## Rules with small adjustable spaceships

For discussion of other cellular automata.
toroidalet
Posts: 1124
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

### Re: Rules with small adjustable spaceships

i'm not sure if these are actually adjustable, because although one could construct most speeds slower than or equal to c/5 that satisfy the given criterion, the sizes of such ships are basically arbitrary (though they should increase with period and displacement).
2c/10 dot puffers:

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``````x = 15, y = 12, rule = B2a3jkq/S01c3e
obo11bo\$4bo3bobo\$4bo3bobo\$obo11bo4\$bo\$2o10bo\$bobobo3bo\$bobobo3bo\$12bo!
``````
a fuse can make them into 2c/10 spaceships:

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``````x = 30, y = 17, rule = B2a3jkq/S01c3e
bo\$o12bo10bo\$3bo13bo5bo\$3bo13bo5bo\$o12bo10bo\$bo2\$18bo\$17bo11bo\$2bo16bo
3bobo\$bo11bobo3bo3bobo\$4bo24bo\$4bo21bo\$bo11bobobobo3bo\$2bo12bobobo3bo\$
14b2o10bo\$15bo!
``````
EDIT:
2c/12 (c/6) ship:

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``````x = 138, y = 6, rule = B2a3jkq/S01c3e
bo\$o136bo\$3bo3bo5bo15bobo7bo3bo7bo5bo5bo9bobobobo3bobobo3bobo11bobo3bo
bo3bo3bobo5bobobo\$3bo3bo5bo15bobo7bo3bo7bo5bo5bo9bobobobo3bobobo3bobo
11bobo3bobo3bo3bobo5bobobo\$o136bo\$bo!
``````
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

LaundryPizza03
Posts: 895
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: Rules with small adjustable spaceships

Goldtiger997's ships from the TFYUCA.

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``````x = 137, y = 2, rule = B2ik3-kqry4-ijky5-i6i7/S02a4i
b3o4b5o4b7o4b9o4b11o4b13o6b61o\$o3bo2bo5bo2bo7bo2bo9bo2bo11bo2bo13bo4bo
61bo!
``````
It doesn't seem to resemble any of those listed here.

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``````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 31150 spaceships and 1205 oscillators from outer-totalistic rules. You are invited to help!

wildmyron
Posts: 1421
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

@LaundryPizza03: That family of ships isn't displayed in the thread, but the first post does link to them (second last link in list of orthogonal ships).

@AbhpzTa: very nice rep-ship family!

@toroidalet: I agree that they don't quite fit the mould of other adjustable ships, but if we don't call them adjustable then there would need to be some other term defined with a meaning very similar to adjustable, and also to engineered, but not quite the same as either of them. I suspect the boundaries between the different definitions would be too hazy to make it worthwhile.
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.

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

### Re: Rules with small adjustable spaceships

Code: Select all

``````x = 9, y = 22, rule = B3-jkn4a/S1e2-a3ijnry4n
4bo\$4bo3\$2o5b2o2\$4bo\$4bo8\$3b3o\$4bo4\$4bo\$4bo!
``````

LaundryPizza03
Posts: 895
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: Rules with small adjustable spaceships

77topaz wrote:A small, unusual adjustable-speed rake:

Code: Select all

``````x = 9, y = 22, rule = B3-jkn4a/S1e2-a3ijnry4n
4bo\$4bo3\$2o5b2o2\$4bo\$4bo8\$3b3o\$4bo4\$4bo\$4bo!
``````
Speed is 3c/(12n+6) orthogonal, n≥6.

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``````x = 135, y = 27, rule = B3-jkn4a/S1e2-a3ijnry4n
4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo13bo13bo13bo13bo13bo13b
o13bo13bo3\$2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o
5b2o5b2o5b2o5b2o5b2o2\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo4\$3b3o\$4bo12b3o\$18bo12b3o\$32bo12b3o\$
46bo12b3o\$4bo55bo12b3o\$4bo13bo55bo12b3o\$18bo13bo55bo12b3o\$32bo13bo55bo
12b3o\$46bo13bo55bo12b3o\$60bo13bo55bo\$74bo13bo\$88bo13bo\$102bo13bo\$116bo
13bo\$130bo!
``````

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 31150 spaceships and 1205 oscillators from outer-totalistic rules. You are invited to help!

muzik
Posts: 3905
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

You've got "adjustable"-period photons for any period 2^n, n>1:

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``````x = 17, y = 80, rule = B2a4i5j/S1e3r
bo\$2o14\$2o\$bo4\$6bo\$5b2o2\$5b2o\$6bo8\$16bo\$15b2o10\$15b2o\$16bo15\$15bo\$14b
2o18\$14b2o\$15bo!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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

### Re: Rules with small adjustable spaceships

Knight-ships:

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``````x = 42, y = 31, rule = B2e3ijn4ijnryz6an7e/S12cen3acijq4qrz5acqr6ei
14\$13b2o\$21b2o\$29b2o\$37b2o3\$10bobo5bobo5bobo5bobo\$11bo7bo7bo7bo2\$11b2o
6b2o6b2o6b2o!``````

Code: Select all

``````x = 30, y = 12, rule = B2ci3a4aiwy5-aeny6ac/S01e2a3ajqr4airtz5ajnq6-e
\$4bo\$12bo\$20bo\$28bo2\$bo7bo7bo7bo\$b3o5b3o5b3o5b3o\$2bo7bo7bo7bo2\$2bo7bo
7bo7bo!``````
both are (2,1)c/(2+4n) spaceships for n>3

Edit1:

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``````x = 26, y = 11, rule = B2ei3ciknr4eiknqrz5ejny6en7c/S12-a3acik4ceqrtw5acekr6ekn8
3b2o\$10b2o\$17b2o\$24b2o4\$obo4bobo4bobo4bobo\$bo6bo6bo6bo2\$b2o5b2o5b2o5b
2o!``````
(2,1)c/(3+4n) knight-ships for n>4

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``````x = 30, y = 13, rule = B2cek3cnr4ejqrty5nry6k7e8/S012-cn3ny4ceiknrt5ikny6e8
\$3bo\$11bo\$19bo\$27bo3\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo\$bo7bo7bo7bo2\$bo7b
o7bo7bo!``````
(2,1)c/4n knight-ships for n>5

