## Rules with small adjustable spaceships

For discussion of other cellular automata.
wildmyron
Posts: 1518
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

### Re: Rules with small adjustable spaceships

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``<snip (2,1) slope ship>``

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``<snip (3,1) slope ship>``
Very nice! And so simple - I was evidently looking at this problem in a convoluted way.
The fastest I can make the (2,1) slope ship go is (4,2)c/52:
(2,1)c/(4n+2), p(8n+4), n>5:

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``````x = 14, y = 20, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e8
2bo\$9bo3bo\$bo8bo\$obo6bo4\$10bobo\$11bo8\$3bo\$8bo3bo\$9bo\$8bo!``````
AforAmpere wrote:Are non-integer slopes possible in this rule? I can't seem to get them to work, but they might exist. All integer slopes are definitely possible:

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``<snip more oblique ships>``
Indeed, all rational slopes are possible. It would be nice to know what the minimum period for any particular slope is, and to write a script to generate the ship of any given slope. It may be worthwhile finding the slide-reflect reaction with the lowest possible repeat time first.

As for non-integer slopes you would need a totally different kind of construction. I can't remember where the discussion about this topic was (fairly recently too) but any pattern which meets the traditional definition of a ship in a regular Moore neighbourhood CA has a rational speed, almost by definition of what is a ship. I liked the idea for creating a pattern which moved with non-rational speed, but it can't be periodic and therefore must grow in size over time. I suppose it might be possible to use these dot movers to do the kind of computation which was discussed, and the construction may not need to be a UC, but it's certainly going to be a lot more complicated than a small rectangle.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

This is the fastest group of ships I could find in all known rules with slide mechanics:

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``````x = 87, y = 38, rule = B2aei3-aijq4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky78
3bo8bo21bo6bo37bo4bo\$ob2o9bo28bo35bo\$bobo9bobo26bo5bo25bo3bo\$12bo28bo
37bo3\$84b2o\$45bo2bo34bo2bo\$46b2o\$34b2o\$33bo2bo34bo2bo\$12bo2bo56b2o\$13b
2o57bo4bo\$78bo\$78bo7bo\$77bo8\$36bo7bo\$45bo\$45b2o\$44bo8\$3b3o7bo\$4bo\$5bo\$
4bo!
``````
The fastest direction of the ships seems to limit at 2c/11, which is much faster than the limit in the other rules.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

wildmyron
Posts: 1518
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

### Re: Rules with small adjustable spaceships

AforAmpere wrote:This is the fastest group of ships I could find in all known rules with slide mechanics:

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``<snip rle>``
The fastest direction of the ships seems to limit at 2c/11, which is much faster than the limit in the other rules.
Adding B3q allows some of these to go a bit quicker:
c/6 diagonal (p24), and (3,1)c/16 (p64)

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``````x = 33, y = 35, rule = B2aei3-aij4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky78
4bo5bo13bo5bo\$3bo19bo\$bobo17bobo\$4bo19bo\$10b2o18b2o\$9bo2bo16bo2bo4\$18b
o2bo\$19b2o\$19bo6bo\$b2o24bo\$o2bo23bo4bo\$26bo17\$3bo6bo\$11bo\$11b2o\$10bo!``````
The (2,1) slope ship can already go faster at (2,1)c/11 (p44) without B3q.

Personally, I prefer the ships made from bouncers with a smaller displacement - this won't result in the fastest ships but it does give the most flexibility in allowable displacements for the knightships, and I think will allow the lowest possible period for any given slope. I think these particular ships are also limited by the sparkiness of the reaction - it might be possible to tailor the search to reduce the extent of the spark somewhat.

Edit: Here's a bouncer which allows for lower period ships:
(n,1)c/(9n+1), p(18n+2), n>0

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``````x = 73, y = 40, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
4bo19bo19bo20bo\$3bo5bo13bo5bo13bo5bo14bo5bo\$bobo17bobo17bobo18bobo\$4bo
4b2o13bo4b2o13bo4b2o14bo4b2o\$8bo2bo16bo2bo16bo2bo17bo2bo3\$60bo2bo\$61b
2o\$68bo\$61bo7bo\$69bobo\$68bo\$b2o18b2o18b2o\$o2bo16bo2bo16bo2bo4\$44bo\$43b
o6bo\$42bo\$44bo6\$29bo\$22bo5bobo2\$28bo6\$2b3o\$10bo\$3bo\$4bo!``````
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

wildmyron wrote: Adding B3q allows some of these to go a bit quicker:
c/6 diagonal (p24), and (3,1)c/16 (p64)
Nice, that's got to be close to the limit.
wildmyron wrote: Personally, I prefer the ships made from bouncers with a smaller displacement - this won't result in the fastest ships but it does give the most flexibility in allowable displacements for the knightships, and I think will allow the lowest possible period for any given slope.
Why are lower periods important, is it aesthetic or is there some use for it? Though I guess the same thing could be asked about speed.

Here's a reliable method to make (4n,4)c/(20n+4) ships for all n > 1:

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``````x = 173, y = 100, rule = B2aei3-aij4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky78
10\$6bo5bo16bo5bo17bo5bo18bo5bo20bo5bo21bo5bo19bo5bo\$5bo22bo23bo24bo26b
o27bo25bo\$3bobo20bobo21bobo22bobo24bobo25bobo23bobo\$6bo22bo23bo24bo26b
o27bo25bo\$12b2o21b2o22b2o23b2o25b2o26b2o24b2o\$11bo2bo19bo2bo20bo2bo21b
o2bo23bo2bo24bo2bo22bo2bo7\$3b2o21b2o22b2o23b2o25b2o26b2o24b2o\$2bo2bo
19bo2bo20bo2bo21bo2bo23bo2bo24bo2bo22bo2bo8\$166bo\$163b3obo\$158bo4bob2o
\$164b3o\$165b3o\$166bo5\$132bo4bo\$138bo\$138bo2bo\$137bo7\$106bo6bo\$105bo\$
104b2o\$106bo7\$77bo6b3o\$85bo\$84bo\$85bo6\$52b3o\$53b2o6bo\$53bo\$54bo\$53bo5\$
34bo2bo\$33bo\$28bo4bo\$34bo7\$5bo4bo\$11bo\$11bo2bo\$10bo!
``````
Take the base ship as the knightship on the far right, and to increase the slope by 1, simply evolve the bottom part 12 steps and move it down 12 cells, and you should get the next oblique ship in the sequence. It works for all integer slopes (seemingly). This is probably doable with a script.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

