Rules with small adjustable spaceships

For discussion of other cellular automata.
muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Rules with small adjustable spaceships

Last edited by muzik on January 5th, 2018, 1:47 pm, edited 2 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

bprentice
Posts: 630
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: Rules with small adjustable spaceships

muzik,

Your post would be more useful if each of the listed rules were pointers to the example patterns. Readers should never be required to search the Forum for referenced material.

Brian Prentice

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

that's that done
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

Here's a rule with adjustable-speed wickstretchers and adjustable-direction spacefillers:
viewtopic.php?f=11&t=803&start=850#p51682
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

All speeds of the form 2c/(4n+2), n>3:

Code: Select all

``````x = 98, y = 24, rule = 1e2-en3aejnr4ir5y7c/2c3a4ak6ack7e/3
.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A\$A.A2.A.A
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A2.A.A2.A.A2.A.A2.A.A\$3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A
2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A\$ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.A
BA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA\$2.A2.A
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A.A2.A.A2.A.A2.A.A2.A.A\$7.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$12.A2.A.A2.A.A2.A.A
2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.
A\$17.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A2.A.A2.A.A\$22.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$27.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A
2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$32.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.
A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$37.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$42.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A\$47.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A
2.A.A2.A.A\$52.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$57.A2.A.
A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$62.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A\$67.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$72.A2.A.A2.A.A2.A.A2.A.A2.
A.A\$77.A2.A.A2.A.A2.A.A2.A.A\$82.A2.A.A2.A.A2.A.A\$87.A2.A.A2.A.A\$92.A
2.A.A\$97.A!
[[ THEME Blues ]]``````
Generations feels like it has a lot more potential for adjustable-speed technology, with the whole one-way-signal mechanic.
Last edited by muzik on February 10th, 2019, 5:26 am, edited 1 time in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

Found another one by myself. 2c/(4n+2), n>1:

Code: Select all

``````x = 39, y = 4, rule = B2c3acjr4y5ci/S01e2ac3en4n5ij6a
3b2o7b2o8b2o9b2o\$3b2o7bo9bo10bo\$3b3o6b2obo6b2o2bo6b2o3bo\$o3bo4bo9bo10b
o!
``````
Can we get more people looking for these?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

Re: Rules with small adjustable spaceships

Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

New c/odd n adjustables:

Code: Select all

``````x = 10, y = 28, rule = 1e23-ai4ain5jy/2c3-in6ack7/3
5.4A\$5.A.B2A\$7.2A3\$4.5A\$4.A2.B2A\$6.3A3\$3.6A\$3.A3.B2A\$5.4A3\$2.7A\$2.A4.
B2A\$4.5A3\$.8A\$.A5.B2A\$3.6A3\$9A\$A6.B2A\$2.7A!
[[ THEME Blues ]]``````
Last edited by muzik on February 10th, 2019, 5:26 am, edited 1 time in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Majestas32
Posts: 524
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

Re: Rules with small adjustable spaceships

muzik wrote:New c/odd n adjustables:

Code: Select all

``````x = 10, y = 28, rule = 1e23-ai4ain5jy/2c3-in6ack7/3
5.4A\$5.A.B2A\$7.2A3\$4.5A\$4.A2.B2A\$6.3A3\$3.6A\$3.A3.B2A\$5.4A3\$2.7A\$2.A4.
B2A\$4.5A3\$.8A\$.A5.B2A\$3.6A3\$9A\$A6.B2A\$2.7A!
``````
WE MUST APGSEARCH
Please, stop spam searching Snowflakes.

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

Re: Rules with small adjustable spaceships

Majestas32 wrote: WE MUST APGSEARCH
Sorry but apgluxe doesnt support nontot generations yet.

Also, muzik, you haven't addrd the 3 wick-rules I found. I'll link them later when I'm on my computer and not on this tiny screen.
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

AbhpzTa
Posts: 481
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Rules with small adjustable spaceships

2c/(2n+1) p(2n+1) spaceships (n>=4):