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``````x = 35, y = 12, rule = B2e3ikn4nqrwyz5cjnqy6ak7e8/S12cen3-kry4acknrw5acejq6k8
\$6b2o\$14b2o\$22b2o\$30b2o3\$3bobo5bobo5bobo5bobo\$4bo7bo7bo7bo2\$4b2o6b2o6b
2o6b2o!``````
(2,1)c/(1+4n) knight-ships for n>4

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

### Re: Rules with small adjustable spaceships

AforAmpere wrote:There is a chance that adjustable ships may exist in B2a rules:

Code: Select all

``````x = 67, y = 4, rule = B2ae3q/S0
o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo
3bo3bo5bo3bobobo3bo3bobo\$o!
``````
This reaction moves at C/7, with replicators and a backend. If someone can find something that can be pushed by the replicators, there might be a new class of adjustable ships.
There exist adjustable spaceships in B2a rules (but using a different 'technology'):

Code: Select all

``````x = 31, y = 10, rule = B2-ck3-aijq4-aiknr5-jny678/S01e2ein3-aijq4-nqtwy5-eiy6-ac78
2bo\$11bo\$20bo\$29bo5\$bobo6bobo6bobo6bobo\$o8bo8bo8bo!
``````
where the fastest one has speed c/6 (all speeds c/n, n>5 are supported), and

Code: Select all

``````x = 25, y = 10, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar678
2bo\$9bo\$16bo\$23bo4\$o2bo3bo2bo3bo2bo3bo2bo\$2bo6bo6bo6bo\$bo6bo6bo6bo!
``````
where the fastest one has speed c/5 (all speeds c/n, n>4 are supported).

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

### Re: Rules with small adjustable spaceships

AforAmpere wrote:There is a chance that adjustable ships may exist in B2a rules:

Code: Select all

``````x = 67, y = 4, rule = B2ae3q/S0
o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo
3bo3bo5bo3bobobo3bo3bobo\$o!
``````
This reaction moves at C/7, with replicators and a backend. If someone can find something that can be pushed by the replicators, there might be a new class of adjustable ships.
Actually, now that I think about it, isn't this pretty similar to the basilisk technology from HighLife? Are there any basilisk "recipes" that would work with this replicator and backend? Also, 2718281828, AbhpzTa did post some example ships using these, so it is known that ships can be constructed from it.

dani
Posts: 1004
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Rules with small adjustable spaceships

Not sure if this one is known, a 2c/14 in that rule:

Code: Select all

``````x = 25, y = 6, rule = B2a3jkq/S01c3e
23bo\$o23bo\$5bo11bo3bo\$5bo11bo3bo\$o23bo\$23bo!
``````
she/her
moose#0915

wildmyron
Posts: 1421
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

2718281828 wrote:
AforAmpere wrote:There is a chance that adjustable ships may exist in B2a rules:

Code: Select all

``````x = 67, y = 4, rule = B2ae3q/S0
o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo
3bo3bo5bo3bobobo3bo3bobo\$o!
``````
This reaction moves at C/7, with replicators and a backend. If someone can find something that can be pushed by the replicators, there might be a new class of adjustable ships.
There exist adjustable spaceships in B2a rules (but using a different 'technology'):

Code: Select all

``````x = 31, y = 10, rule = B2-ck3-aijq4-aiknr5-jny678/S01e2ein3-aijq4-nqtwy5-eiy6-ac78
2bo\$11bo\$20bo\$29bo5\$bobo6bobo6bobo6bobo\$o8bo8bo8bo!
``````
where the fastest one has speed c/6 (all speeds c/n, n>5 are supported), and

Code: Select all

``````x = 25, y = 10, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar678
2bo\$9bo\$16bo\$23bo4\$o2bo3bo2bo3bo2bo3bo2bo\$2bo6bo6bo6bo\$bo6bo6bo6bo!
``````
where the fastest one has speed c/5 (all speeds c/n, n>4 are supported).
These 2c/2n ships are very nice - I'm glad to see you found examples using dots and with minimum population of 4 cells.

There were some other examples posted earlier in the thread: moon bouncers which bounce the moon along the direction of travel rather than perpendicular to it, adjustable period c/2 spaceships, and of course AbhpzTa posted a method to construct different speed ships using AforAmpere's reaction in the very next post - perhaps not adjustable in the sense of easily modifying the ship to adjust the period/speed.
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.

muzik
Posts: 3905
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Hans anyone attempted to find 3c/n, etc. ships yet?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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

### Re: Rules with small adjustable spaceships

muzik wrote:Hans anyone attempted to find 3c/n, etc. ships yet?
Not 3c/n, but it should exist.

some bouncer using c/3 ships with certain speeds:

c/(6n+1):

Code: Select all

``````x = 27, y = 12, rule = B2cik3akq4-aekqyz5aknry6a7/S012ck3aejqy4acekrw5cjr678
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
c/(6n+2):

Code: Select all

``````x = 27, y = 12, rule = B2cik3ackq4-acekyz5-ijkr6i78/S012ckn3-iknr4ekqrty5-acny6-n78
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
c/(6n+3):

Code: Select all

``````x = 27, y = 12, rule = B2ckn3aceky4-acekr5ay6ci78/S012-an3ejkq4acikwy5-ceij6-ai
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
c/(6n+4):

Code: Select all

``````x = 27, y = 12, rule = B2cik3-ejnr4-aenrwz5cejry6k7e/S012cik3ej4-cjyz5eqr6cei7c8
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
c/(6n+5):

Code: Select all

``````x = 27, y = 12, rule = B2cik3acq4ijnqrw5jknqy6ein7e8/S012cik3ejqry4aceky5-eijq6-ek7c
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
c/6:

Code: Select all

``````x = 27, y = 12, rule = B2-ae3acqy4ceijkt5cjkq6ei/S012cik3aejr4ceikqry5-eijq6-n7e
2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!
``````
something related, speeds 2/6n n>10 (a 2c/3 ship is travelling between the dots)

Code: Select all

``````x = 28, y = 15, rule = B2-ei3cknqr4-aciqt5eknqy6-c78/S012ek3jkr4artyz5ainry6ck
3bo2\$11bo2\$19bo2\$27bo3\$3bo7bo7bo7bo\$ob2o4bob2o4bob2o4bob2o\$bobo5bobo5b
obo5bobo3\$2bo7bo7bo7bo!
``````
Something very fast (fastest is c/3):

Code: Select all