The method works with diagonal (2,2) pushes as well:

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``````x = 22, y = 30, rule = B3-eqr4-inqrt5ceijy6cek7c8/S02-i3-aeiy4ciqrwz5-aejy6ein7c
6\$4bo3\$7bo\$5bobo\$6b2o4\$10b2o\$9b3o\$8bo2bo\$8b3o6\$4bo!
``````

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``````x = 29, y = 29, rule = B3aijkn4ajwy5cj6k7c/S02-in3-aeiy4iqr5ciknr6e7c
15bo6\$21bo\$22bo\$20b3o\$4bo\$2b2o\$3b2o2\$o2\$28bo\$24bo\$23bo\$23b3o5\$10bo\$11b
o\$9b3o3\$13bo!
``````
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

dani
Posts: 1029
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Rules with small adjustable spaceships

(4,1)c/19 in one of the rules (-S2i so it's not explosive):

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``````x = 7, y = 6, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2aen4ciknr5aknq6k7e8
2o\$2o2\$o5bo2\$4bobo!
``````
EDIT: p54:

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``````x = 11, y = 7, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2aen4ciknr5aknq6k7e8
o2bo\$4bo\$3bo2\$4bo2\$10bo!
``````
she/her

bprentice
Posts: 786
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Rules with small adjustable spaceships

Danny,

Your puffer and oscillator seem to be misplaced, they are not related to small adjustable spaceships.

Brian Prentice

dani
Posts: 1029
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Rules with small adjustable spaceships

bprentice wrote:Danny,

Your puffer and oscillator seem to be misplaced, they are not related to small adjustable spaceships.

