Slowest 2-state spaceships of each cell count

For discussion of other cellular automata.
Post Reply
User avatar
Saka
Posts: 3627
Joined: June 19th, 2015, 8:50 pm
Location: Indonesia
Contact:

Slowest 2-state spaceships of each cell count

Post by Saka » September 16th, 2017, 9:10 am

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:

Code: Select all

x = 1, y = 1, rule = MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!
For 2 cells, here is BlinkerSpawn's, a c/11o ship:

Code: Select all

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:

Code: Select all

x = 2, y = 3, rule = B2cen3jkq4eiqrz5-jn6eik7e8/S02n3anq4knqr5jy6ein7c
bo$o$bo!
4 cells (wildmyron), c/141:

Code: Select all

x = 3, y = 3, rule = B2cn3-ejqr4aeiknty5einqr6-ac7e/S02ac3anr4nqz5ir8
2bo$obo$2bo!
Provide a ruleTable (Unless you have a MAP generated) and an RLE
Last edited by Saka on October 11th, 2017, 8:25 am, edited 3 times in total.

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » September 16th, 2017, 9:13 am

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...

User avatar
Saka
Posts: 3627
Joined: June 19th, 2015, 8:50 pm
Location: Indonesia
Contact:

Re: Slowest 2-state spaceships of each cell count

Post by Saka » September 16th, 2017, 9:16 am

muzik wrote: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 wrote:A direction is not needed, just a speed.
So basically it doesnt matter

Rocknlol
Posts: 125
Joined: April 15th, 2012, 9:06 am

Re: Slowest 2-state spaceships of each cell count

Post by Rocknlol » September 16th, 2017, 4:17 pm

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

Code: Select all

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

wildmyron
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Slowest 2-state spaceships of each cell count

Post by wildmyron » September 24th, 2017, 11:58 pm

@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:

Code: Select all

x = 3, y = 3, rule = B2cn3-ejqr4aeiknty5einqr6-ac7e/S02ac3anr4nqz5ir8
2bo$obo$2bo!
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » October 10th, 2017, 6:13 am

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

Code: Select all

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

wildmyron
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Slowest 2-state spaceships of each cell count

Post by wildmyron » October 10th, 2017, 6:45 am

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

Code: Select all

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.
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

User avatar
Saka
Posts: 3627
Joined: June 19th, 2015, 8:50 pm
Location: Indonesia
Contact:

Re: Slowest 2-state spaceships of each cell count

Post by Saka » October 10th, 2017, 7:11 am

wildmyron wrote: No. Gen 3 to gen 4 requires birth transition which would cause undesired birth after gen 1.
Actually;

Code: Select all

@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
Posts: 1542
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Slowest 2-state spaceships of each cell count

Post by wildmyron » October 10th, 2017, 8:09 am

Saka wrote:
wildmyron wrote: No. Gen 3 to gen 4 requires birth transition which would cause undesired birth after gen 1.
Actually;

Code: Select all

@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.
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » October 10th, 2017, 8:21 am

So what's its MAP string?

User avatar
BlinkerSpawn
Posts: 1992
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Slowest 2-state spaceships of each cell count

Post by BlinkerSpawn » October 10th, 2017, 9:00 am

muzik wrote:So what's its MAP string?
What's the MAP string for this (c/11)?

Code: Select all

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

Code: Select all

@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
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Image

User avatar
Saka
Posts: 3627
Joined: June 19th, 2015, 8:50 pm
Location: Indonesia
Contact:

Re: Slowest 2-state spaceships of each cell count

Post by Saka » October 10th, 2017, 9:15 am

BlinkerSpawn wrote:
muzik wrote:So what's its MAP string?
What's the MAP string for this (c/11)?

Code: Select all

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

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

User avatar
Saka
Posts: 3627
Joined: June 19th, 2015, 8:50 pm
Location: Indonesia
Contact:

Re: Slowest 2-state spaceships of each cell count

Post by Saka » October 11th, 2017, 8:26 am

Updated

User avatar
BlinkerSpawn
Posts: 1992
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Slowest 2-state spaceships of each cell count

Post by BlinkerSpawn » October 11th, 2017, 9:41 am

Saka wrote: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.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Image

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » October 15th, 2017, 7:02 am

muzik wrote:So what's its MAP string?
Still no answer.

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » February 21st, 2023, 7:29 am

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:

Code: Select all

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:

Code: Select all

#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.

Code: Select all

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.

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » February 21st, 2023, 9:29 am

BlinkerSpawn wrote:
October 10th, 2017, 9:00 am
muzik wrote:So what's its MAP string?
What's the MAP string for this (c/11)?

Code: Select all

x = 3, y = 1, rule = 2CellSlug
obo!
Here's one at half that speed, for c/22:

Code: Select all

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

AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

Re: Slowest 2-state spaceships of each cell count

Post by AforAmpere » February 22nd, 2023, 3:50 pm

C/268:

Code: Select all

x = 3, y = 1, rule = MAPBTPfc2Ai8i8UKZQ1gWgJgDJA6qgxIQQMSZrAJAICZwQRRvaIBALhoBYAuMAGwCQAUAiGAJkRAK6AAQAAxAACKA
obo!
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

User avatar
NimbleRogue
Posts: 524
Joined: January 11th, 2021, 11:48 pm

Re: Slowest 2-state spaceships of each cell count

Post by NimbleRogue » February 23rd, 2023, 5:45 am

muzik wrote:
February 21st, 2023, 7:29 am
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

Code: Select all

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

Code: Select all

x = 4, y = 3, rule = B3-cnqy4e5kr6n7c/S2-i3-ay4einrtyz5cejn6cin78
bo$3o$ob2o!

Code: Select all

#14c/85265o
x = 10, y = 4, rule = B2-an3-iqy4iknrtz5aijqy6aei78/S02ck3nqy4eiqrtwy5-ekq6-i78
2bo4bo$3b4o$ob6obo$2b6o!

User avatar
muzik
Posts: 5612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Slowest 2-state spaceships of each cell count

Post by muzik » February 23rd, 2023, 6:12 am

NimbleRogue wrote:
February 23rd, 2023, 5:45 am
muzik wrote:
February 21st, 2023, 7:29 am
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

Code: Select all

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.

Post Reply