``````x = 28, y = 14, rule = B2ae3aknr4aeinty5ckqr6-in7c8/S01e2-ck3jknqr4cijnqr5cry6ce8
3bo\$11bo\$3bo15bo\$11bo15bo\$19bo\$27bo3\$o2bo4bo2bo4bo2bo4bo2bo\$b2o6b2o6b
2o6b2o2\$bo7bo7bo7bo2\$bo7bo7bo7bo!``````
something similar (larger):

Code: Select all

``````x = 29, y = 17, rule = B2a3acjkn4cqrtwy5acjky6-ac78/S1c2-ce3cijy4aeknrz5cnqy6-ik7
2bo\$3bo\$10bo\$11bo\$18bo\$19bo\$26bo\$27bo3\$bobo5bobo5bobo5bobo2\$2ob2o3b2ob
2o3b2ob2o3b2ob2o3\$bo7bo7bo7bo\$o7bo7bo7bo!
``````

AforAmpere
Posts: 1125
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

2718281828 wrote: Something very fast (fastest is c/3):
That rule can actually go to 2c/5!:

Code: Select all

``````x = 6, y = 10, rule = B2ae3aknr4aeinty5ckqr6-in7c8/S01e2-ck3jknqr4cijnqr5cry6ce8
2bo2\$2bo\$b2o\$o2bo3\$bobobo\$5o\$bobobo!
``````
I think that is the fastest ever adjustable speed ship, nice find of this rule! I wonder if any can even get above that speed.

EDIT, 4c/2n for n>6 at 6 cells minimum:

Code: Select all

``````x = 18, y = 12, rule = B2aen3akq4-jqtz5eiry6-in7c8/S02an3airy4ew5ejqy6-ek7e8
2bo13bo2\$2bo13bo2\$o2bo10bo2bo4\$o\$14bo\$o\$14bo!
``````
EDIT 2, down to 5 cells:

Code: Select all

``````x = 4, y = 7, rule = B2aei3-aijq4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky78
3bo5\$b3o\$o!
``````
EDIT 3, 5 cell maximum for 6c/2n for n>11:

Code: Select all

``````x = 15, y = 9, rule = B2-ck3anq4ejkrtyz5-acny6-ck7/S02en3-ceqy4cejkrwy5acqry6eik7e8
4bo9bo5\$10bo2bo\$o2bo8bo\$2bo8bo\$bo!
``````
EDIT 4, the fastest adjustable ship I could find with 6-cell displacement, at 3c/10:

Code: Select all

``````x = 5, y = 12, rule = B2-ci3knqr4cijkqyz5-iry6-ac78/S01e2en3cknqr4iknryz5eky6ei8
4bo2\$4bo3\$o2bo\$b2o3\$bo2\$bo!
``````
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: 1125
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

Another one of the questionable adjustable ship families, this rule is like the rule Muzik found with most if not all orthogonal speed under C/3. This rule has probably most speeds under C/9, but I've only found these so far, so it is hard to tell at the moment. Interestingly, these don't have a set backend like Muzik's rule, so they can form oscillators as well. Here are the known ships:

Code: Select all

``````x = 319, y = 74, rule = B2ce3cj6e/S12-in3-ci4ijkwy5k
11b4o90b2obo58b3o81b4o60b4o\$10b2o2bo89b2o60b2o2bo79b2o2bo59b2o2bo\$9b2o
3bo88b2o3bo56b2obobo78b2o3bo58b2o3bo\$8b2obob2o87b2o3b2o55b2o3b2o77b2ob
ob2o57b2o3b2o\$7b2o3b2o87b2obob2o55b2obob2o77b2o3b2o57b2o3b2o\$6b2obob2o
87b2o3b2o55b2o3b2o77b2obob2o57b2obob2o\$5b2o3b2o87b2obob2o55b2obob2o77b
2o3b2o57b2o3b2o\$4b2o3b2o87b2o3b2o55b2o3b2o77b2obob2o57b2o3b2o\$3b2obob
2o87b2obob2o55b2obob2o77b2o3b2o57b2o3b2o\$2b2o3b2o87b2obob2o55b2o3b2o
77b2o3b2o57b2obob2o\$b2o3b2o87b2o3b2o55b2o3b2o77b2o3b2o57b2o3b2o\$bo3b2o
87b2o3b2o55b2o3b2o77b2obob2o57b2obob2o\$o3b2o87b2o3b2o55b2obob2o77b2o3b
2o57b2o3b2o\$3b2o87b2o3b2o55b2obob2o77b2o3b2o57b2obob2o\$2bo88b2o3b2o55b
2o3b2o77b2o3b2o57b2o3b2o\$90b2obob2o55b2o3b2o77b2o3b2o57b2o3b2o\$89b2obo
b2o55b2o3b2o77b2o3b2o57b2o3b2o\$88b2o3b2o55b2o3b2o77b2obob2o57b2o3b2o\$
87b2o3b2o56bo3b2o77b2o3b2o57b2o3b2o\$86b2o3b2o56bo3b2o77b2obob2o57b2o3b
2o\$85b2obob2o60b2o77b2obob2o57b2o3b2o\$84b2o3b2o60bo78b2o3b2o57b2obob2o
\$83b2obob2o139b2o3b2o57b2o3b2o\$82b2o3b2o139b2o3b2o57b2obob2o\$81b2obob
2o139b2obob2o57b2o3b2o\$80b2obob2o139b2o3b2o57b2o3b2o\$79b2o3b2o139b2o3b
2o57b2o3b2o\$78b2obob2o139b2o3b2o57b2o3b2o\$77b2o3b2o139b2o3b2o57b2o3b2o
\$76b2o3b2o139b2obob2o57b2o3b2o\$75b2obob2o139b2o3b2o57b2o3b2o\$74b2o3b2o
139b2o3b2o57b2obob2o\$73b2obob2o139b2o3b2o57b2o3b2o\$72b2o3b2o139b2obob
2o57b2o3b2o\$71b2o3b2o139b2o3b2o57b2o3b2o\$70b2o3b2o139b2o3b2o57b2o3b2o\$
69b2o3b2o139b2o3b2o57b2o3b2o\$68b2o3b2o139b2o3b2o57b2o3b2o\$67b2o3b2o
139b2obob2o58bo3b2o\$66b2o3b2o139b2o3b2o59b2ob2o\$65b2obob2o139b2obob2o
60b4o\$64b2o3b2o139b2o3b2o\$63b2o3b2o139b2obob2o\$62b2o3b2o139b2o3b2o\$61b
2o3b2o139b2obob2o\$60b2o3b2o139b2o3b2o\$59b2o3b2o139b2o3b2o\$58b2obob2o
139b2o3b2o\$57b2o3b2o139b2o3b2o\$56b2o3b2o139b2obob2o\$55b2obob2o139b2o3b
2o\$54b2o3b2o139b2obob2o\$53b2obob2o139b2o3b2o\$52b2obob2o139b2obob2o\$51b
2o3b2o139b2o3b2o\$50b2obob2o139b2o3b2o\$49b2o3b2o139b2o3b2o\$48b2o3b2o
139b2o3b2o\$47b2o3b2o139b2o3b2o\$46b2o3b2o139b2o3b2o\$45b2obob2o140bo3b2o
\$44b2o3b2o140bo3b2o\$43b2obob2o144b2o\$42b2obob2o144bo\$41b2o3b2o\$40b2o3b
2o\$39b2o3b2o\$38b2obob2o\$37b2o3b2o\$36b2obob2o\$36bo3b2o\$35bo3b2o\$38b2o\$
37bo!
``````
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: 1004
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Rules with small adjustable spaceships