Brian Prentice
Well, I guess it is, but the rule has adjustable spaceships and was posted earlier. I didn't want to point this out again in a different thread, so I chose here.
she/her

calcyman
Posts: 2391
Joined: June 1st, 2009, 4:32 pm

### Re: Rules with small adjustable spaceships

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``````x = 25, y = 44, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e8
2bo\$9bo13bo\$10bo\$bo7bo\$obo19bo\$21bobo35\$3bo\$10bo13bo\$11bo\$10bo!
``````

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``````x = 37, y = 72, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e8
10\$5bo\$12bo12bo\$13bo\$12bo\$24bo\$23bobo12\$4bo\$3bobo38\$6bo\$13bo12bo\$14bo\$
13bo!
``````
Wow! This is seriously impressive -- has anyone looked at the isotropic rulemin and rulemax to see whether there's a non-explosive rule supporting this family of ships?
What do you do with ill crystallographers? Take them to the mono-clinic!

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

calcyman wrote: Has anyone looked at the isotropic rulemin and rulemax to see whether there's a non-explosive rule supporting this family of ships?
Unfortunately, there doesn't seem to be a non-explosive rule in there. However, literally any rule with the same push reaction has this property, so if someone can find a rule with the push reaction that is non-explosive, we have adjustable-slope ships in a non-explosive rule.

EDIT, here's one:

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``````x = 135, y = 28, rule = B3-cry4j5ci6c/S02ae3aijnr4r5ijny6ae
o46bo\$122bo\$2bo46bo\$3bo16bo29bo\$b3o17bo26b3o\$19b3o\$51bo\$5bo16bo105bo\$
129bo\$127b3o\$110bo\$109b2o\$108bob2o\$109b2o2\$131bo2bo\$130bo\$130b3o5\$117b
o\$118bo\$116b3o3\$120bo!
``````
This rule has the same reaction, but diagonal, and is non-explosive.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

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``````x = 99, y = 5, rule = B2ce3-knq4eqrwy5-ckq78/S012ck3cjnqy4cintz5acekq6in7c
39bo17bo40bo\$o28bo36bo5bo\$9bo5bo\$29b2o34b2o5b2o\$8b2o5b2o!
``````
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

muzik
Posts: 3960
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

What does this one cover, exactly?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

What do you mean by cover? Smaller adjustable-slope ships in area are available and more generalized speeds:

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``````x = 45, y = 49, rule = B2ce3-knq4eqrwy5-ckq78/S012ck3cjnqy4cintz5acekq6in7c
2\$3bo14bo9bo14bo2\$18b2o7b2o13\$40bo\$40bobo15\$o\$obo9\$2bo17bo3bo17bo\$22bo
2\$20bobobo\$22bo!``````
This rule has a 2c/164, 4c/164 and 6c/164, which isn't something possible in previous rules as far as I am aware.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

muzik
Posts: 3960
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

AforAmpere wrote:What do you mean by cover?
Are there any values of nc/x for where n isn't achievable at all?

Also, is this the minimum possible rule for these spaceships? Sadly it seems explosive.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

muzik wrote: Are there any values of nc/x for where n isn't achievable at all?
All even displacements should be possible. The minimal rule is this:

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``B2ce3-knq4erwy5-ckq7c8/S012ck3jny4cintz5akq6in7c``
Unfortunately it is still explosive. If you search with LLS for rules with the same bouncing reactions, you may be able to find a non-explosive rule.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

LaundryPizza03
Posts: 1241
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: Rules with small adjustable spaceships

Here's one for orthogonal:

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``````x = 23, y = 63, rule = B2ce3cen4ekt6kn/S01c2aen4cknr5aknq8
4bo\$11bo10bo\$12bo\$11bo3\$19bobo\$20bo8\$bobo\$2bo2\$3bo\$16bo4bo\$17bo\$16bo5\$
21bo\$3bo13bo\$16bo\$17bo18\$18bobo\$19bo8\$obo\$bo2\$2bo\$15bo4bo\$16bo\$15bo!
``````

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``````x = 64, y = 64, rule = B2ce3cen4ekt6kn/S01c2aen4cknr5aknq8
b2obobob2obo2b5o2bo5b5ob3o3bo2b2obo2bob2obob2o3b3o\$3bobo2b3ob4o3bob2ob
obo2b8obo5b5o2bobo3b4ob2o\$2bob2o2bo4bobo3b2ob2o7bo2b2ob3ob3o2b4o2b3o2b
2o3b2o\$3bo3bobo4b2o2b2ob2o2b2o2bo2bo8b2obo2bo2b2o4b4ob2o\$b2ob3obob3ob
2ob2ob5ob2ob3o4bo2b2ob3o2b2obob3ob2o2b4o\$o2b3o2bo2bo2bo2b4ob2o2bobob2o
bobo3bobob2obob2o2b5obob3o\$bo2bo4b3o3bobo4b3o3b2o3bo4b5ob2o2bo2bob2obo
3bo2bo\$4obo5b5o2b3o2bo2bo2bo2b2o3bobo4b2o2b4o2b3ob3o\$2ob7o4b2o2bo2bobo
3b2ob5obob2o5b2ob5obo2bo3b3o\$2o3bob6obo2bo2b7obob2ob2obobob4obo6bo2bob
ob3obo\$o2b4ob3ob2ob2ob2ob2o4b4obob2o2bob2o2bob3o10bo2bo\$b4obobo2b4obob
2obobobo2bobo2b3obo2bo6b4obo5b2o\$2bo7bo3bo2bo3b3o2b3o4bobobob2o7b2o2bo
2b3o2b3o\$2obobo2bo3bo3b3obob3o2bo4bobo3b2o4b2o4bo2b3o3b2obo\$5obo2b2o2b
obobo5bo2bobo2bo3b4o3bo3bobobob2ob2obob2o\$b6o4bob3obo2bob2ob2obobo3b2o
bo4b2o7bob2o2b2o\$2obo4b3obo2bob4obo3bo3bob2o2bo2bo4b3obob7ob2o2bo\$2bo
4bobob3o3b5obob2o3bo3bobo2bo3bobo3b4o2bo6b2o\$obo2b2o3b3obob4o3bo2b4o3b
2o2b2o4bo6b2ob2o2bob3o\$3o2b2obo4b2ob2o2b2obo3b2obob2o2bob2obob2o5b2ob
3o2bo2bobo\$6b4obo3bo2b2obob2o4b2obob3o2b2o3bob2o4b2o2b2o3bobo\$bob2obo
3bobo2bo5b2obo7bo2bo2b5obo3b3obobo3b3o\$2ob4o2bo3bo3bobobo3bob4ob2ob3o
3bo3b2obob3o7bob2o\$5bo2bo4bo5b2o2bobo2bo2b3obob4o2bob2o3b3o2b4o3b2o\$5b
o3bobob2ob3obo2b6ob2ob2o4b2o5bo2bo2bo7bo\$obo3bo2b2o2b4obo3bobo4b2o2b2o
2bob2obob3ob6ob2o2b4o\$5b4ob2o2bob3ob2o2bo2bob2obo6bobob2obobo4b5o2b4o\$
2b2ob2o2bob2ob2obob4obo2b4obo2bobob4o3bobo3bo2bob2obo2bo\$3ob3o3bo3bobo
