## Rules with small adjustable spaceships

For discussion of other cellular automata.

### 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:
`x = 15, y = 12, rule = B2a3jkq/S01c3eobo11bo\$4bo3bobo\$4bo3bobo\$obo11bo4\$bo\$2o10bo\$bobobo3bo\$bobobo3bo\$12bo!`

a fuse can make them into 2c/10 spaceships:
`x = 30, y = 17, rule = B2a3jkq/S01c3ebo\$o12bo10bo\$3bo13bo5bo\$3bo13bo5bo\$o12bo10bo\$bo2\$18bo\$17bo11bo\$2bo16bo3bobo\$bo11bobo3bo3bobo\$4bo24bo\$4bo21bo\$bo11bobobobo3bo\$2bo12bobobo3bo\$14b2o10bo\$15bo!`

EDIT:
2c/12 (c/6) ship:
`x = 138, y = 6, rule = B2a3jkq/S01c3ebo\$o136bo\$3bo3bo5bo15bobo7bo3bo7bo5bo5bo9bobobobo3bobobo3bobo11bobo3bobo3bo3bobo5bobobo\$3bo3bo5bo15bobo7bo3bo7bo5bo5bo9bobobobo3bobobo3bobo11bobo3bobo3bo3bobo5bobobo\$o136bo\$bo!`
`x = 4, y = 2, rule = B3/S23ob2o\$2obo!`

(Check Gen 2)

toroidalet

Posts: 905
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### Re: Rules with small adjustable spaceships

Goldtiger997's ships from the TFYUCA.
`x = 137, y = 2, rule = B2ik3-kqry4-ijky5-i6i7/S02a4ib3o4b5o4b7o4b9o4b11o4b13o6b61o\$o3bo2bo5bo2bo7bo2bo9bo2bo11bo2bo13bo4bo61bo!`

It doesn't seem to resemble any of those listed here.
`x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o\$b2o\$2o!`

LaundryPizza03 at Wikipedia

LaundryPizza03

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Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### 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.
wildmyron

Posts: 942
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

`x = 9, y = 22, rule = B3-jkn4a/S1e2-a3ijnry4n4bo\$4bo3\$2o5b2o2\$4bo\$4bo8\$3b3o\$4bo4\$4bo\$4bo!`

77topaz

Posts: 1222
Joined: January 12th, 2018, 9:19 pm

### Re: Rules with small adjustable spaceships

77topaz wrote:A small, unusual adjustable-speed rake:
`x = 9, y = 22, rule = B3-jkn4a/S1e2-a3ijnry4n4bo\$4bo3\$2o5b2o2\$4bo\$4bo8\$3b3o\$4bo4\$4bo\$4bo!`

Speed is 3c/(12n+6) orthogonal, n≥6.
`x = 135, y = 27, rule = B3-jkn4a/S1e2-a3ijnry4n4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo3\$2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o2\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo4\$3b3o\$4bo12b3o\$18bo12b3o\$32bo12b3o\$46bo12b3o\$4bo55bo12b3o\$4bo13bo55bo12b3o\$18bo13bo55bo12b3o\$32bo13bo55bo12b3o\$46bo13bo55bo12b3o\$60bo13bo55bo\$74bo13bo\$88bo13bo\$102bo13bo\$116bo13bo\$130bo!`
`x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o\$b2o\$2o!`

LaundryPizza03 at Wikipedia

LaundryPizza03

Posts: 255
Joined: December 15th, 2017, 12:05 am
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### Re: Rules with small adjustable spaceships

You've got "adjustable"-period photons for any period 2^n, n>1:
`x = 17, y = 80, rule = B2a4i5j/S1e3rbo\$2o14\$2o\$bo4\$6bo\$5b2o2\$5b2o\$6bo8\$16bo\$15b2o10\$15b2o\$16bo15\$15bo\$14b2o18\$14b2o\$15bo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3217
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Knight-ships:
`x = 42, y = 31, rule = B2e3ijn4ijnryz6an7e/S12cen3acijq4qrz5acqr6ei14\$13b2o\$21b2o\$29b2o\$37b2o3\$10bobo5bobo5bobo5bobo\$11bo7bo7bo7bo2\$11b2o6b2o6b2o6b2o!`
`x = 30, y = 12, rule = B2ci3a4aiwy5-aeny6ac/S01e2a3ajqr4airtz5ajnq6-e\$4bo\$12bo\$20bo\$28bo2\$bo7bo7bo7bo\$b3o5b3o5b3o5b3o\$2bo7bo7bo7bo2\$2bo7bo7bo7bo!`