These ships work in rules B2ce3cj6e/S1c2aek3ajnqr4ijkwy5k - B2ce3cjknry4eijknqtyz5ejqry678/S12aceik3aejknqry4ceijkntwyz5ceijknry678, so perhaps there is a more interesting rule to be explored in there. I'll probably do some kerfuffling later today.
she/her
moose#0915

dani
Posts: 1004
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Rules with small adjustable spaceships

Some ships in one of those rules posted above:

Code: Select all

``````x = 663, y = 100, rule = B2a3ejkqy/S01c3e
4bobobo6bo\$14b2o10bo\$4bo10bobobo3bo\$15bobobo3bo\$4bobobo5b2o10bo\$15bo\$
8bo2\$4bobobo3\$75bo10bo\$4bobobo6bo49bo8b2o3bobo3bo\$14b2o34bo13b2o8b2o3b
obo3bo8bo\$8bo6bobobobo3bobobo5bobobobo3bo19bobobobo4bobo3bo3bobo\$15bob
obobo3bobobo5bobobobo3bo19bobobobo4bobo3bo3bobo\$8bo5b2o34bo13b2o8b2o3b
obo3bo8bo\$15bo49bo8b2o3bobo3bo\$8bo66bo10bo2\$8bo4\$4bobobo6bo\$14b2o56bo\$
4bo3bo6bobobobobo3bo3bo5bobobo3bobobo3bo3bobo3bobobobo\$15bobobobobo3bo
3bo5bobobo3bobobo3bo3bobo3bobobobo\$4bobobo5b2o56bo\$15bo\$8bo2\$8bo4\$4bo
3bo6bo\$14b2o52bo\$4bo3bo6bobobobobobo3bobobo3bo5bobobobo3bobo3bobobo\$
15bobobobobobo3bobobo3bo5bobobobo3bobo3bobobo\$4bo3bo5b2o52bo\$15bo\$4bo
3bo2\$4bo3bo4\$o3bobobo6bo199bo4bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo
11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3bobobo5bo3bobobo
bo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo5bobobo7bobobob
obo3bo5bobobo3bo3bobobo9bobobo3bo\$14b2o184bo13b2o4bo7bobobo7bobo5bo5bo
5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13b
o3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo
9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo10bo74bo\$o7bo6bobob
obobobobo3bo3bobobobo5bobo5bo3bo3bo3bobo3bo5bobobo11bobo3bobobo3bobobo
3bobobobobo5bo5bo5bobobo3bo5bo3bo3bo7bobobobo5bobobobobobobo17bo13bobo
bobo7bo3bo3bo3bobobobobobobo3bobobo3bo5bo9bo3bobo5bobo5bobo9bo3bobo3bo
bo3bo5bobobo3bobobobobobo5bo7bo3bo13bo3bo11bobo3bobo5bobo5bo9bobo7bo5b
o7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo8bo3bo3b
o7bo3bobo3bobobo11bobobobobobobobobo3bo7bo\$15bobobobobobobo3bo3bobobob
o5bobo5bo3bo3bo3bobo3bo5bobobo11bobo3bobobo3bobobo3bobobobobo5bo5bo5bo
bobo3bo5bo3bo3bo7bobobobo5bobobobobobobo17bo13bobobobo7bo3bo3bo3bobobo
bobobobo3bobobo3bo5bo9bo3bobo5bobo5bobo9bo3bobo3bobo3bo5bobobo3bobobob
obobo5bo7bo3bo13bo3bo11bobo3bobo5bobo5bo9bobo7bo5bo7bobobo7bobo5bo5bo
5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo8bo3bo3bo7bo3bobo3bobobo11b
obobobobobobobobo3bo7bo\$o3bobobo5b2o184bo13b2o4bo7bobobo7bobo5bo5bo5bo
bo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3b
obobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo
5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo10bo74bo\$15bo199bo4bo
7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobo
bobo3bo3bo7bobo13bo3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bo
bobobobo5bobo3bobo9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo\$
o7bo2\$o3bobobo14\$21bobo6bobo\$15bo4b2obo3bo\$14b2o4bo6bo4bo\$15bo7bo8bo\$
14b2o6b2o5bo2bo\$15bob2o2bobobo\$15bob2o2bobobo\$14b2o6b2o5bo2bo\$15bo7bo
8bo\$14b2o4bo6bo4bo\$15bo4b2obo3bo\$21bobo6bobo9\$21bobobo22bo30bo53bobobo
bobo3bo57bo6bo3bo11bo2bobo48bobo5bobobo\$15bo4b2obobo4bobo3bobo3bo26bob
o6bo6bo3bobo12bo20bobo5bobobobobo3b2o5bo16bo23bobobobo7bobo4bo8bo5bobo
10bo22bobo7bobo2bobo4b2obobo4bobo3bo11bo\$14b2o4bo9bobo3bobo3bo5bo16bo
3bob2obo7bo2bo3bobo3bobobo15bo8b2obo18bo5bo6bo7bo17bo7bobobobo2bo2bobo
4bo3bobobo2bo5bobobobo19bo9bobo7bobo4bo4bo9bobo3bobo3bo\$15bobo3bobo3bo
bo13bobo18b2o6bobo7bo12bobobo4bo9b2o8bo10bobo21bo7b2obo13b2o19bobobo2b
o3bobobo10bobobo6bo11b2o49bo3bo5bo\$15bobo3bobo3bobo13bobo19bobobo5bobo
3bobo3bo10bo3bo12bobo3bobo3bobo7bo5bobo2bo3bobo5bobo22bobo3bobo3bobo9b
obo3bobo3bobo14bo16bo3bo5bobobo7bobobobobo3bobo3bobo12bobo\$14b2o4bo9bo
bo3bobo3bo5bo16bobobo5bobo3bobo3bo10bo3bo12bobo3bobo3bobo7bo5bobo2bo3b
obo5bobo22bobo3bobo3bobo9bobo3bobo3bobo14bo16bo3bo5bobobo7bobobobobo3b
obo3bobo12bobo\$15bo4b2obobo4bobo3bobo3bo21b2o6bobo7bo12bobobo4bo9b2o8b
o10bobo21bo7b2obo13b2o19bobobo2bo3bobobo10bobobo6bo11b2o49bo3bo5bo\$21b
obobo22bo16bo3bob2obo7bo2bo3bobo3bobobo15bo8b2obo18bo5bo6bo7bo17bo7bob
obobo2bo2bobo4bo3bobobo2bo5bobobobo19bo9bobo7bobo4bo4bo9bobo3bobo3bo\$
69bobo6bo6bo3bobo12bo20bobo5bobobobobo3b2o5bo16bo23bobobobo7bobo4bo8bo
5bobo10bo22bobo7bobo2bobo4b2obobo4bobo3bo11bo\$79bo53bobobobobo3bo57bo
6bo3bo11bo2bobo48bobo5bobobo!
``````
Notice the B3j-using ships. very cool
EDIT: The top ships still work without B3ey, which is a non-explosive rule. i may apgsearch on d8_4