Code: Select all

``````x = 14, y = 39, rule = B2c3aejr4ijr5i7e/S12-en3einr4eijt5ry6e7e8
6bo\$2bo4bo\$o2b6o\$b2o4bo\$6bo3\$7bo\$2bo6bo\$o2b7o\$b2o6bo\$7bo4\$2bo7bo\$o2b8o
\$b2o7bo5\$2bo8bo\$o2b9o\$b2o8bo5\$2bo9bo\$o2b10o\$b2o9bo5\$2bo10bo\$o2b11o\$b2o
10bo!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

muzik
Posts: 3632
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

So that's all the 2c/n speeds proven possible then?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

Re: Rules with small adjustable spaceships

All the diagonal adjustable wickships, because you requested it.
22+66n, n >= 0

62+6n, n >= 0

29+6n, n >= 0
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

wildmyron
Posts: 1329
Joined: August 9th, 2013, 12:45 am

Re: Rules with small adjustable spaceships

c/(2n+1) diagonal for n>=3

Code: Select all

``````x = 41, y = 35, rule = B3aeijq4awyz5jr/S1c2in3ackqr4q5a6e
30b3o2bo\$34bo\$33bobo\$36bo\$37bo\$38bo\$39bo\$40bo3\$20b3o2bo\$24bo\$23bobo\$
26bo\$27bo\$28bo\$29bo4\$10b3o2bo\$14bo\$13bobo\$16bo\$17bo\$18bo5\$3o2bo\$4bo\$3b
obo\$6bo\$7bo!``````
A variation on the above (same allowed speeds)

Code: Select all

``````x = 39, y = 37, rule = B3aeijk4az5j/S1c2ein3ack4q5a6ae
30bo\$30bo\$30bo2bo\$32bo\$31bobo\$34bo\$35bo\$36bo\$37bo\$38bo\$20bo\$20bo\$20bo
2bo\$22bo\$21bobo\$24bo\$25bo\$26bo\$27bo2\$10bo\$10bo\$10bo2bo\$12bo\$11bobo\$14b
o\$15bo\$16bo3\$o\$o\$o2bo\$2bo\$bobo\$4bo\$5bo!``````
Another variation but with a stable tail-end (same allowed speeds)

Code: Select all

``````x = 40, y = 35, rule = B3aeijk4a/S1c2en3ackqr4q5aq6e
31bo2bo\$30bo2bo\$32bobo\$35bo\$36bo\$37bo\$38bo\$39bo3\$21bo2bo\$20bo2bo\$22bob
o\$25bo\$26bo\$27bo\$28bo4\$11bo2bo\$10bo2bo\$12bobo\$15bo\$16bo\$17bo5\$bo2bo\$o
2bo\$2bobo\$5bo\$6bo!``````
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.

AbhpzTa
Posts: 481
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Rules with small adjustable spaceships

(1,0)c/(3n+2) p(3n+2) spaceships (n>=3):

Code: Select all

``````x = 13, y = 54, rule = B2c3aj4k5cnr/S2-n3-ajky4j5jn
bo\$ob5o\$bo5bo\$6b2o7\$bo\$ob6o\$bo6bo\$7b2o7\$bo\$ob7o\$bo7bo\$8b2o7\$bo\$ob8o\$bo
8bo\$9b2o7\$bo\$ob9o\$bo9bo\$10b2o7\$bo\$ob10o\$bo10bo\$11b2o!``````
EDIT:
(2,1)c/3n p3n spaceships (n>=5):

Code: Select all

``````x = 12, y = 38, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
o8b2o\$9o2bo\$9b2o5\$o7b2o\$8o2bo\$8b2o5\$o6b2o\$7o2bo\$7b2o5\$o5b2o\$6o2bo\$6b2o
5\$o4b2o\$5o2bo\$5b2o5\$o3b2o\$4o2bo\$4b2o!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

AforAmpere
Posts: 1066
Joined: July 1st, 2016, 3:58 pm

Re: Rules with small adjustable spaceships

AbhpzTa wrote: (2,1)c/3n p3n spaceships (n>=5):

Code: Select all

``````x = 12, y = 38, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
o8b2o\$9o2bo\$9b2o5\$o7b2o\$8o2bo\$8b2o5\$o6b2o\$7o2bo\$7b2o5\$o5b2o\$6o2bo\$6b2o
5\$o4b2o\$5o2bo\$5b2o5\$o3b2o\$4o2bo\$4b2o!``````
Nice! I somehow didn't see this until now.
C/32+4n for n>0:

Code: Select all

``````x = 23, y = 23, rule = B2cik3aik4cir5ekqr6i7e8/S02aen3eij4cinwz5aeijr6ei7e
2bobo13bobo8\$2bobo13bobo\$2b3o13b3o3\$3bo\$b5o13bo\$bo3bo11b5o\$2obob2o10bo
3bo\$bo3bo10b2obob2o\$b5o11bo3bo\$3bo13b5o\$19bo2\$3bo\$19bo!
``````
This means that all speeds C/40+4n for n>0 have max population of 29:

Code: Select all