both are (2,1)c/(2+4n) spaceships for n>3

Edit1:
`x = 26, y = 11, rule = B2ei3ciknr4eiknqrz5ejny6en7c/S12-a3acik4ceqrtw5acekr6ekn83b2o\$10b2o\$17b2o\$24b2o4\$obo4bobo4bobo4bobo\$bo6bo6bo6bo2\$b2o5b2o5b2o5b2o!`
(2,1)c/(3+4n) knight-ships for n>4
`x = 30, y = 13, rule = B2cek3cnr4ejqrty5nry6k7e8/S012-cn3ny4ceiknrt5ikny6e8\$3bo\$11bo\$19bo\$27bo3\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo\$bo7bo7bo7bo2\$bo7bo7bo7bo!`
(2,1)c/4n knight-ships for n>5
`x = 35, y = 12, rule = B2e3ikn4nqrwyz5cjnqy6ak7e8/S12cen3-kry4acknrw5acejq6k8\$6b2o\$14b2o\$22b2o\$30b2o3\$3bobo5bobo5bobo5bobo\$4bo7bo7bo7bo2\$4b2o6b2o6b2o6b2o!`
(2,1)c/(1+4n) knight-ships for n>4

2718281828

Posts: 510
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:
`x = 67, y = 4, rule = B2ae3q/S0o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$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'):
`x = 31, y = 10, rule = B2-ck3-aijq4-aiknr5-jny678/S01e2ein3-aijq4-nqtwy5-eiy6-ac782bo\$11bo\$20bo\$29bo5\$bobo6bobo6bobo6bobo\$o8bo8bo8bo!`
where the fastest one has speed c/6 (all speeds c/n, n>5 are supported), and
`x = 25, y = 10, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar6782bo\$9bo\$16bo\$23bo4\$o2bo3bo2bo3bo2bo3bo2bo\$2bo6bo6bo6bo\$bo6bo6bo6bo!`
where the fastest one has speed c/5 (all speeds c/n, n>4 are supported).

2718281828

Posts: 510
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:
`x = 67, y = 4, rule = B2ae3q/S0o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$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.

77topaz

Posts: 1222
Joined: January 12th, 2018, 9:19 pm

### Re: Rules with small adjustable spaceships

Not sure if this one is known, a 2c/14 in that rule:
`x = 25, y = 6, rule = B2a3jkq/S01c3e23bo\$o23bo\$5bo11bo3bo\$5bo11bo3bo\$o23bo\$23bo!`
Please stop using my full name. Refer to me as dani.

she/they

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

Posts: 878
Joined: October 27th, 2017, 3:43 pm
Location: i love to eat bees

### Re: Rules with small adjustable spaceships

2718281828 wrote:
AforAmpere wrote:There is a chance that adjustable ships may exist in B2a rules:
`x = 67, y = 4, rule = B2ae3q/S0o\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$4bo9bo5bobobo3bobo3bo3bo3bo5bo3bobobo3bo3bobo\$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'):
`x = 31, y = 10, rule = B2-ck3-aijq4-aiknr5-jny678/S01e2ein3-aijq4-nqtwy5-eiy6-ac782bo\$11bo\$20bo\$29bo5\$bobo6bobo6bobo6bobo\$o8bo8bo8bo!`
where the fastest one has speed c/6 (all speeds c/n, n>5 are supported), and
`x = 25, y = 10, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar6782bo\$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.
wildmyron

Posts: 942
Joined: August 9th, 2013, 12:45 am

### 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!
muzik

Posts: 3217
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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):
`x = 27, y = 12, rule = B2cik3akq4-aekqyz5aknry6a7/S012ck3aejqy4acekrw5cjr6782bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`
c/(6n+2):
`x = 27, y = 12, rule = B2cik3ackq4-acekyz5-ijkr6i78/S012ckn3-iknr4ekqrty5-acny6-n782bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`
c/(6n+3):
`x = 27, y = 12, rule = B2ckn3aceky4-acekr5ay6ci78/S012-an3ejkq4acikwy5-ceij6-ai2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`
c/(6n+4):
`x = 27, y = 12, rule = B2cik3-ejnr4-aenrwz5cejry6k7e/S012cik3ej4-cjyz5eqr6cei7c82bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`
c/(6n+5):
`x = 27, y = 12, rule = B2cik3acq4ijnqrw5jknqy6ein7e8/S012cik3ejqry4aceky5-eijq6-ek7c2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`
c/6:
`x = 27, y = 12, rule = B2-ae3acqy4ceijkt5cjkq6ei/S012cik3aejr4ceikqry5-eijq6-n7e2bo\$10bo\$18bo\$26bo4\$2bo7bo7bo7bo\$obo5bobo5bobo5bobo3\$o7bo7bo7bo!`

something related, speeds 2/6n n>10 (a 2c/3 ship is travelling between the dots)
`x = 28, y = 15, rule = B2-ei3cknqr4-aciqt5eknqy6-c78/S012ek3jkr4artyz5ainry6ck3bo2\$11bo2\$19bo2\$27bo3\$3bo7bo7bo7bo\$ob2o4bob2o4bob2o4bob2o\$bobo5bobo5bobo5bobo3\$2bo7bo7bo7bo!`