EDIT2: Is there a pattern?:

Code: Select all

``````x = 3, y = 6, rule = B2a3jkq/S01c3e
2bo\$2bo\$o\$o\$2bo\$2bo!
``````
she/her
moose#0915

Goldtiger997
Posts: 619
Joined: June 21st, 2016, 8:00 am

### Re: Rules with small adjustable spaceships

AforAmpere wrote:Another one of the questionable adjustable ship families, this rule is like the rule Muzik found with most if not all orthogonal speed under C/3. This rule has probably most speeds under C/9, but I've only found these so far, so it is hard to tell at the moment...
I found this c/17 with gfind:

Code: Select all

``````x = 300, y = 300, rule = B2ce3cj6e/S12-in3-ci4ijkwy5k
297bo\$295b2o\$294b2o3bo\$293b2o3bo\$292b2o3b2o\$291b2o3b2o\$290b2o3b2o\$289b
2o3b2o\$288b2o3b2o\$287b2o3b2o\$286b2o3b2o\$285b2o3b2o\$284b2obob2o\$283b2ob
ob2o\$282b2o3b2o\$281b2o3b2o\$280b2o3b2o\$279b2obob2o\$278b2o3b2o\$277b2o3b
2o\$276b2o3b2o\$275b2o3b2o\$274b2obob2o\$273b2o3b2o\$272b2obob2o\$271b2o3b2o
\$270b2obob2o\$269b2o3b2o\$268b2o3b2o\$267b2obob2o\$266b2o3b2o\$265b2obob2o\$
264b2o3b2o\$263b2o3b2o\$262b2o3b2o\$261b2o3b2o\$260b2o3b2o\$259b2o3b2o\$258b
2obob2o\$257b2o3b2o\$256b2obob2o\$255b2o3b2o\$254b2o3b2o\$253b2o3b2o\$252b2o
bob2o\$251b2obob2o\$250b2o3b2o\$249b2obob2o\$248b2o3b2o\$247b2obob2o\$246b2o
3b2o\$245b2o3b2o\$244b2o3b2o\$243b2o3b2o\$242b2obob2o\$241b2o3b2o\$240b2obob
2o\$239b2o3b2o\$238b2o3b2o\$237b2o3b2o\$236b2obob2o\$235b2o3b2o\$234b2obob2o
\$233b2o3b2o\$232b2o3b2o\$231b2obob2o\$230b2o3b2o\$229b2o3b2o\$228b2o3b2o\$
227b2o3b2o\$226b2o3b2o\$225b2o3b2o\$224b2o3b2o\$223b2o3b2o\$222b2o3b2o\$221b
2o3b2o\$220b2obob2o\$219b2o3b2o\$218b2o3b2o\$217b2o3b2o\$216b2obob2o\$215b2o
3b2o\$214b2o3b2o\$213b2obob2o\$212b2o3b2o\$211b2obob2o\$210b2o3b2o\$209b2o3b
2o\$208b2obob2o\$207b2o3b2o\$206b2obob2o\$205b2o3b2o\$204b2obob2o\$203b2o3b
2o\$202b2o3b2o\$201b2o3b2o\$200b2o3b2o\$199b2o3b2o\$198b2o3b2o\$197b2obob2o\$
196b2o3b2o\$195b2o3b2o\$194b2o3b2o\$193b2o3b2o\$192b2o3b2o\$191b2o3b2o\$190b
2o3b2o\$189b2o3b2o\$188b2o3b2o\$187b2o3b2o\$186b2obob2o\$185b2o3b2o\$184b2o
3b2o\$183b2o3b2o\$182b2o3b2o\$181b2o3b2o\$180b2o3b2o\$179b2obob2o\$178b2o3b
2o\$177b2obob2o\$176b2o3b2o\$175b2obob2o\$174b2o3b2o\$173b2o3b2o\$172b2o3b2o
\$171b2o3b2o\$170b2obob2o\$169b2o3b2o\$168b2o3b2o\$167b2o3b2o\$166b2obob2o\$