6b2ob3obob4obobob4o2bo2b4ob2obo2bo\$2b3ob2o4b2o3b2obob2o6b3obo2bo2b2ob
2obo2b2o2b7obobo\$2bo2bob2obob2obob2o3b2obo4b3ob2o2bo2b2o2b3o2b2o3bo2b
2obobo\$2b4o2b2obobo3bob6o5b2ob3obo4bo4b2obobo4b2o2bobo\$o4b3obobob6o3b
2o2bo2b2o5bob2o4bo4bob7ob4o\$b2o2bob7ob2obob2ob3o2b2obobo3b4obo2b2o2b2o
bob2ob7o\$o5bo2bob2o3b3o2bo3b5ob2ob2ob2o3bo4bo2b3o2bo3bob2o\$bo2bobo6bob
3ob5ob3obo2b3o2b2o2b2o3bo2b2o2bo2bo2b2o\$obobo3bobobob5o2bob3ob4obobob
2o2bo2b4obo2b9ob2o\$3bo4b3ob5ob2o3b3ob8obob3obob2ob2o2b2ob3ob5o\$bo2b2ob
o2bo3bo2b2o3bo2b3ob4ob7o3bobo4b2obo2bob3obo\$4o7bobob2o2b2o3bob2o2bo2b
3ob2o5bobob3o4b2o3bo2bo\$5o4b2ob4o10bobob2ob2o3b2obo2b7ob2ob5ob2o\$2bo3b
obob2o3bobo2bob3o4bo3b3o4b2obo4bo5b2o6bo\$3b4o2bo3b3obobo6bobo4bobo2bob
ob7obo2bob3obo2b2o\$2b3ob5ob3o2b2o2bob3o2b3o2bo2bo4b6o6b6o3bo\$5bob6obob
obo3bo2bobo2b3obo3bob2ob2ob2obo2b4obob4o\$2ob2obobo3b2obob2o7b2ob3ob2ob
o2bo2b2o2b3o4b2o5bobo\$obo3b2ob4o2bob2o2b2ob3obobob4o4b5o8b3obob5o\$2bo
3bo3b2ob3o2bo4bob3obo2bobobob2o2b2o2b5obobobob2o2b2o\$o3bo4bob2ob2obo2b
3o3b3obo2b4ob3o3b3obobo2b2obob3o\$o2bob2ob2o2b2o4b2ob2o3bob2ob2o2bo2bo
2bo5b2obobob2obo4b2o\$6o2bo2bobobo3bo2b3o2bob4ob2obo3b7obo2bob2obob2o2b
o\$bobobob2o3bobobo2bob4obob2ob3o5b2o2b2o3b3ob2ob5o\$2bobo3b7o2bobob3o2b
3ob2o2b2ob2o4bob5o3bob3o3bobo\$bobobobo2b3o3b3o5bo3b2obo2b7ob3ob4o3b6ob
2obo\$o2b2o3bobo2b4o7b3o5b3obo2bo2b4o2bo4b3ob7o\$o5bobobob2obo2bob2ob2ob
o2b2o8b2ob2o3bobo5b2o3b4o\$bob2ob3obob2ob3obo2b3ob2o2b5obobo5bob4obo3bo
3bobobo\$o3b4obobob2o3b3o4bob2o2bob3obob2obob4o2bob2obo2b2ob3o\$o4b2obob
2obo6bo2bo2b2ob2ob4o6bob2o4bobo3b4o2bo\$3b3o2b3o3bo3bo8b2ob2o3bob2ob4ob
4ob4o2bo2bo3bo\$bobobo5b6ob3o2b2o3bob2o7b3obo2b4o3bo4bobo\$2o3bo3b2ob7o
3b3o2b2obobo3bobob3obob2obob2o5b3obo\$obob2o3b2obo4b2o2bob4o2bo4bob2o3b
4ob2obo2bo3bo2b2ob2o\$bo4b3o2b2obobob2obo4bo2bo2b3obo2bob2ob3o4b2obo2b
4obo!
``````
Note that this is similar to a rule previously posted in this thread.