Something very fast (fastest is c/3):
`x = 28, y = 14, rule = B2ae3aknr4aeinty5ckqr6-in7c8/S01e2-ck3jknqr4cijnqr5cry6ce83bo\$11bo\$3bo15bo\$11bo15bo\$19bo\$27bo3\$o2bo4bo2bo4bo2bo4bo2bo\$b2o6b2o6b2o6b2o2\$bo7bo7bo7bo2\$bo7bo7bo7bo!`

something similar (larger):
`x = 29, y = 17, rule = B2a3acjkn4cqrtwy5acjky6-ac78/S1c2-ce3cijy4aeknrz5cnqy6-ik72bo\$3bo\$10bo\$11bo\$18bo\$19bo\$26bo\$27bo3\$bobo5bobo5bobo5bobo2\$2ob2o3b2ob2o3b2ob2o3b2ob2o3\$bo7bo7bo7bo\$o7bo7bo7bo!`

2718281828

Posts: 510
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

2718281828 wrote:Something very fast (fastest is c/3):

That rule can actually go to 2c/5!:
`x = 6, y = 10, rule = B2ae3aknr4aeinty5ckqr6-in7c8/S01e2-ck3jknqr4cijnqr5cry6ce82bo2\$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:
`x = 18, y = 12, rule = B2aen3akq4-jqtz5eiry6-in7c8/S02an3airy4ew5ejqy6-ek7e82bo13bo2\$2bo13bo2\$o2bo10bo2bo4\$o\$14bo\$o\$14bo!`

EDIT 2, down to 5 cells:
`x = 4, y = 7, rule = B2aei3-aijq4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky783bo5\$b3o\$o!`

EDIT 3, 5 cell maximum for 6c/2n for n>11:
`x = 15, y = 9, rule = B2-ck3anq4ejkrtyz5-acny6-ck7/S02en3-ceqy4cejkrwy5acqry6eik7e84bo9bo5\$10bo2bo\$o2bo8bo\$2bo8bo\$bo!`

EDIT 4, the fastest adjustable ship I could find with 6-cell displacement, at 3c/10:
`x = 5, y = 12, rule = B2-ci3knqr4cijkqyz5-iry6-ac78/S01e2en3cknqr4iknryz5eky6ei84bo2\$4bo3\$o2bo\$b2o3\$bo2\$bo!`
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 864
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:
`x = 319, y = 74, rule = B2ce3cj6e/S12-in3-ci4ijkwy5k11b4o90b2obo58b3o81b4o60b4o\$10b2o2bo89b2o60b2o2bo79b2o2bo59b2o2bo\$9b2o3bo88b2o3bo56b2obobo78b2o3bo58b2o3bo\$8b2obob2o87b2o3b2o55b2o3b2o77b2obob2o57b2o3b2o\$7b2o3b2o87b2obob2o55b2obob2o77b2o3b2o57b2o3b2o\$6b2obob2o87b2o3b2o55b2o3b2o77b2obob2o57b2obob2o\$5b2o3b2o87b2obob2o55b2obob2o77b2o3b2o57b2o3b2o\$4