``````x = 21, y = 25, rule = B2cik3aik4cir5ekqr6i7e8/S02aen3eij4cinwz5aeijr6ei7e
2bobo11bobo7\$2bobo11bobo\$2b3o11b3o6\$3bo\$b5o11bo\$bo3bo9b5o\$2obob2o8bo3b
o\$bo3bo8b2obob2o\$b5o9bo3bo\$3bo11b5o\$17bo2\$3bo\$17bo!
``````
Last edited by AforAmpere on February 17th, 2018, 9:26 am, edited 2 times in total.
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)

dani
Posts: 973
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

Re: Rules with small adjustable spaceships

AbhpzTa wrote: (2,1)c/3n p3n spaceships (n>=5):
What a great rule! It has this small c/8 spaceship:

Code: Select all

``````x = 2, y = 3, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
o\$2o\$o!
``````
A c/2 spaceship too:

Code: Select all

``````x = 4, y = 8, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
2bo\$ob2o\$b2o3\$b2o\$ob2o\$2bo!
``````
Last but not least, the wickstrecher:

Code: Select all

``````x = 9, y = 4, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
7bo\$6ob2o\$o5b2o\$6bo!
``````
I will apgsearch soon.
moose#0915

AforAmpere
Posts: 1066
Joined: July 1st, 2016, 3:58 pm

Re: Rules with small adjustable spaceships

Another 2c/4n, this time, for n>=3:

Code: Select all

``````x = 38, y = 4, rule = B2e3eijr4aijknrw6akn7e/S02aci3anr4ijrty5ey6e7c
5bo14bo16bo\$o2bo10bo2bo12bo2bo\$2bo13bo15bo\$3bo13bo15bo!
``````
EDIT, 2c/76+8n for n>=0:

Code: Select all

``````x = 22, y = 25, rule = B2ci3ai4cir6kn7c8/S02ae3aeij4ciz5akqr6ai7e
3bo14bo\$b5o10b5o\$bo3bo10bo3bo\$2obob2o8b2obob2o\$bo3bo10bo3bo\$b5o10b5o\$
3bo14bo3\$2b3o12b3o\$2bobo12bobo4\$3bo\$b5o12bo\$bo3bo10b5o\$2obob2o9bo3bo\$b
o3bo9b2obob2o\$b5o10bo3bo\$3bo12b5o\$18bo2\$3bo\$18bo!
``````
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)

Gamedziner
Posts: 796
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

Re: Rules with small adjustable spaceships

danny wrote: What a great rule! It has this small c/8 spaceship:

Code: Select all

``````x = 2, y = 3, rule = B2cin3aej4kr5cnr/S1c2-n3enr4jr5anq6i7c
o\$2o\$o!
``````
*c/4

Code: Select all

``````x = 81, y = 96, rule = LifeHistory
58.2A\$58.2A3\$59.2A17.2A\$59.2A17.2A3\$79.2A\$79.2A2\$57.A\$56.A\$56.3A4\$27.
A\$27.A.A\$27.2A21\$3.2A\$3.2A2.2A\$7.2A18\$7.2A\$7.2A2.2A\$11.2A11\$2A\$2A2.2A
\$4.2A18\$4.2A\$4.2A2.2A\$8.2A!
``````

wildmyron
Posts: 1329
Joined: August 9th, 2013, 12:45 am

Re: Rules with small adjustable spaceships

AforAmpere wrote:This means that all speeds C/40+4n for n>0 have max population of 29:
This limit can be reduced to 5 for all speeds c/n (given 3 cell ships for most speeds c/n where n<100)

(1,0)c/4n, p(4n), n>=4:

Code: Select all

``````x = 9, y = 24, rule = B2ein3inr4ikw5jky6cei8/S012-an3ijkqy4acjkq5jkq6in7
2bo\$5bo\$6bobo\$5bo7\$bo\$5bo\$6bobo\$5bo7\$o\$5bo\$6bobo\$5bo!``````
(1,0)c/(4n+1), p(4n+1), n>=2:

Code: Select all

``````x = 8, y = 34, rule = B2e3ijknq4aeijqr5ekqr6e78/S01c2cen3aenqr4anqrtw5enqr6aen7c
3bo\$b4o\$2b2obobo\$3b2o7\$2bo\$4bo\$5bobo\$4bo7\$bo\$4bo\$5bobo\$4bo7\$o\$4bo\$5bob
o\$4bo!``````
(1,0)c/(4n+2), p(4n+2), n>=4:

Code: Select all

``````x = 8, y = 24, rule = B2en3ainq4aceiknr5-ceij6aik78/S01c2-ak3ijkry4ajnrty5ijq6ein7e8
2bo\$4bo\$5bobo\$4bo7\$bo\$4bo\$5bobo\$4bo7\$o\$4bo\$5bobo\$4bo!``````
(1,0)c/(4n+3), p(4n+3), n>=3:

Code: Select all

``````x = 8, y = 24, rule = B2en3ainq4-ackt5acekn6-ac7c8/S01c2cen3-acek4cjt5-aeqr6-ce7e8
2bo\$4bo\$5bobo\$4bo7\$bo\$4bo\$5bobo\$4bo7\$o\$4bo\$5bobo\$4bo!``````
There are many more similar ships, even with the same c/2, I've just chosen a set with minimum population of 5 covering all speeds c/n (for n>15).

----

(1,0)c/2n, p(2n), n>=7 (moon bouncer):

Code: Select all

``````x = 12, y = 35, rule = B2aen3aen4inqtwyz5-ekny6aen7e8/S1e2n3ejry4knqrtw5cnq678
7bo\$8bo\$4bo3bo\$3bobobo2bo\$11bo6\$7bo\$8bo\$2bobo3bo\$3bo3bo2bo\$11bo6\$7bo\$
8bo\$2bo5bo\$bobo3bo2bo\$11bo6\$7bo\$8bo\$obo5bo\$bo5bo2bo\$11bo!``````
I tried to find stable reflectors but didn't have any luck completing a ship with that restriction, so I tried p2 instead.

Edit: Actually, just found one with stable reflectors and smaller minimum population:

(1,0)c/2n, p(2n), n>=6:

Code: Select all

``````x = 11, y = 36, rule = B2-ci3nqr4aceqry5ceqy6cn/S01e2i3-aein4jkqr5k6ek
2bobo\$3b3o\$3b2obobobo\$3b2obo\$3b3o\$2bobo5\$2bo\$5bo\$6bobobo\$6bo\$5bo\$2bo5\$
bo\$5bo\$6bobobo\$6bo\$5bo\$bo5\$o\$5bo\$6bobobo\$6bo\$5bo\$o!``````
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: 1329
Joined: August 9th, 2013, 12:45 am

Re: Rules with small adjustable spaceships

wildmyron wrote:
AforAmpere wrote:This means that all speeds C/40+4n for n>0 have max population of 29:
This limit can be reduced to 5 for all speeds c/n (given 3 cell ships for most speeds c/n where n<100)
This set of adjustable speed spaceships reduces the upper limit on population for all speeds c/n and also 2c/n to 4 cells (given 3 cell examples for all c/n and 2c/n with n < 25 [except 2c/3 which is 4 cells]). Several of them convert the ship to a different 3 cell ship traveling in the backwards direction, specifically, the c/n ships - there are similar ships at 2c/n not shown here.

(1,0)c/4n, p(4n), n>=5:

Code: Select all

``````x = 10, y = 33, rule = B2ek3aij4eir5a6ac/S01c2-an3eiqy4aenrt5aiq6ik7e
3bo3bo\$9bo\$7bo8\$2bo4bo\$9bo\$7bo8\$bo5bo\$9bo\$7bo8\$o6bo\$9bo\$7bo!``````
(1,0)c/(4n+1), p(4n+1), n>=5:

Code: Select all

``````x = 9, y = 33, rule = B2ek3aiq4ai5y6k/S01c2-an3acekr4ey5ijkqy6cik
3bo2bo\$8bo\$6bo8\$2bo3bo\$8bo\$6bo8\$bo4bo\$8bo\$6bo8\$o5bo\$8bo\$6bo!``````
(1,0)c/(4n+2), p(4n+2), n>=4:

Code: Select all

``````x = 10, y = 33, rule = B2ek3ai4eir6ac/S01c2-an3eiqy4anrt5aeiq6k
3bo3bo\$9bo\$7bo8\$2bo4bo\$9bo\$7bo8\$bo5bo\$9bo\$7bo8\$o6bo\$9bo\$7bo!``````
(1,0)c/(4n+3), p(4n+3), n>=5:

Code: Select all

``````x = 10, y = 33, rule = B2ek3aik4einrwyz5a6c/S01c2-an3eqy4ajkqrt5-cknr6k8
3bo3bo\$9bo\$7bo8\$2bo4bo\$9bo\$7bo8\$bo5bo\$9bo\$7bo8\$o6bo\$9bo\$7bo!``````
(2,0)c/4n, p(4n), n>=4 (With n=4 the forward direction ship doesn't actually fully form):

Code: Select all

``````x = 9, y = 43, rule = B2ek3ij4ry5e/S012cei3ijqr4ar5aeky6i
4bobo\$8bo\$6bo8\$3bo2bo\$8bo\$6bo8\$2bo3bo\$8bo\$6bo8\$bo4bo\$8bo\$6bo8\$o5bo\$8bo
\$6bo!``````
(2,0)c/(4n+1), p(4n+1), n>=5:

Code: Select all

``````x = 9, y = 33, rule = B2ek3ij4rwz5e7e/S012-an3ijqr4aer5ai6c7e
3bo2bo\$8bo\$6bo8\$2bo3bo\$8bo\$6bo8\$bo4bo\$8bo\$6bo8\$o5bo\$8bo\$6bo!``````
(2,0)c/(4n+2), p(4n+2), n>=5:

Code: Select all

``````x = 9, y = 33, rule = B2e3ijqry4nr5r6k7e/S012-an3eir4a5q6c
3bo2bo\$8bo\$6bo8\$2bo3bo\$8bo\$6bo8\$bo4bo\$8bo\$6bo8\$o5bo\$8bo\$6bo!``````
(2,0)c/(4n+3), p(4n+3), n>=4:

Code: Select all

``````x = 9, y = 33, rule = B2e3ijry4qr5ek7e/S012cei3eij4aj5e7e
3bo2bo\$8bo\$6bo8\$2bo3bo\$8bo\$6bo8\$bo4bo\$8bo\$6bo8\$o5bo\$8bo\$6bo!``````
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: 1329
Joined: August 9th, 2013, 12:45 am

Re: Rules with small adjustable spaceships

Here's something a bit different: a family of c/2 ships with adjustable period and fixed minimum population. They consist of a c/2 diagonal ship bouncing between two c/2 orthogonal ships

(1,0)c/2, p(4n), n>3, 20 cells (except p12 which has min pop 21 in phase 1)

Code: Select all

``````x = 50, y = 17, rule = B2aei3cekq4jknrt5ejkry6-kn8/S1c2-ae3cinqr4aentw5-ackr6ace7c
2bo14bo14bo14bo\$2o2bo10b2o2bo10b2o2bo10b2o2bo\$2bobo12bobo12bobo12bobo\$
o3bo10bo3bo10bo3bo10bo3bo2\$obo12bobo12bobo12bobo\$3bo14bo14bo14bo\$46bo\$
3bo14bo14bo14bo\$43bob2o\$45bo3bo\$30bo3bo12bobo\$15bo3bo12bobo10b2o2bo\$o
3bo12bobo10b2o2bo12bo\$2bobo10b2o2bo12bo\$2o2bo12bo\$2bo!``````
Finding similar constructions for other periods is more difficult because two different reactions are required. I haven't tried searching for such ships yet, though I can say there are a lot of similar ships to the one above (this is just the smallest I could find). Here's a reflection which restores the diagonal ship after an odd number of generations (again, just one of many):

Code: Select all

``````x = 6, y = 11, rule = B2aei3cekn4ciknqt5cjnqr6in78/S12ci3ceiqr4-acer5cjq6i78
bo2bo\$3b3o\$obo2bo\$3b3o\$bo2bo3\$bobo\$4bo2\$4bo!``````
It's probably feasible to search for compatible pairs of reflections which can bounce the ship with period of 4n+2 (the other reflection has to delay the diagonal ship by 2 gen overall so that it matches speed with the two escorts). I haven't tried this search yet.

Does anybody know what the smallest such ships in Life are? And are there examples with period not divisible by 4?

P.S. Thanks again to Macbi for lls, which is extremely useful in this kind of endeavour.
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.

LaundryPizza03
Posts: 491
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: Rules with small adjustable spaceships

muzik wrote:All speeds of the form 2c/(4n+2), n>3:

Code: Select all

