Smallest Spaceships Supporting Specific Speeds (5s) Project

[muzik]

Anyone found that (7,1)c/8 yet, and if not, how exactly would I go about finding one?

[AforAmpere]

No, and try using LLS for progressively larger bounding boxes. I am fairly sure that in the slight chance that one exists, it is not possible to find.

[Moosey]

2c/48, 7 cells
Though I suppose there's a smaller one.

Code: Select all

x = 3, y = 4, rule = B34ky5e/S23-a4ity6c
2bo$b2o$obo$2o!

EDIT:
8c/104 in a rule compatible with it, 10 cells

Code: Select all

x = 19, y = 4, rule = B34ky5cy/S23-a4ity6c7
2bo$ob2o$b2o13b3o$bo!

I call the rule 104life. It is not usually explosive, but occasionally explodes.

[Macbi]

No, and try using LLS for progressively larger bounding boxes. I am fairly sure that in the slight chance that one exists, it is not possible to find.

You could use calcyman's MetaSAT as your SAT solver. It's the best solver available for difficult problems.

[Hdjensofjfnen]

No, and try using LLS for progressively larger bounding boxes. I am fairly sure that in the slight chance that one exists, it is not possible to find.

You could use calcyman's MetaSAT as your SAT solver. It's the best solver available for difficult problems.

Yes, but you'd get turned away at the door. A good TI-84 calculator for section 4 is a better investment.

[Moosey]

14,21c/83

Code: Select all

x = 6, y = 5, rule = B2k3acijr4ijqy6n7c/S2aek3ijnqr4it5n
2b4o$b2o2bo$2o2bo$bo2bo$2b2o!

[77topaz]

I don't expect the database already had a (37,19)c/224:

Code: Select all

x = 56, y = 24, rule = B3-nqy4aqz5cn6n8/S2-i3-a4inqz7c8
25b2o$21b2o2b2o$21bo5b2o$21bob3o2bo$22b2o2bobo$25b3o$26bo3$45b2ob2o$5bo38b2ob
4o$3ob3o38b3o2bo3b2o$o5bo39b5o4bo$3ob2o42bo5bo2$3bo5bo44bo$b5ob5o13b3o26b2o$o
4bobo3bo12bo2bo$o4bobo3b2o11bo2bo$3ob2ob2ob2o12b3o2$28b2o$28b3o$29bo!

The rule is known as "zombielife" on the Discord, and it will probably get a thread soon as it has numerous other interesting patterns as well.

[Moosey]

I don't expect the database already had a (37,19)c/224:

Code: Select all

x = 56, y = 24, rule = B3-nqy4aqz5cn6n8/S2-i3-a4inqz7c8
25b2o$21b2o2b2o$21bo5b2o$21bob3o2bo$22b2o2bobo$25b3o$26bo3$45b2ob2o$5bo38b2ob
4o$3ob3o38b3o2bo3b2o$o5bo39b5o4bo$3ob2o42bo5bo2$3bo5bo44bo$b5ob5o13b3o26b2o$o
4bobo3bo12bo2bo$o4bobo3b2o11bo2bo$3ob2ob2ob2o12b3o2$28b2o$28b3o$29bo!

The rule is known as "zombielife" on the Discord, and it will probably get a thread soon as it has numerous other interesting patterns as well.

A bit off topic, but:
Is that the rule I nicknamed zombielife?

[77topaz]

Yes, it's the same rule - as you could see by simply looking at the rulestrings.

[wildmyron]

Unfortunately the first post of this thread does not have a link to the most up to date 5S collection. It is hosted on my Google Drive and is the most comprehensive reference available. Thanks to AforAmpere for the big New Year's update.

2c/48, 7 cells
Though I suppose there's a smaller one.

Code: Select all

x = 3, y = 4, rule = B34ky5e/S23-a4ity6c
2bo$b2o$obo$2o!

The 5S collection contains this 3-cell 2c/48 ship:

Code: Select all

x = 3, y = 4, rule = B2-ai3knqr4acijknw5i/S02n4r
o3$obo!