b2o3b2o87b2o3b2o55b2o3b2o77b2obob2o57b2o3b2o\$3b2obob2o87b2obob2o55b2obob2o77b2o3b2o57b2o3b2o\$2b2o3b2o87b2obob2o55b2o3b2o77b2o3b2o57b2obob2o\$b2o3b2o87b2o3b2o55b2o3b2o77b2o3b2o57b2o3b2o\$bo3b2o87b2o3b2o55b2o3b2o77b2obob2o57b2obob2o\$o3b2o87b2o3b2o55b2obob2o77b2o3b2o57b2o3b2o\$3b2o87b2o3b2o55b2obob2o77b2o3b2o57b2obob2o\$2bo88b2o3b2o55b2o3b2o77b2o3b2o57b2o3b2o\$90b2obob2o55b2o3b2o77b2o3b2o57b2o3b2o\$89b2obob2o55b2o3b2o77b2o3b2o57b2o3b2o\$88b2o3b2o55b2o3b2o77b2obob2o57b2o3b2o\$87b2o3b2o56bo3b2o77b2o3b2o57b2o3b2o\$86b2o3b2o56bo3b2o77b2obob2o57b2o3b2o\$85b2obob2o60b2o77b2obob2o57b2o3b2o\$84b2o3b2o60bo78b2o3b2o57b2obob2o\$83b2obob2o139b2o3b2o57b2o3b2o\$82b2o3b2o139b2o3b2o57b2obob2o\$81b2obob2o139b2obob2o57b2o3b2o\$80b2obob2o139b2o3b2o57b2o3b2o\$79b2o3b2o139b2o3b2o57b2o3b2o\$78b2obob2o139b2o3b2o57b2o3b2o\$77b2o3b2o139b2o3b2o57b2o3b2o\$76b2o3b2o139b2obob2o57b2o3b2o\$75b2obob2o139b2o3b2o57b2o3b2o\$74b2o3b2o139b2o3b2o57b2obob2o\$73b2obob2o139b2o3b2o57b2o3b2o\$72b2o3b2o139b2obob2o57b2o3b2o\$71b2o3b2o139b2o3b2o57b2o3b2o\$70b2o3b2o139b2o3b2o57b2o3b2o\$69b2o3b2o139b2o3b2o57b2o3b2o\$68b2o3b2o139b2o3b2o57b2o3b2o\$67b2o3b2o139b2obob2o58bo3b2o\$66b2o3b2o139b2o3b2o59b2ob2o\$65b2obob2o139b2obob2o60b4o\$64b2o3b2o139b2o3b2o\$63b2o3b2o139b2obob2o\$62b2o3b2o139b2o3b2o\$61b2o3b2o139b2obob2o\$60b2o3b2o139b2o3b2o\$59b2o3b2o139b2o3b2o\$58b2obob2o139b2o3b2o\$57b2o3b2o139b2o3b2o\$56b2o3b2o139b2obob2o\$55b2obob2o139b2o3b2o\$54b2o3b2o139b2obob2o\$53b2obob2o139b2o3b2o\$52b2obob2o139b2obob2o\$51b2o3b2o139b2o3b2o\$50b2obob2o139b2o3b2o\$49b2o3b2o139b2o3b2o\$48b2o3b2o139b2o3b2o\$47b2o3b2o139b2o3b2o\$46b2o3b2o139b2o3b2o\$45b2obob2o140bo3b2o\$44b2o3b2o140bo3b2o\$43b2obob2o144b2o\$42b2obob2o144bo\$41b2o3b2o\$40b2o3b2o\$39b2o3b2o\$38b2obob2o\$37b2o3b2o\$36b2obob2o\$36bo3b2o\$35bo3b2o\$38b2o\$37bo!`
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 864
Joined: July 1st, 2016, 3:58 pm

