

That's really cool! I'll update it tomorrow and find the MAP string.

[Saka]

Updated

[BlinkerSpawn]

Updated

Trivial counter-update (Sorry!):
Replacing death on 00011100 with death on 00011110 (for the canonical orientation in the OP) increases the period to 12.

[muzik]

So what's its MAP string?

Still no answer.

[muzik]

Here's one of the slowest 3-cell orthogonal spaceships in the 5s collection I could find (iOS's text search function doesn't permit over 1000 results), at c/1746:

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x = 2, y = 3, rule = B2-an3-eijn4cnw5-cjq6-kn78/S1c3-nqy4acktwy5-ijkr6ein78
o$bo$o!

Also, for 1-cell spaceships, assuming we permit B0, there's the following c/714 from the one-cell spaceships thread:

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#C by gameoflifemaniac and blah
x = 1, y = 1, rule = MAPhhPAmAASJAQAQgAACQCAAAEAAACAABEACAAEAAAAAAAAAQAAEAAAAAwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

It's been known since 2018 at the latest that for 2 states and 4 cells, arbitrarily slow spaceships can exist, so we can narrow our goal down to optimising spaceships with 1, 2 and 3 cells.

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x = 10, y = 33, rule = B2ek3aij4eir5a6ac/S01c2-an3eiqy4aenrt5aiq6ik7e
3bo3bo$9bo$7bo8$2bo4bo$9bo$7bo8$bo5bo$9bo$7bo8$o6bo$9bo$7bo!

It seems highly likely to me that there may exist a way to construct arbitrarily-slow 3-cell spaceships using the wickstretcher principle that was used for allowing arbitrarily-high-period 3-cell oscillators back in 2020.

EDIT: Turns out that indeed has already been done - by the same person. I did have a feeling that something of that nature would end up being discovered when searching for twelve rules where the configuration doesn't translate. So currently the only populations we can really optimise for are 1 and 2.

I'm not sure how we'd be able to do adjustable 2-cell spaceships. We'd likely need a rule where a single cell becomes slow wickstretchers that decay quickly like two cells do in the 3-cell case, and both wickstretchers must interact with each other in just the right way. Since the rule will necessarily be non-isotropic, we'll probably have more wiggle room.

[muzik]

So what's its MAP string?

What's the MAP string for this (c/11)?

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x = 3, y = 1, rule = 2CellSlug
obo!

Here's one at half that speed, for c/22:

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x = 3, y = 1, rule = MAPBTDXciAA8gQEAIAkAAAAACAAoKAAAAAEAICAIAAABAAAAKQAAAAgoAAAAAAAgAAAAACAAIAAAASAAAAAAAAAAA
obo!

[AforAmpere]

C/268:

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x = 3, y = 1, rule = MAPBTPfc2Ai8i8UKZQ1gWgJgDJA6qgxIQQMSZrAJAICZwQRRvaIBALhoBYAuMAGwCQAUAiGAJkRAK6AAQAAxAACKA
obo!

[NimbleRogue]

Here's one of the slowest 3-cell orthogonal spaceships in the 5s collection I could find (iOS's text search function doesn't permit over 1000 results), at c/1746:

c/2642 from a excel search

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x = 2, y = 3, rule = B2-a3-eijn4cnw5-cjq6cn7e8/S1c2n3-nqy4acjktw5-ijr6i78
bo$o$bo!

[muzik]

Here's one of the slowest 3-cell orthogonal spaceships in the 5s collection I could find (iOS's text search function doesn't permit over 1000 results), at c/1746:

c/2642 from a excel search

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x = 2, y = 3, rule = B2-a3-eijn4cnw5-cjq6cn7e8/S1c2n3-nqy4acjktw5-ijr6i78
bo$o$bo!

As impressive as this may be for minimum bounding box, it isn't breaking any new 3-cell speed records.

[AforAmpere]

C/268:

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x = 3, y = 1, rule = MAPBTPfc2Ai8i8UKZQ1gWgJgDJA6qgxIQQMSZrAJAICZwQRRvaIBALhoBYAuMAGwCQAUAiGAJkRAK6AAQAAxAACKA
obo!

C/2765:

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x = 3, y = 1, rule = MAPBTLfc2Ai8i8UK5Q1gWgZoDJA66gxIUQMSZrCJAISZwQRRvaIBELhsBYg/swVwWyBUAiHMJlRAK6KFTDBxABCqA
obo!

[LittleLWSS]

So what's its MAP string?

What's the MAP string for this (c/11)?

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obo!

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Ruletable

Maybe offtopic, but wickstretcher found:

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x = 4, y = 25, rule = 2CellSlug
3bo$b3o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o$4o
$4o$b2o!

hotdogPi: flipped pattern vertically; did not work before