If you have a look through the collection you will find very many 3-cell ships, and you'll see that very many speeds of the form kc/P for small k and P <= 100 have smallest known ships with populations <= 5 cells (mostly 3 cells for k=1, 2 or 3).

8c/104 in a rule compatible with it, 10 cells

Code: Select all

x = 19, y = 4, rule = B34ky5cy/S23-a4ity6c7
2bo$ob2o$b2o13b3o$bo!

I call the rule 104life. It is not usually explosive, but occasionally explodes.

8c/104, 3-cells

Code: Select all

x = 3, y = 4, rule = B2-an3-ijny4i5ciky6a/S02ci3enqr4cqrtw5jnry6-en
2bo$o2$o!

14,21c/83

Code: Select all

x = 6, y = 5, rule = B2k3acijr4ijqy6n7c/S2aek3ijnqr4it5n
2b4o$b2o2bo$2o2bo$bo2bo$2b2o!

That's a nice little oblique ship (with minimum population of 9 cells) and is a new speed for the collection. Here it is in 5S orientation and phase:

Code: Select all

x = 5, y = 5, rule = B2k3acijr4ijqy6n7c/S2aek3ijnqr4it5n
2o$o2bo$4bo$4bo$2b3o!

I don't expect the database already had a (37,19)c/224:

Code: Select all

x = 56, y = 24, rule = B3-nqy4aqz5cn6n8/S2-i3-a4inqz7c8
25b2o$21b2o2b2o$21bo5b2o$21bob3o2bo$22b2o2bobo$25b3o$26bo3$45b2ob2o$5bo38b2ob
4o$3ob3o38b3o2bo3b2o$o5bo39b5o4bo$3ob2o42bo5bo2$3bo5bo44bo$b5ob5o13b3o26b2o$o
4bobo3bo12bo2bo$o4bobo3b2o11bo2bo$3ob2ob2ob2o12b3o2$28b2o$28b3o$29bo!

In fact, there are no ships with that displacement at any period. Minimum population is actually 99 cells:

Code: Select all

x = 56, y = 25, rule = B3-nqy4aqz5cn6n8/S2-i3-a4inqz7c8
29b2o$28b3o$27b2o$27bo25bo$30bo15b3o$31bo14b3o2b2ob2o$3bo24bo2bo13bo3b
obo3bo$3bo25b3o13b5ob5o2$2obo$bo2bo$47bo3b2ob2o$bobo3b2o35b2o5bo3bo$b
2o4bob2o38bob2ob2o$7b2ob2o$8bobo42bo2$33bo$33bo$30b2o$29b2ob3o$29bob2o
2bo$29bo5bo$30b5o$32b2o!

I expect a smaller variant could be found with one of the Rulesrc or searchRule Python scripts which were used to find many of the ships in this thread. Some of these scripts can be found in the Rulesrc thread. Sadly this is one of my many unfinished projects.

==========

Here is a script which I use to canonise ships for this project.

Code: Select all

# canonise5Sship.py
# Adjust phase and orientation of a ship in the current layer to the 5S project standard
# Return SSS representation of ship
# SSS format: minpop, 'rulestr', dx, dy, period, 'shiprle'

import golly as g
import sss

maxgen = 10000
r = g.getrect()
if not r:
    g.exit('Pattern is empty')
rulestr = g.getrule()
minpop, speed = sss.testShip('', '', maxgen)
if speed:
    shiprle = sss.giveRLE(g.getcells(g.getrect()))
    newship = (minpop, rulestr)+speed+(shiprle,)
    newship = sss.canon5Sship(newship, maxgen)
    g.show(str(newship))
    g.getstring("SSS format string:", ', '.join(map(str, newship)), "canonise5Sship.py")
else:
    g.show('No periodic behaviour detected after %d generations.' % maxgen)

It depends on the sss.py module which is attached to this post. I was developing sss.py as a collection of functions to aid in the search for small spaceships. It uses a format I termed SSS to represent small spaceships which is derived from David Eppstein's glider database format.