### 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.
Please stop using my full name. Refer to me as dani.

she/they

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

Posts: 878
Joined: October 27th, 2017, 3:43 pm
Location: i love to eat bees

### Re: Rules with small adjustable spaceships

Some ships in one of those rules posted above:
`x = 663, y = 100, rule = B2a3ejkqy/S01c3e4bobobo6bo\$14b2o10bo\$4bo10bobobo3bo\$15bobobo3bo\$4bobobo5b2o10bo\$15bo\$8bo2\$4bobobo3\$75bo10bo\$4bobobo6bo49bo8b2o3bobo3bo\$14b2o34bo13b2o8b2o3bobo3bo8bo\$8bo6bobobobo3bobobo5bobobobo3bo19bobobobo4bobo3bo3bobo\$15bobobobo3bobobo5bobobobo3bo19bobobobo4bobo3bo3bobo\$8bo5b2o34bo13b2o8b2o3bobo3bo8bo\$15bo49bo8b2o3bobo3bo\$8bo66bo10bo2\$8bo4\$4bobobo6bo\$14b2o56bo\$4bo3bo6bobobobobo3bo3bo5bobobo3bobobo3bo3bobo3bobobobo\$15bobobobobo3bo3bo5bobobo3bobobo3bo3bobo3bobobobo\$4bobobo5b2o56bo\$15bo\$8bo2\$8bo4\$4bo3bo6bo\$14b2o52bo\$4bo3bo6bobobobobobo3bobobo3bo5bobobobo3bobo3bobobo\$15bobobobobobo3bobobo3bo5bobobobo3bobo3bobobo\$4bo3bo5b2o52bo\$15bo\$4bo3bo2\$4bo3bo4\$o3bobobo6bo199bo4bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo\$14b2o184bo13b2o4bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo10bo74bo\$o7bo6bobobobobobobo3bo3bobobobo5bobo5bo3bo3bo3bobo3bo5bobobo11bobo3bobobo3bobobo3bobobobobo5bo5bo5bobobo3bo5bo3bo3bo7bobobobo5bobobobobobobo17bo13bobobobo7bo3bo3bo3bobobobobobobo3bobobo3bo5bo9bo3bobo5bobo5bobo9bo3bobo3bobo3bo5bobobo3bobobobobobo5bo7bo3bo13bo3bo11bobo3bobo5bobo5bo9bobo7bo5bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo8bo3bo3bo7bo3bobo3bobobo11bobobobobobobobobo3bo7bo\$15bobobobobobobo3bo3bobobobo5bobo5bo3bo3bo3bobo3bo5bobobo11bobo3bobobo3bobobo3bobobobobo5bo5bo5bobobo3bo5bo3bo3bo7bobobobo5bobobobobobobo17bo13bobobobo7bo3bo3bo3bobobobobobobo3bobobo3bo5bo9bo3bobo5bobo5bobo9bo3bobo3bobo3bo5bobobo3bobobobobobo5bo7bo3bo13bo3bo11bobo3bobo5bobo5bo9bobo7bo5bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo8bo3bo3bo7bo3bobo3bobobo11bobobobobobobobobo3bo7bo\$o3bobobo5b2o184bo13b2o4bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo10bo74bo\$15bo199bo4bo7bobobo7bobo5bo5bo5bobo3bo3bo3bo11bo11bobo3bo7bo9bobobobo11bo7bo13bobobobo3bo3bo7bobo13bo3bobobo5bo3bobobobo5bobobo3bo7bobo5bo3bobobobobo7bobobobobo5bobo3bobo9bo5bobobo7bobobobobo3bo5bobobo3bo3bobobo9bobobo3bo\$o7bo2\$o3bobobo14\$21bobo6bobo\$15bo4b2obo3bo\$14b2o4bo6bo4bo\$15bo7bo8bo\$14b2o6b2o5bo2bo\$15bob2o2bobobo\$15bob2o2bobobo\$14b2o6b2o5bo2bo\$15bo7bo8bo\$14b2o4bo6bo4bo\$15bo4b2obo3bo\$21bobo6bobo9\$21bobobo22bo30bo53bobobobobo3bo57bo6bo3bo11bo2bobo48bobo5bobobo\$15bo4b2obobo4bobo3bobo3bo26bobo6bo6bo3bobo12bo20bobo5bobobobobo3b2o5bo16bo23bobobobo7bobo4bo8bo5bobo10bo22bobo7bobo2bobo4b2obobo4bobo3bo11bo\$14b2o4bo9bobo3bobo3bo5bo16bo3bob2obo7bo2bo3bobo3bobobo15bo8b2obo18bo5bo6bo7bo17bo7bobobobo2bo2bobo4bo3bobobo2bo5bobobobo19bo9bobo7bobo4bo4bo9bobo3bobo3bo\$15bobo3bobo3bobo13bobo18b2o6bobo7bo12bobobo4bo9b2o8bo10bobo21bo7b2obo13b2o19bobobo2bo3bobobo10bobobo6bo11b2o49bo3bo5bo\$15bobo3bobo3bobo13bobo19bobobo5bobo3bobo3bo10bo3bo12bobo3bobo3bobo7bo5bobo2bo3bobo5bobo22bobo3bobo3bobo9bobo3bobo3bobo14bo16bo3bo5bobobo7bobobobobo3bobo3bobo12bobo\$14b2o4bo9bobo3bobo3bo5bo16bobobo5bobo3bobo3bo10bo3bo12bobo3bobo3bobo7bo5bobo2bo3bobo5bobo22bobo3bobo3bobo9bobo3bobo3bobo14bo16bo3bo5bobobo7bobobobobo3bobo3bobo12bobo\$15bo4b2obobo4bobo3bobo3bo21b2o6bobo7bo12bobobo4bo9b2o8bo10bobo21bo7b2obo13b2o19bobobo2bo3bobobo10bobobo6bo11b2o49bo3bo5bo\$21bobobo22bo16bo3bob2obo7bo2bo3bobo3bobobo15bo8b2obo18bo5bo6bo7bo17bo7bobobobo2bo2bobo4bo3bobobo2bo5bobobobo19bo9bobo7bobo4bo4bo9bobo3bobo3bo\$69bobo6bo6bo3bobo12bo20bobo5bobobobobo3b2o5bo16bo23bobobobo7bobo4bo8bo5bobo10bo22bobo7bobo2bobo4b2obobo4bobo3bo11bo\$79bo53bobobobobo3bo57bo6bo3bo11bo2bobo48bobo5bobobo!`

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?:
`x = 3, y = 6, rule = B2a3jkq/S01c3e2bo\$2bo\$o\$o\$2bo\$2bo!`
Please stop using my full name. Refer to me as dani.