165b2obob2o\$164b2o3b2o\$163b2o3b2o\$162b2o3b2o\$161b2obob2o\$160b2o3b2o\$
159b2o3b2o\$158b2obob2o\$157b2o3b2o\$156b2o3b2o\$155b2o3b2o\$154b2obob2o\$
153b2obob2o\$152b2o3b2o\$151b2obob2o\$150b2o3b2o\$149b2o3b2o\$148b2o3b2o\$
147b2o3b2o\$146b2o3b2o\$145b2o3b2o\$144b2o3b2o\$143b2o3b2o\$142b2o3b2o\$141b
2o3b2o\$140b2obob2o\$139b2o3b2o\$138b2obob2o\$137b2o3b2o\$136b2o3b2o\$135b2o
3b2o\$134b2o3b2o\$133b2o3b2o\$132b2obob2o\$131b2o3b2o\$130b2o3b2o\$129b2o3b
2o\$128b2obob2o\$127b2o3b2o\$126b2o3b2o\$125b2obob2o\$124b2o3b2o\$123b2o3b2o
\$122b2o3b2o\$121b2obob2o\$120b2o3b2o\$119b2o3b2o\$118b2o3b2o\$117b2o3b2o\$
116b2obob2o\$115b2o3b2o\$114b2obob2o\$113b2o3b2o\$112b2o3b2o\$111b2o3b2o\$
110b2obob2o\$109b2o3b2o\$108b2o3b2o\$107b2obob2o\$106b2o3b2o\$105b2o3b2o\$
104b2o3b2o\$103b2obob2o\$102b2o3b2o\$101b2o3b2o\$100b2o3b2o\$99b2o3b2o\$98b
2o3b2o\$97b2o3b2o\$96b2o3b2o\$95b2obob2o\$94b2o3b2o\$93b2obob2o\$92b2o3b2o\$
91b2o3b2o\$90b2o3b2o\$89b2o3b2o\$88b2o3b2o\$87b2o3b2o\$86b2o3b2o\$85b2o3b2o\$
84b2o3b2o\$83b2o3b2o\$82b2obob2o\$81b2o3b2o\$80b2o3b2o\$79b2o3b2o\$78b2o3b2o
\$77b2o3b2o\$76b2o3b2o\$75b2o3b2o\$74b2obob2o\$73b2o3b2o\$72b2o3b2o\$71b2o3b
2o\$70b2obob2o\$69b2obob2o\$68b2o3b2o\$67b2obob2o\$66b2o3b2o\$65b2obob2o\$64b
2o3b2o\$63b2obob2o\$62b2o3b2o\$61b2o3b2o\$60b2o3b2o\$59b2o3b2o\$58b2obob2o\$
57b2o3b2o\$56b2obob2o\$55b2o3b2o\$54b2o3b2o\$53b2o3b2o\$52b2o3b2o\$51b2o3b2o
\$50b2o3b2o\$49b2obob2o\$48b2o3b2o\$47b2o3b2o\$46b2o3b2o\$45b2obob2o\$44b2o3b
2o\$43b2o3b2o\$42b2o3b2o\$41b2o3b2o\$40b2obob2o\$39b2o3b2o\$38b2obob2o\$37b2o
3b2o\$36b2obob2o\$35b2o3b2o\$34b2obob2o\$33b2obob2o\$32b2o3b2o\$31b2obob2o\$
30b2o3b2o\$29b2obob2o\$28b2o3b2o\$27b2obob2o\$26b2o3b2o\$25b2o3b2o\$24b2obob
2o\$23b2o3b2o\$22b2o3b2o\$21b2o3b2o\$20b2o3b2o\$19b2o3b2o\$18b2o3b2o\$17b2o3b
2o\$16b2o3b2o\$15b2o3b2o\$14b2o3b2o\$13b2obob2o\$12b2obob2o\$11b2o3b2o\$10b2o
bob2o\$9b2o3b2o\$8b2o3b2o\$7b2o3b2o\$6b2o3b2o\$5b2o3b2o\$4b2o3b2o\$3b2o3b2o\$
2b2o3b2o\$b2o3b2o\$2o3b2o\$o3b2o\$o2b2o\$4o!``````
It seems likely to me that this rule does have all speeds below c/9. However, I have much better evidence for the equivalent statement it muzik's original rule (so for all speeds below c/3). From ntzfind here are ships of speeds c/3, 3c/10, 2c/7, 3c/11, c/4, 2c/9, c/5, 2c/11, c/6, c/7, c/8, c/9, c/10, c/11:

Code: Select all