[Moosey]

10c/210d

Code: Select all

x = 18, y = 7, rule = B2i3-q4eqz5y/S23-a4iyz
15b3o$b2ob2o$o3bob2o$4bo2bo$7bo$2b2o2bo$4bo!

[Hdjensofjfnen]

Hmm... a 9-cell (5,0)c/13 turned up in Mooselife:

c/2 and 5c/13:

Code: Select all

x = 23, y = 6, rule = B34kz5e7c/S23-a4ityz5k
3o4b3o10bo$o2bo2bo2bo10bo$o8bo10b2o$2bo4bo13bo$20bobo$20b2o!

The former is the teardrop ship, and is known. The latter is not.

Is that a new speed? 5c/13?

[wildmyron]

10c/210d

Code: Select all

x = 18, y = 7, rule = B2i3-q4eqz5y/S23-a4iyz
15b3o$b2ob2o$o3bob2o$4bo2bo$7bo$2b2o2bo$4bo!

That ship has a minimum population of 11 cells. This one from the 5S collection has 5 cells:

(10, 10)c/210, 5 cells

Code: Select all

x = 3, y = 3, rule = B2n3-cnqy4z5ckry6i8/S2-i3-a4einrtyz5ajkr6aci7
2o$bo$obo!

Hmm... a 9-cell (5,0)c/13 turned up in Mooselife:

Is that a new speed? 5c/13?

No, it is not a new speed. From the 5S collection:

(5, 0)c/13, 3 cells

Code: Select all

x = 2, y = 3, rule = B2cen3ai4-acerz5q8/S02-cn3ejr4ijwz5-ijkr6-ae7c
o$bo$o!

Furthermore, the 5c/13 in Mooselife is period 26 which for the purpose of this thread is referred to as 10c/26. Yes, this is out of step with many other pattern collections, particularly in CGoL, but it just kind of started out that way and makes maintaining this collection a bit easier. For the record, there is also a 3-cell 10c/26 ship:

(10, 0)c/26, 3 cells

Code: Select all

x = 3, y = 5, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
2bo2$2bo2$o!

The most comprehensive and up to date reference available for the 5S collection is hosted in a folder on my Google Drive.

If for some reason you are unable to use these files there was a parallel project to host the collection on the LifeWiki. Up to period 28 the smallest ships of all known speeds are tabulated there. There was also a summary page maintained by muzik, but I think it is out of date now.

Edit: Corrected cell count for 10c/210d shaip and removed superfluous commentary.

[77topaz]

(10, 0)c/26, 3 cells

Code: Select all

x = 3, y = 5, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
2bo2$2bo2$o!

Interestingly, this rule also has a three-cell (1,0)c/16:

Code: Select all

x = 3, y = 5, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
obo4$bo!

As well as a more common (1,0)c/2:

Code: Select all

x = 3, y = 3, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
obo2$bo!

EDIT: The c/16 can be extended as a sort of wick:

Code: Select all

x = 16, y = 5, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
15bo$4bo9bo$o2bobo$4bo9bo$15bo!

EDIT 2: A natural puffer made from two interacting copies of the 10c/26:

Code: Select all

x = 16, y = 16, rule = B2-ai3nry4ciqrty5aery6n7e/S02k4etz5y6a
4ob3obo4b2o$ob2o5bobob2o$b2o2b2o2b3o2bo$b2ob4obob5o$o2bob3o3b3o$2b2o3b
o2b3o$2bo2bo2b2ob3o$2b2obob2obob2o$o3b2o2b5obo$5o3b3o3b2o$bobobob4ob2o
bo$2ob2o2b3ob2ob2o$b2o3bo2bo2b3o$4b2o6b2o$2obobo4bo2b2o$bobobobobo2b2o
!

[muzik]

If for some reason you are unable to use these files there was a parallel project to host the collection on the LifeWiki. Up to period 28 the smallest ships of all known speeds are tabulated there. There was also a summary page maintained by muzik, but I think it is out of date now.

Edit: Corrected cell count for 10c/210d shaip and removed superfluous commentary.

I've updated the summary page for shaips up to period 36.