she/they

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

Posts: 878
Joined: October 27th, 2017, 3:43 pm
Location: i love to eat bees

### 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:

`x = 300, y = 300, rule = B2ce3cj6e/S12-in3-ci4ijkwy5k297bo\$295b2o\$294b2o3bo\$293b2o3bo\$292b2o3b2o\$291b2o3b2o\$290b2o3b2o\$289b2o3b2o\$288b2o3b2o\$287b2o3b2o\$286b2o3b2o\$285b2o3b2o\$284b2obob2o\$283b2obob2o\$282b2o3b2o\$281b2o3b2o\$280b2o3b2o\$279b2obob2o\$278b2o3b2o\$277b2o3b2o\$276b2o3b2o\$275b2o3b2o\$274b2obob2o\$273b2o3b2o\$272b2obob2o\$271b2o3b2o\$270b2obob2o\$269b2o3b2o\$268b2o3b2o\$267b2obob2o\$266b2o3b2o\$265b2obob2o\$264b2o3b2o\$263b2o3b2o\$262b2o3b2o\$261b2o3b2o\$260b2o3b2o\$259b2o3b2o\$258b2obob2o\$257b2o3b2o\$256b2obob2o\$255b2o3b2o\$254b2o3b2o\$253b2o3b2o\$252b2obob2o\$251b2obob2o\$250b2o3b2o\$249b2obob2o\$248b2o3b2o\$247b2obob2o\$246b2o3b2o\$245b2o3b2o\$244b2o3b2o\$243b2o3b2o\$242b2obob2o\$241b2o3b2o\$240b2obob2o\$239b2o3b2o\$238b2o3b2o\$237b2o3b2o\$236b2obob2o\$235b2o3b2o\$234b2obob2o\$233b2o3b2o\$232b2o3b2o\$231b2obob2o\$230b2o3b2o\$229b2o3b2o\$228b2o3b2o\$227b2o3b2o\$226b2o3b2o\$225b2o3b2o\$224b2o3b2o\$223b2o3b2o\$222b2o3b2o\$221b2o3b2o\$220b2obob2o\$219b2o3b2o\$218b2o3b2o\$217b2o3b2o\$216b2obob2o\$215b2o3b2o\$214b2o3b2o\$213b2obob2o\$212b2o3b2o\$211b2obob2o\$210b2o3b2o\$209b2o3b2o\$208b2obob2o\$207b2o3b2o\$206b2obob2o\$205b2o3b2o\$204b2obob2o\$203b2o3b2o\$202b2o3b2o\$201b2o3b2o\$200b2o3b2o\$199b2o3b2o\$198b2o3b2o\$197b2obob2o\$196b2o3b2o\$195b2o3b2o\$194b2o3b2o\$193b2o3b2o\$192b2o3b2o\$191b2o3b2o\$190b2o3b2o\$189b2o3b2o\$188b2o3b2o\$187b2o3b2o\$186b2obob2o\$185b2o3b2o\$184b2o3b2o\$183b2o3b2o\$182b2o3b2o\$181b2o3b2o\$180b2o3b2o\$179b2obob2o\$178b2o3b2o\$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\$141b2o3b2o\$140b2obob2o\$139b2o3b2o\$138b2obob2o\$137b2o3b2o\$136b2o3b2o\$135b2o3b2o\$134b2o3b2o\$133b2o3b2o\$132b2obob2o\$131b2o3b2o\$130b2o3b2o\$129b2o3b2o\$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\$98b2o3b2o\$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\$71b2o3b2o\$70b2obob2o\$69b2obob2o\$68b2o3b2o\$67b2obob2o\$66b2o3b2o\$65b2obob2o\$64b2o3b2o\$63b2obob2o\$62b2o3b2o\$61b2o3b2o\$60b2o3b2o\$59b2o3b2o\$58b2obob2o\$57b2o3b2o\$56b2obob2o\$55b2o3b2o\$54b2o3b2o\$53b2o3b2o\$52b2o3b2o\$51b2o3b2o\$50b2o3b2o\$49b2obob2o\$48b2o3b2o\$47b2o3b2o\$46b2o3b2o\$45b2obob2o\$44b2o3b2o\$43b2o3b2o\$42b2o3b2o\$41b2o3b2o\$40b2obob2o\$39b2o3b2o\$38b2obob2o\$37b2o3b2o\$36b2obob2o\$35b2o3b2o\$34b2obob2o\$33b2obob2o\$32b2o3b2o\$31b2obob2o\$30b2o3b2o\$29b2obob2o\$28b2o3b2o\$27b2obob2o\$26b2o3b2o\$25b2o3b2o\$24b2obob2o\$23b2o3b2o\$22b2o3b2o\$21b2o3b2o\$20b2o3b2o\$19b2o3b2o\$18b2o3b2o\$17b2o3b2o\$16b2o3b2o\$15b2o3b2o\$14b2o3b2o\$13b2obob2o\$12b2obob2o\$11b2o3b2o\$10b2obob2o\$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:

`x = 70, y = 1052, rule = B2c3aj4a6ack7/S1e2-an3ejnr4i6k7ebo4bo4bo4bo\$obo2bobo2bobo2bobo3bo4bo4bo4bo4bo5bo4bo5bo4bo4bo\$3o2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$obo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$2bo2b3o2b3o2b3o2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2bobo2b3o2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5b3o2b3o2b3o2bobo2bobo2bobo2bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2bobo2b2o3bobo2bobo3b3o2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo2bobo2bo4bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2b3o7bobo2b3o3bobo2bobo3b3o2bobo2bobo\$5b3o2b3o2bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2b3o7b3o2b3o3b3o2bobo3bobo2bobo2b3o\$5bobo2b3o2b3o2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo2bobo7bobo2b3o3b3o2b3o3bobo2bobo2bobo\$5bobo2bobo2bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2b3o7bobo2bobo3b3o2b3o3bobo2bobo2b3o\$5b3o2b3o2bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo2bobo2bobo2b3o2bobo7bobo2bobo3b3o2b3o3b3o2b3o2bobo\$5b3o2bo4bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo2bobo2bobo7bobo2bobo3bobo2bobo3b3o2b3o2b3o\$5b3o7bobo2bobo2bobo7bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo2bobo4bo7bobo2bobo3bobo2b3o3b3o2b3o2b3o\$5bobo7bobo2bobo12bobo2bobo3bobo2bobo3b3o2bobo2bobo\$5bobo7bobo2bobo12bobo2b3o3b3o2bobo3bobo2bobo2bobo\$5b3o7bobo2bobo12bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo2b3o12bobo2b3o3b3o2bobo3bobo2bobo2b3o\$5b3o7bobo2bobo12bobo2bobo3bobo2bobo3bobo2bobo2bobo\$5bobo7bobo4bo12bobo2b3o3b3o2b3o3bobo2b3o2b3o\$5bobo7bobo17bobo2bobo3bobo2bobo3b3o2bobo2bobo\$5bobo7bobo17bobo2b3o3bobo2b3o3bobo2b3o2bobo\$5bobo7b3o17bobo2bobo3bo4bobo3bobo2bobo2bobo\$5bobo9bo17bobo2b3o8b3o3bobo2bobo2b3o\$5b3o8bo18b3o2bobo8bobo3b3o2bobo2bobo\$5bobo27bobo2b3o8bobo3bobo2bobo2bobo\$5bobo27bobo3bo9bobo3bobo2bobo2bobo\$5bobo27bobo3bo9b3o3bobo2bobo2bobo\$5bobo27b3o2b3o8bobo3bobo2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2bobo2b3o\$5bobo27bobo2b3o8bobo3b3o2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2b3o2b3o\$5bobo27b3o2b3o8bobo3b3o2bobo2bobo\$5bobo27bobo2bobo8b3o3bobo2bobo2bobo\$5b3o27b3o2b3o8bobo3b3o2bobo2bobo\$5bobo27bobo2bobo8b3o3bobo2bobo2b3o\$5b3o27bobo2bobo8bobo3bobo2bobo2bobo\$5bobo27bobo2bobo8bobo3bobo2b3o2bobo\$5bobo27b3o4bo8bobo3bobo2bobo2bobo\$5bobo27bobo13b3o3bobo2bobo2b3o\$5b3o27b3o13bobo3bobo2bobo2bobo\$5bobo27bobo13bobo5bo2b3o2b3o\$5b3o27b3o13bobo8bobo2bobo\$5bobo27bobo13bobo8b3o2b3o\$5bobo27b3o13bobo8bobo2bobo\$5bobo27bobo13b3o8bobo2bobo\$5bobo27bobo13bobo8bobo2bobo\$5bobo27bobo13b3o8bobo2bobo\$5bobo27bobo13bobo8bobo2bobo\$5bobo27b3o13b3o8b3o2bobo\$5bobo27bobo13bobo8bobo2b3o\$5bobo27bobo13b3o8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27bobo13bobo8bobo2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27b3o13b3o8b3o2bobo\$5b3o27bobo13bobo8bobo2bobo\$5bobo27b3o13bobo8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27b3o13bobo8b3o2bobo\$5b3o27bobo13bobo8bobo2b3o\$5bobo27bo15b3o8bobo2bobo\$5b3o43bobo8b3o2bobo\$5bobo43b3o8bobo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43bobo8bobo2bobo\$5b3o43bobo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5b3o43bobo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5bobo43bobo8bobo2bobo\$5bobo43bobo8bobo2bobo\$5bobo43bobo8bobo2bobo\$5bobo43b3o8bobo2bobo\$5b3o43bobo8b3o2b3o\$5bobo43bobo8bobo2bobo\$5bobo43bobo8bobo2bobo\$5bobo43b3o8bobo2bobo\$5bobo43bobo8bobo2b3o\$5bobo43bobo8bobo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43bobo8bobo2bobo\$5bobo43bobo8b3o2b3o\$5bobo43b3o8bobo2bobo\$5b3o43bobo8b3o2bobo\$5bobo43b3o8bobo2bobo\$5b3o43bobo8bobo2b3o\$5bobo43b3o8bobo2bobo\$5bobo43bobo8bobo2b3o\$5bobo43bobo8bobo2bobo\$5bobo43b3o8bobo2b3o\$5bobo43bobo8bobo2bobo\$5b3o43b3o8bobo2b3o\$5bobo43bobo8bobo2bobo\$5bobo43b3o8bobo2b3o\$5bobo43bobo8bobo4bo\$5bobo43b3o8b3o3bo\$5bobo43bobo8bobo\$5b3o43bobo8bobo\$5bobo43bobo8b3o\$5b3o43b3o8bobo\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5b3o43b3o8bobo\$5bobo43bobo8b3o\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5b3o43bobo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5bobo43bobo8bobo\$5bobo43bobo8b3o\$5b3o43b3o8bobo\$5bobo43bobo8bobo\$5bobo43b3o8bobo\$5bobo43bobo8bobo\$5b3o44b2o8bobo\$5bobo45bo8b3o\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5b3o54bobo\$5bobo54b3o\$5bobo54bobo\$5bobo54bobo\$5bobo54bobo\$5bobo5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[[ Z 2 Y -500 ]]`