``````x = 70, y = 1052, rule = B2c3aj4a6ack7/S1e2-an3ejnr4i6k7e
bo4bo4bo4bo\$obo2bobo2bobo2bobo3bo4bo4bo4bo4bo5bo4bo5bo4bo4bo\$3o2bobo2b
obo2bobo2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$obo2bobo2bo
bo2bobo2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$2bo2b3o2b3o
2b3o2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo
2b3o2bobo2b3o2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5b3o2b3o2b3o2bobo2bob
o2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2bobo2b2o
3bobo2bobo3b3o2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo2bobo2bo4bobo2b
obo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2b3o7bobo2b3o3bobo2bob
o3b3o2bobo2bobo\$5b3o2b3o2bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo
2bobo\$5bobo2bobo2bobo2b3o2b3o7b3o2b3o3b3o2bobo3bobo2bobo2b3o\$5bobo2b3o
2b3o2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo
2bobo7bobo2b3o3b3o2b3o3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo2bobo7bobo2b
obo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2b3o7bobo2bobo3b3o2b3o
3bobo2bobo2b3o\$5b3o2b3o2bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2b
obo\$5bobo2bobo2bobo2b3o2bobo7bobo2bobo3b3o2b3o3b3o2b3o2bobo\$5b3o2bo4bo
bo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo2bobo2bobo7b
obo2bobo3bobo2bobo3b3o2b3o2b3o\$5b3o7bobo2bobo2bobo7bobo2bobo3bobo2bobo
3bobo2bobo2bobo\$5bobo7bobo2bobo4bo7bobo2bobo3bobo2b3o3b3o2b3o2b3o\$5bob
o7bobo2bobo12bobo2bobo3bobo2bobo3b3o2bobo2bobo\$5bobo7bobo2bobo12bobo2b
3o3b3o2bobo3bobo2bobo2bobo\$5b3o7bobo2bobo12bobo2bobo3bobo2bobo3bobo2bo
bo2bobo\$5bobo7bobo2b3o12bobo2b3o3b3o2bobo3bobo2bobo2b3o\$5b3o7bobo2bobo
12bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo4bo12bobo2b3o3b3o2b3o3b
obo2b3o2b3o\$5bobo7bobo17bobo2bobo3bobo2bobo3b3o2bobo2bobo\$5bobo7bobo
17bobo2b3o3bobo2b3o3bobo2b3o2bobo\$5bobo7b3o17bobo2bobo3bo4bobo3bobo2bo
bo2bobo\$5bobo9bo17bobo2b3o8b3o3bobo2bobo2b3o\$5b3o8bo18b3o2bobo8bobo3b
3o2bobo2bobo\$5bobo27bobo2b3o8bobo3bobo2bobo2bobo\$5bobo27bobo3bo9bobo3b
obo2bobo2bobo\$5bobo27bobo3bo9b3o3bobo2bobo2bobo\$5bobo27b3o2b3o8bobo3bo
bo2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2bobo2b3o\$5bobo27bobo2b3o8bobo
3b3o2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2b3o2b3o\$5bobo27b3o2b3o8bobo
3b3o2bobo2bobo\$5bobo27bobo2bobo8b3o3bobo2bobo2bobo\$5b3o27b3o2b3o8bobo
3b3o2bobo2bobo\$5bobo27bobo2bobo8b3o3bobo2bobo2b3o\$5b3o27bobo2bobo8bobo
3bobo2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2b3o2bobo\$5bobo27b3o4bo8bobo
3bobo2bobo2bobo\$5bobo27bobo13b3o3bobo2bobo2b3o\$5b3o27b3o13bobo3bobo2bo
bo2bobo\$5bobo27bobo13bobo5bo2b3o2b3o\$5b3o27b3o13bobo8bobo2bobo\$5bobo
27bobo13bobo8b3o2b3o\$5bobo27b3o13bobo8bobo2bobo\$5bobo27bobo13b3o8bobo
2bobo\$5bobo27bobo13bobo8bobo2bobo\$5bobo27bobo13b3o8bobo2bobo\$5bobo27bo
bo13bobo8bobo2bobo\$5bobo27b3o13b3o8b3o2bobo\$5bobo27bobo13bobo8bobo2b3o
\$5bobo27bobo13b3o8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27bobo13bobo
8bobo2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27b3o13b3o8b3o2bobo\$5b3o27bo
bo13bobo8bobo2bobo\$5bobo27b3o13bobo8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o
\$5bobo27b3o13bobo8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27bo15b3o8bo
bo2bobo\$5b3o43bobo8b3o2bobo\$5bobo43b3o8bobo2bobo\$5bobo43bobo8b3o2b3o\$
5bobo43bobo8bobo2bobo\$5b3o43bobo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5b3o43bo
bo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43b3o8bobo2bo
bo\$5bobo43bobo8bobo2bobo\$5bobo43bobo8bobo2bobo\$5bobo43bobo8bobo2bobo\$
5bobo43b3o8bobo2bobo\$5b3o43bobo8b3o2b3o\$5bobo43bobo8bobo2bobo\$5bobo43b
obo8bobo2bobo\$5bobo43b3o8bobo2bobo\$5bobo43bobo8bobo2b3o\$5bobo43bobo8bo
bo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43bobo8bobo2bobo\$5bobo43bobo8b3o2b3o\$
5bobo43b3o8bobo2bobo\$5b3o43bobo8b3o2bobo\$5bobo43b3o8bobo2bobo\$5b3o43bo
bo8bobo2b3o\$5bobo43b3o8bobo2bobo\$5bobo43bobo8bobo2b3o\$5bobo43bobo8bobo
2bobo\$5bobo43b3o8bobo2b3o\$5bobo43bobo8bobo2bobo\$5b3o43b3o8bobo2b3o\$5bo
bo43bobo8bobo2bobo\$5bobo43b3o8bobo2b3o\$5bobo43bobo8bobo4bo\$5bobo43b3o
8b3o3bo\$5bobo43bobo8bobo\$5b3o43bobo8bobo\$5bobo43bobo8b3o\$5b3o43b3o8bob
o\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5b3o43b3o8bobo\$5bo
bo43bobo8b3o\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5b3o43bobo8bobo\$5bobo43b
obo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo
8bobo\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5bobo43bobo8bobo\$5bobo43bobo8b
3o\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$
5b3o43b3o8bobo\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5b3o
44b2o8bobo\$5bobo45bo8b3o\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bo
bo\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54b3o
\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b
3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5b3o
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5bobo
54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5b3o
54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5bobo
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5bobo
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5bobo
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5bobo
54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b3o
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5b3o
54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bo
bo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b
3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5b
3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54bobo\$5b
3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$
5bobo54bobo\$5bobo54bo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b
3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5b
obo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bob
o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo
\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$
5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bo
bo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo
\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$
5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5b
obo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bo
bo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bob
o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bo
bo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bob
o\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo
\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo
\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$
5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo
\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo
\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$
5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bo
bo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo
\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$
5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bob
o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo
\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5b
obo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bo
bo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bob
o\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$
5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bo
bo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o
\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5b
obo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5b
obo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$
5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$
5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b
3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b
3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bob
o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o
\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo\$5bobo
\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5b3o\$5bobo\$5bobo\$
5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5bobo\$5bobo\$5b3o\$5bobo\$5b3o\$5b
obo\$7bo! [[ Z 2 Y -500 ]]``````
Some of them start getting really long though...

wildmyron
Posts: 1421
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

I was thinking about adjustable knightships and had an idea about reactions which could support adjustable slope ships. Here's a sample reaction - a series of push-reflect reactions which shift the ship onto the lane which the reflector is on.