Personally I think it might be a better idea to retire the longer pages, and only use these summary pages. The numbers would link to the ship's Catagolue page.

[muzik]

I've updated the table up to 42.

Is there any way that MediaWiki can support a three-dimensional version of this table, so we can fit all slopes in as well? For example, some sort of two-dimensional tab system?

It'd also be helpful if someone helped to fill in some more Catagolue links (even posting a bunch of the links here so I can include them would do just fine).

[AforAmpere]

Thanks everyone. I've added the new ships to my local copy of the file, but will not update the Drive for a bit, as I will be running some searches for more ships soon. The table is also looking good, but I don't think we can make it 3-dimensional.

EDIT, 28c/176, 158 cells:

Code: Select all

x = 67, y = 87, rule = B2k3-cnq4ejz5kr6c/S2-n3-ay4ceinrt5jkn6cn7c8
6bo$6bo2b2o$10bo4$11b2o$12b2o$3bo7bo2bo3bo$11b5obo$19b2o$4bo9bo2b3o$b
4o8b2o2b2o$4b4o5bobobo$2bobobobo4bob3o$o3bo2bo5b2o$4bo2bo6b3o$2b2o11bo
$2bo$3bo$bo2bo$bo$bo$3bo22$29b3o$28bo2bo$28bo$28b5o$30bobo$29bo$28bo$
30b4o$29bo2bo$28bo2b2o$32bo$28bo2bo$28b3o13$45b3o$45bobo$44b2obo$47b2o
$43bo$43b6o$45bo2bo$40b2o6bo$40bo2b3obo3bo$40b4o5b3o7b3o$58bo2bo$58bo$
58b2o$59bo2b2ob2o$59b4ob2o$58bo3bo$59b3o!

EDIT 2, also, since no C/97 d's have been found, I'll put in this one.
C/97 diagonal, 50 cells:

Code: Select all

x = 49, y = 49, rule = B3aceij4k/S1c2-ei3cjnr4cq5ac6e
2bo$bo$obo$3bo$4bo$5bo$6bo$7bo$8bo$9bo$10bo$11bo$12bo$13bo$14bo$15bo$
16bo$17bo$18bo$19bo$20bo$21bo$22bo$23bo$24bo$25bo$26bo$27bo$28bo$29bo$
30bo$31bo$32bo$33bo$34bo$35bo$36bo$37bo$38bo$39bo$40bo$41bo$42bo$43bo$
44bo$45bo$46bo$47bo$48bo!

[testitemqlstudop]

Somehow no one (correct me if i'm wrong) posted c/3 diagonal, so I'll just add the sailing boat:

Code: Select all

x = 3, y = 3, rule = B2ce3ikn4aqr5n/S02k3an4in
2o$obo$bo!

[Ian07]

Somehow no one (correct me if i'm wrong) posted c/3 diagonal, so I'll just add the sailing boat:

Code: Select all

x = 3, y = 3, rule = B2ce3ikn4aqr5n/S02k3an4in
2o$obo$bo!

Actually, all possible speeds with a period of up to 7 have been documented, though not necessarily in this thread, and so there is a 3-cell c/3 diagonal ship:

Code: Select all

x = 3, y = 3, rule = B2cei3a/S02i3i
2bo2$obo!

[AforAmpere]

I wish I could just add a requirement where any person that posts has to check the files first, but there really isn't a way to enforce it.

[77topaz]

(9,2)c/101, 39 cells:

Code: Select all

x = 28, y = 27, rule = B3-k4c/S2-i34c8
b2o$b2o9$2bo$3b2o$2ob2o$bob2o$2bo2$24b2o$24b2o3$21bo$19bo$18b2obo$11bo
5bo2bo$11b2o5b2ob2o$10b2o14b2o$26b2o!

[wildmyron]

(9,2)c/101, 39 cells:

Code: Select all

x = 28, y = 27, rule = B3-k4c/S2-i34c8
b2o$b2o9$2bo$3b2o$2ob2o$bob2o$2bo2$24b2o$24b2o3$21bo$19bo$18b2obo$11bo
5bo2bo$11b2o5b2ob2o$10b2o14b2o$26b2o!