Some of them start getting really long though...
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 482
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### 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.
`x = 9, y = 17, rule = B2en3-aejy4-cqry5aeky67e/S02-kn3ijq4cijnqz5acekq6ack7e3b2o\$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
`x = 11, y = 21, rule = B2en3-aejy4-cqry5aeky67e/S02-kn3ijq4cijnqz5acekq6ack7e4b2o\$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
wildmyron

Posts: 942
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
`x = 11, y = 11, rule = B2-an3ckqy4aeiq5-i6ckn7c8/S012-c3cinq4cijknry5ajkry6eik7e82o2b3o2bo\$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.
`x = 8, y = 17, rule = B2-an3ckqy4aeiq5-i6ckn7c8/S012-c3cinq4cijknry5ajkry6eik7e82o\$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.
`x = 8, y = 17, rule = B2-an3cknq4ijknqwy5-aeir6-e78/S012-c3ciknq4-acetz5ajn6-ai7e82o\$obo2bo\$2o5\$2o\$obo\$2o3bo5\$2o4b2o\$obo3bo\$2o!`

Corresponding ship -
c/(4n) diagonal, p(4n), mod(2n), n > 5
`x = 11, y = 11, rule = B2-an3cknq4ijknqwy5-aeir6-e78/S012-c3ciknq4-acetz5ajn6-ai7e8bo2b3o2bo\$2o2b2o\$4b3o2\$8b3o\$8b3o\$8bobo3\$8b2o\$8bo!`
wildmyron

Posts: 942
Joined: August 9th, 2013, 12:45 am

### Re: Rules with small adjustable spaceships

I was thinking somewhat on the lines of this:
`x = 19, y = 19, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7eo\$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):
`x = 19, y = 35, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7eo\$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:
`x = 23, y = 40, rule = B2-an3-ajry4cjky5-eijk6cn7c/S012akn3aery4acitwy5ij6ik7e2bo\$9bo11bo\$10bo\$9bo\$bo\$obo17bo\$19bobo30\$3bo\$10bo11bo\$11bo\$10bo!`
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 864
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

`x = 25, y = 44, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e82bo\$9bo13bo\$10bo\$bo7bo\$obo19bo\$21bobo35\$3bo\$10bo13bo\$11bo\$10bo!`

`x = 37, y = 72, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e810\$5bo\$12bo12bo\$13bo\$12bo\$24bo\$23bobo12\$4bo\$3bobo38\$6bo\$13bo12bo\$14bo\$13bo!`
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 864
Joined: July 1st, 2016, 3:58 pm

### 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!
muzik

Posts: 3217
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Well done! This is better than Sir Robin.

Brian Prentice
bprentice

Posts: 532
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### 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:
`x = 143, y = 88, rule = B2ce3cen4ekt6kn/S01c2ae4cknr5akn2bo38bo40bo39bo\$9bo11bo26bo11bo28bo11bo27bo11bo\$10bo38bo40bo39bo\$bo7bo30bo7bo32bo7bo31bo7bo\$obo17bo18bobo17bo20bobo17bo19bobo17bo\$19bobo36bobo38bobo37bobo31\$123bo\$130bo11bo\$131bo\$130bo13\$102bo\$83bo14bo\$97bo\$98bo13\$42bo\$49bo11bo\$50bo\$49bo13\$22bo\$3bo12bo\$15bo\$16bo!`

EDIT, 4/3 slope:
`x = 35, y = 45, rule = B2ce3cen4ekt6kn/S01c2ae4cknr5akn3bo\$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):
`x = 23, y = 22, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar67816bo\$bo15bo\$17bo2bo\$16bo8\$b2o\$o2bo16b2o\$19bo2bo5\$4bo\$3bo17bo\$2bo\$4bo!`

The speed of diagonal ships can get very fast:
`x = 15, y = 14, rule = B2aen3an4cntwyz5678/S02ain3-ajnq4-nrwy5-ar6788bo\$o3bo2bo4bo\$b3o3bo\$ob2o4bo\$3bo\$bo2bo\$2b2o8b2o\$11bo2bo3\$7bo\$2bo5bo\$8bo4bo\$7bo!`

EDIT, faster:
`x = 16, y = 16, rule = B2aei3-aijq4einrtyz5-ace6cei7e8/S01e2in3-ein4cejrz5eky788bo4bo\$7bo\$3bo3bo\$8bo3\$13b2o\$12bo2bo3\$o2bo\$b2o\$bo4bo\$7bo\$7bo7bo\$6bo!`
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 864
Joined: July 1st, 2016, 3:58 pm

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