``````x = 98, y = 24, rule = 1e2-en3aejnr4ir5y7c/2c3a4ak6ack7e/3
.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A4.A\$A.A2.A.A
2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.
A2.A.A2.A.A2.A.A2.A.A\$3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A
2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A\$ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.A
BA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA2.ABA\$2.A2.A
.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A\$7.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$12.A2.A.A2.A.A2.A.A
2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.
A\$17.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A2.A.A2.A.A\$22.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$27.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A
2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$32.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.
A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$37.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$42.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.
A.A2.A.A2.A.A2.A.A2.A.A\$47.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A
2.A.A2.A.A\$52.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$57.A2.A.
A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$62.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A
.A2.A.A\$67.A2.A.A2.A.A2.A.A2.A.A2.A.A2.A.A\$72.A2.A.A2.A.A2.A.A2.A.A2.
A.A\$77.A2.A.A2.A.A2.A.A2.A.A\$82.A2.A.A2.A.A2.A.A\$87.A2.A.A2.A.A\$92.A
2.A.A\$97.A!
``````
Generations feels like it has a lot more potential for adjustable-speed technology, with the whole one-way-signal mechanic.
I think it's actually 2c/(4n+6), n≥3; the fastest is actually a 2c/18.

Here's a slightly different set of ships that do travel at 2c/(4n+2), n≥3:

Code: Select all

``````x = 17, y = 63, rule = 12-en3ejnr4r5jry/2c3a4a6ack7e/3
12.4A\$14.B2A\$13.3A3\$11.5A\$14.B2A\$12.4A3\$10.6A\$14.B2A\$11.5A3\$9.7A\$14.B
2A\$10.6A3\$8.8A\$14.B2A\$9.7A3\$7.9A\$14.B2A\$8.8A3\$6.10A\$14.B2A\$7.9A3\$5.
11A\$14.B2A\$6.10A3\$4.12A\$14.B2A\$5.11A3\$3.13A\$14.B2A\$4.12A3\$2.14A\$14.B
2A\$3.13A3\$.15A\$14.B2A\$2.14A3\$16A\$14.B2A\$.15A!
``````

Code: Select all

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

AforAmpere
Posts: 1066
Joined: July 1st, 2016, 3:58 pm

Re: Rules with small adjustable spaceships

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.
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)

AbhpzTa
Posts: 481
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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.
(m/g,0)c/(n/g) , period n [g=gcd(m,n) , (m=1 AND n=5) OR (0<5m<n AND m==n(mod 2))]

m=1 and n={5,7,9,11} (reaction={(5),(7),(9),(11)}):

Code: Select all

``````x = 114, y = 36, rule = B2a3jkq/S01c3e
103bo\$102bo10bo\$106bo5bo\$106bo5bo\$102bo10bo\$103bo5\$79bo\$78bo34bo\$85bob
o5bo3bo7bobobo\$85bobo5bo3bo7bobobo\$78bo34bo\$79bo5\$bo\$o112bo\$3bobo5bo7b
o3bobo7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo\$3bobo5bo7bo3bobo
7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo\$o112bo\$bo5\$7bo\$6bo106b
o\$13bobo9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo\$13bobo
9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo\$6bo106bo\$7bo!``````
m=3 and n=17 (reaction=(5,5,7)):

Code: Select all

``````x = 540, y = 6, rule = B2a3jkq/S01c3e
bo\$o538bo\$7bobo3bo5bo9bobo11bo3bo5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bo
bobobo7bobo11bo3bo3bobo7bo3bo5bo3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo
5bo7bobo3bobobo5bobobo3bobo3bo9bobobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo
3bo7bobo3bobo3bobobo3bobo5bobobo5bo5bobo9bo3bobo7bo11bobobo5bobo11bobo
bo9bobo3bobo9bo3bo3bo5bobo11bobo7bo3bobo3bobo\$7bobo3bo5bo9bobo11bo3bo
5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bobobobo7bobo11bo3bo3bobo7bo3bo5bo
3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo5bo7bobo3bobobo5bobobo3bobo3bo9bo
bobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo3bo7bobo3bobo3bobobo3bobo5bobobo
5bo5bobo9bo3bobo7bo11bobobo5bobo11bobobo9bobo3bobo9bo3bo3bo5bobo11bobo
7bo3bobo3bobo\$o538bo\$bo!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).