I quite like that engine, and the higher period (puffer) versions of it which appeared in the related rule, particularly the way that the interaction suppresses all of the higher period behaviour. But would you believe that there's already a small ship with that speed in the 5S collection? No? Me neither.

(9,2)c/101, 5 cells

Code: Select all

x = 3, y = 3, rule = B2n3aijkr4j5cek6ci7c8/S2-ci3-acky4einrtz5anr6c7
b2o$2o$bo!

By the way, oscar.lua seems to report spaceship speed as (dy,dx)c/P whereas we've been using (dx,dy)c/P, where dx>dy, in this project. I'm not sure where the discrepancy originated but it means that the speed of oblique ships in this project doesn't match the speed reported by oscar when that ship is directly viewed in Golly.

@testitemqlstudop: As it happens, a c/3 diagonal ship was posted very early on in the thread. Unfortunately, it's pretty much impossible to use the forum's search function to find posts relating to low period ships or oscillators within this thread due to the 3 character limit. Also, the original collection appears to no longer be available, and many ships have been added to the collection by AforAmpere and myself without being posted here. The wiki version is an easy place to see ships of all the known low period speeds if you haven't got a copy of the full collection (specifically the three .rle.txt files).

I've updated the table up to 42.

Thank you. I'm a bit confused about how the table is presented though. Could you add a key on the page? I'm sure I saw the meaning of the colours posted in this thread a long time ago, but I can't find it. Are they meant to be the same as on the other wiki page? In that case I think it's just that some of them are out of date, e.g. 5c/6. You mention two updates, but I only see one recent change in the history - am I looking at the most up to date version? Edit: No, I wasn't - don't use this link.

It'd also be helpful if someone helped to fill in some more Catagolue links (even posting a bunch of the links here so I can include them would do just fine).

I'm sure I'm looking at the wrong page now, which Catagolue links are you after?

I wish I could just add a requirement where any person that posts has to check the files first, but there really isn't a way to enforce it.

Hey, relax I reckon the recent interest in contributing to this project suggests we need an easier way for people to check the known speeds and to see if a candidate ship is a new record smallest. It would be great to have something (web page, script in Golly, whatever) which shows off the amazing array of ships already collected and to make it easier for people to contribute.

[77topaz]

Re: the wiki pages, no oblique ships at all appear on the "periods 100 to 110" page (and the individual oblique pages haven't been created yet), which is why I didn't know there was already a (9,2)c/101 in the 5S collection.

[wildmyron]

Re: the wiki pages, no oblique ships at all appear on the "periods 100 to 110" page (and the individual oblique pages haven't been created yet), which is why I didn't know there was already a (9,2)c/101 in the 5S collection.

Indeed. I've tried to be consistent in mentioning that the wiki is only up to date for low(ish) periods and that the text files are the most comprehensive source. In fact I don't really know where the wiki is at because I haven't personally contributed to it, and I honestly feel that this project is at a stage where it can only be reliably maintained with the assistance of an automated system. There is such a system for the .rle.txt files hosted on the Drive folder, and that's why AforAmpere and I keep directing people to them. Is anybody unable to access those files? AFAIK my settings for that directory allow anyone with the link to have access, no Google account needed.

I think it's worth mentioning that there are over 33,000 ships in the collection, including over 14,700 oblique ships. And we're not even close to finding ships for all possible speeds with period less than 100, let alone 1000.

Edit: A couple of ships from a search inspired by the (9,2)c/101

30c/508 diagonal, 9 cells

Code: Select all

x = 4, y = 4, rule = B2n3-k5c6i7c/S2-i34c5e6ci7e
bobo$ob2o$bobo$b2o!

(10,5)c/143, 6 cells

Code: Select all

x = 3, y = 4, rule = B3-k5c7c/S2-i3-c6c7
o$2o$2bo$b2o!

[muzik]

http://www.conwaylife.com/wiki/LifeWiki ... ew/Slope_0

Shouldn't be too hard to find, given it's linked on the main 5s page.