Code: Select all

``````x = 9, y = 17, rule = B2en3-aejy4-cqry5aeky67e/S02-kn3ijq4cijnqz5acekq6ack7e
3b2o\$o4bo2bo\$3b2o5\$3b2o\$o4bo\$3b2o3bo4\$3b2o\$o4bo\$3b2o\$8bo!``````
Here's a demo pattern which works for one cycle of a (2,1) slope ship

Code: Select all

``````x = 11, y = 21, rule = B2en3-aejy4-cqry5aeky67e/S02-kn3ijq4cijnqz5acekq6ack7e
4b2o\$o5bo2bo\$4b2o2\$8bobo\$8bobo\$9bo14\$9bo!``````
There are two ways I can see to complete such a ship: 1) find suitable push-reflect reactions and replace the reflectors at the end of the arms with pull-reflect reactions which shift the reflector instead of the ship, or 2) combine the push-reflect reactions with pull-reflect reactions which also shit the ship's lane and arrange four ships in a rectangular shape.

Given the diversity of push-reflect and pull-reflect reactions I'm confident that a rule exists which supports one of these schemes, but I'm not sure if it is feasible to find one.

P. S. @2718281828: nice adjustable knightships
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.

wildmyron
Posts: 1421
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

Here's an adjustable period ship using the idea from the post above, but it's diagonal so only two reactions are required. (No rule golfing performed)

c/(4n+2) diagonal, p(4n+2), mod(2n+1), n > 4

Code: Select all

``````x = 11, y = 11, rule = B2-an3ckqy4aeiq5-i6ckn7c8/S012-c3cinq4cijknry5ajkry6eik7e8
2o2b3o2bo\$bo2b2o\$4b3o2\$8b3o\$8bobo\$9bo3\$8b2o\$9bo!``````
The rule also supports the push-reflect reaction without shift, but not the pull reflect without shift required for an adjustable period knightship.

Code: Select all

``````x = 8, y = 17, rule = B2-an3ckqy4aeiq5-i6ckn7c8/S012-c3cinq4cijknry5ajkry6eik7e8
2o\$obo2bo\$2o5\$2o\$obo\$2o3bo5\$2o4bo\$obo3b2o\$2o!``````
With the fourth required reaction this construction would actually be an adjustable SMoS (Spaceship Made of Spaceships). Has anyone found something like that yet?

Interestingly, a very similar set of reactions exists in a nearby rule, note the flipped version, and different timing, of the pull-reflector.

Code: Select all

``````x = 8, y = 17, rule = B2-an3cknq4ijknqwy5-aeir6-e78/S012-c3ciknq4-acetz5ajn6-ai7e8
2o\$obo2bo\$2o5\$2o\$obo\$2o3bo5\$2o4b2o\$obo3bo\$2o!``````
Corresponding ship -
c/(4n) diagonal, p(4n), mod(2n), n > 5

Code: Select all

``````x = 11, y = 11, rule = B2-an3cknq4ijknqwy5-aeir6-e78/S012-c3ciknq4-acetz5ajn6-ai7e8
bo2b3o2bo\$2o2b2o\$4b3o2\$8b3o\$8b3o\$8bobo3\$8b2o\$8bo!``````
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: 1125
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

I was thinking somewhat on the lines of this:

Code: Select all

``````x = 19, y = 19, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7e
o\$4bo12bo\$5bo\$4bo2\$16bo\$15bobo12\$18bo!
``````
Obviously it doesn't become a spaceship, but it does not explode. If there is some pull reaction at (2,2) that works with the push, we might be able to create adjustable slope ships.

Here's another example in this rule, pushing the dot at (2,1):

Code: Select all

``````x = 19, y = 35, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7e
o\$4bo12bo\$5bo\$4bo2\$16bo\$15bobo28\$18bo!
``````
EDIT, never mind, the (2,2) thing does not work.

EDIT 2, so close, I don't understand why the desync happens:

Code: Select all

``````x = 23, y = 40, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7e
2bo\$9bo11bo\$10bo\$9bo\$bo\$obo17bo\$19bobo30\$3bo\$10bo11bo\$11bo\$10bo!
``````
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: 1125
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

Code: Select all

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

Code: Select all

``````x = 37, y = 72, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e8
10\$5bo\$12bo12bo\$13bo\$12bo\$24bo\$23bobo12\$4bo\$3bobo38\$6bo\$13bo12bo\$14bo\$
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

muzik
Posts: 3905
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Congratulations.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

bprentice
Posts: 686
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Rules with small adjustable spaceships

Well done! This is better than Sir Robin.

Brian Prentice

AforAmpere
Posts: 1125
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

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:

Code: Select all

``````x = 143, y = 88, rule = B2ce3cen4ekt6kn/S01c2ae4cknr5akn
2bo38bo40bo39bo\$9bo11bo26bo11bo28bo11bo27bo11bo\$10bo38bo40bo39bo\$bo7bo
30bo7bo32bo7bo31bo7bo\$obo17bo18bobo17bo20bobo17bo19bobo17bo\$19bobo36bo
bo38bobo37bobo31\$123bo\$130bo11bo\$131bo\$130bo13\$102bo\$83bo14bo\$97bo\$98b
o13\$42bo\$49bo11bo\$50bo\$49bo13\$22bo\$3bo12bo\$15bo\$16bo!
``````
EDIT, 4/3 slope:

Code: Select all

``````x = 35, y = 45, rule = B2ce3cen4ekt6kn/S01c2ae4cknr5akn
3bo\$22bo10bo\$23bo\$22bo\$32bo\$31bobo4\$obo\$bo31\$34bo\$2bo19bo\$21bo\$22bo!
``````
EDIT, I think this works in any rule with a (2,0) push reaction (credits to wildmyron):

Code: Select all

``````x = 23, y = 22, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar678
16bo\$bo15bo\$17bo2bo\$16bo8\$b2o\$o2bo16b2o\$19bo2bo5\$4bo\$3bo17bo\$2bo\$4bo!
``````
The speed of diagonal ships can get very fast:

Code: Select all

``````x = 15, y = 14, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar678
8bo\$o3bo2bo4bo\$b3o3bo\$ob2o4bo\$3bo\$bo2bo\$2b2o8b2o\$11bo2bo3\$7bo\$2bo5bo\$
8bo4bo\$7bo!
``````
EDIT, faster:

Code: Select all

``````x = 16, y = 16, rule = B2aei3-aijq4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky78
8bo4bo\$7bo\$3bo3bo\$8bo3\$13b2o\$12bo2bo3\$o2bo\$b2o\$bo4bo\$7bo\$7bo7bo\$6bo!
``````
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