Code: Select all

``````x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o\$b2o\$2o!
``````
LaundryPizza03 at Wikipedia

The latest edition of new-gliders.db.txt and oscillators.db.txt have 31531 spaceships and 1293 oscillators from outer-totalistic rules. You are invited to help!

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

LaundryPizza03 wrote:Here's one for orthogonal:
This rule does not have the other bouncing reaction (where the ships bump each other up) if you were responding to the above by muzik. Regardless, that is the first orthogonal non-explosive rule that has the first bouncing reaction that I have seen, nice job.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

This is a adjustable rule that allows for various speeds, as the 'reflector' can act colour preserving and changing:

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``````x = 59, y = 134, rule = B2-ak3a4-cqrwz5iny6ck7e8/S01c2an3aeij4eiqz5jr6ak
14\$31bo4\$28b2o\$28bobo3\$30bo6\$31bo4\$29b2o\$29bobo3\$31bo5\$31bo4\$29b2o\$29b
obo3\$30bo4\$31bo5\$28b2o\$28bobo3\$30bo5\$31bo5\$29b2o\$29bobo3\$31bo4\$31bo5\$
29b2o\$29bobo3\$30bo10\$39bo\$40bo2bo\$32bo5b2o11\$43bo\$42bobo\$32bo11bo\$30bo
bo\$31bo3\$41bo\$42bobo\$31bo8b2o!
``````
All periods except mod4=3 are possible (p14,16,17,18,20,21,22,...)
Just check:
https://catagolue.appspot.com/census/b2 ... z5jr6ak/C1

Edit1:
A similar rule (also apg-searchable https://catagolue.appspot.com/census/b2 ... w5cjn6k/C1 with e.g. an xq834 (in C1!) ):

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``````x = 13, y = 6, rule = B2c3aejnr4ciknty5in/S12kn3cejkr4jnrtw5cjn6k
bo9bo\$obo7bobo3\$bo8bo\$2bo8bo!
``````

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

In B1e all slopes are possible as well:

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``````x = 95, y = 126, rule = B1e2cei3jn4akqyz5cjn6ack7/S12a3-ijky4n5j6c7c8
67b2o\$67bobo13b2o\$50b2o15b2o14b2o\$50b2o2\$83bo\$50bo31bobo\$49bobo30b3o\$
49b3o8\$78b2o\$78bobo3b2o\$51b2o25b2o4b2o\$51b2o23\$50b2o\$2b3o3b2o3b2o35b2o
\$2bobo3b2o3b2o4b3o\$3bo15bobo\$20bo27b3o\$48bobo\$49bo\$20b2o\$20b2o27b2o\$
49b2o8\$49b2o\$49b2o4\$47b3o\$47bobo\$48bo2\$48b2o\$48b2o6\$49b2o\$49b2o5\$47b3o
\$47bobo\$48bo2\$48b2o\$48b2o6\$49b2o\$49b2o6\$47b3o\$47bobo\$48bo2\$48b2o\$48b2o
8\$49b2o\$49b2o7\$47b3o\$47bobo\$48bo2\$48b2o\$48b2o!
``````

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

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``````x = 42, y = 66, rule = B2ce3a5y7e8/S01c2-e3-i45-r6-c7c8
3o5b3o5b3o4b3o5b3o5b3o\$obo5b3o5b3o4b3o5bobo5bobo\$3o5b3o5bobo4bobo5bobo
5b3o\$3o5bobo5b3o4b3o5b3o5bobo\$3o5b3o5b3o4b3o5b3o5b3o\$3o5b3o5b3o4bobo5b
3o5b3o\$obo5b3o5bobo4b3o5bobo5b3o\$3o5b3o5b3o4b3o5b3o5b3o\$3o5bo7bobo4b3o
5b3o5b3o\$3o13b3o4bobo5bobo5b3o\$3o13bobo5bo6b3o5b3o\$o15bobo3b5o4b3o5b3o
\$16b3o3bo3bo4b3o5b3o\$16b3o12b3o5b3o\$16b3o12b3o5b3o\$16b3o12b3o7bo\$16bob
o12bobo\$16b3o12b3o\$16bobo12b3o\$16b3o12bobo\$16bobo12b3o\$16b3o12b3o\$16b
3o12b3o\$16bobo12b3o\$16b3o12bobo\$16bobo12b3o\$16b3o12b3o\$16bobo12b3o\$16b
3o12b3o\$16bobo12b3o\$16b3o12bobo\$16bo14bobo\$31b3o\$31b3o\$31b3o\$31bobo\$
31b3o\$31b3o\$31b3o\$31b3o\$31bobo\$31b3o\$31b3o\$31b3o\$31bobo\$31bobo\$31b3o\$
31bobo\$31b3o\$31b3o\$31b3o\$31b3o\$31bobo\$31b3o\$31bobo\$31b3o\$31b3o\$31b3o\$
31bobo\$31b3o\$31b3o\$31b3o\$31bobo\$31b3o\$31b3o\$31bo!
``````
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

A class that is similar to what we know anyway, but with some delaying options:

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``````x = 45, y = 59, rule = B2-ae3ajqr4ijntz5-ajy6k7c/S01e2cek3jn4aekn5aknqy6e7c
2\$6bo10bo10bo10bo\$6bo10bo10bo10bo5\$6bo10bo10bo10bo\$4bobo8bobo8bobo8bob
o3\$5b2o3\$5b2o9b2o3\$5b2o9b2o9b2o4\$5bo10bo10bo10bo\$5bo10bo10bo10bo13\$5bo
10bo10bo10bo\$5bo10bo10bo10bo4\$5bo10bo10bo10bo\$3bobo8bobo8bobo8bobo3\$4b
2o3\$4b2o9b2o3\$4b2o9b2o9b2o4\$4bo10bo10bo10bo\$4bo10bo10bo10bo!
``````

muzik
Posts: 3960
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

A similar concept from drc posted a few years ago:

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``````x = 3, y = 3, rule = B346/S12/G3
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````

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``````x = 3, y = 3, rule = B346/S12/G4
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````

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``````x = 3, y = 3, rule = B346/S12/G5
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````

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``````x = 3, y = 3, rule = B346/S12/G6
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````

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``````x = 3, y = 3, rule = B346/S12/G7
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````

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``````x = 3, y = 3, rule = B346/S12/G256
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

toroidalet
Posts: 1267
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

### Re: Rules with small adjustable spaceships

A while ago I had an idea which would result in all rational speeds below a certain value (including unreduced speeds). Here is a proof of concept (except that there is only a push reaction; in such a ship the other side would pull the dot instead of push it):

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``````x = 8, y = 35, rule = B2cek3-jkqr4kqrtwy5-cy6-kn/S02-kn3ir4ijknwyz5cin
o6\$bo\$obo22\$7bo4\$bo\$obo!
``````
Actually, it's a lot like a moving glider loop. To ensure that all speeds can be reached, the phase changes need to be a specific way (so that the ships with 1 signal inside have a period of 4n).

Perhaps a different ship without B2c should be used because then there only needs to be 1 column of space between the lanes.
[off-topic]
Coincidentally, the above rule has a second reflection reaction with this ship and a dot:

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``````x = 5, y = 7, rule = B2cek3-jkqr4kqrtwy5-cy6-kn/S02-kn3ir4ijknwyz5cin
o5\$3bo\$2bobo!
``````
It allows for really satisfying things like this:

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``````x = 43, y = 35, rule = B2cek3-jkqr4kqrtwy5-cy6-kn/S02-kn3ir4ijknwyz5cin
20bo9\$10bo3\$13bo\$12bobo\$28bo2\$o\$15bo7\$7bo4\$21bo20bo6\$33bo!
``````
[/off-topic]
"But if you close your eyes—does it almost feel like nothing's changed at all?
And if you close your eyes—does it almost feel like you've been here before..."

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

I've been trying to find a reaction that can pull and flip in the same rule as a push and flip reaction, but no luck yet. I had actually tried to find a ship with this idea before, but I could not find anything.
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

77topaz
Posts: 1497
Joined: January 12th, 2018, 9:19 pm

### Re: Rules with small adjustable spaceships

muzik wrote:A similar concept from drc posted a few years ago:

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``````x = 3, y = 3, rule = B346/S12/G3
.A\$A.A\$A.A!
[[ THEME Blues ]]
``````
Here's another Generations ship which can be slowed by increasing the number of states:

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``````x = 7, y = 5, rule = 235678/3456/7
2.3A\$.5A\$AF.CDCA\$.5A\$2.3A!
``````

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``````x = 7, y = 5, rule = 235678/3456/8
2.3A\$.5A\$AG.CDCA\$.5A\$2.3A!
``````

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``````x = 7, y = 5, rule = 235678/3456/9
2.3A\$.5A\$AH.CDCA\$.5A\$2.3A!
``````

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``````x = 7, y = 5, rule = 235678/3456/10
2.3A\$.5A\$AI.CDCA\$.5A\$2.3A!
``````
...

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``````x = 7, y = 5, rule = 235678/3456/100
2.3A\$.5A\$AsC.CDCA\$.5A\$2.3A!
``````
With six states, the ship still sort of works, but behaves somewhat differently:

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``````[code]x = 7, y = 5, rule = 235678/3456/6
2.3A\$.5A\$AE.CDCA\$.5A\$2.3A!
``````