Rules with small adjustable spaceships

For discussion of other cellular automata.
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silversmith
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Joined: June 15th, 2020, 6:20 pm

Re: Rules with small adjustable spaceships

Post by silversmith » November 25th, 2020, 4:22 pm

Box ships:

Code: Select all

x = 140, y = 64, rule = B2ci3aejy4ekrw5ikny6in7/S1e2-an3-ijqy4acjntwy5any6acn
13$3b30o$3bo29b8o14b63o$3bo28bo7bo5b9o62bo6b9o$2bobo35bo5bo8bo61bo6bo
7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4b
o35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5b
o70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6b
o7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4b
o35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5b
o70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6b
o7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4b
o35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo35bo5bo70bo6bo7bo$4bo33bob
o4bobo69bo6bo7bo$4bo34bo7bo69bo4bobo5bobo$4bo34bo7bo69bo5bo7bo$4bo34b
o7bo69bo5bo7bo$4bo34bo7bo69bo5bo7bo$4bo34bo7bo67bobo5bo7bo$4bob34o7b40o
29bo6bo7bo$4b2o81b30o6b9o$6bo79bo!

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

Re: Rules with small adjustable spaceships

Post by AforAmpere » November 30th, 2020, 3:14 pm

silversmith wrote:
November 25th, 2020, 4:22 pm
Box ships:
Those are really nice!

True period glider based adjustable slope ships, an example at (3,1)c/156:

Code: Select all

x = 27, y = 28, rule = B2i3-ceqr4akt5cek6cn7e/S2aek3ajnr4inwz5n6a
17b2o$17b2o2$22bo$20bobo$21b2o$12b3o$14bo$13bo$25b2o$25b2o2$22bo$21bo$
21b3o4$2o$2o2$3bobo$4b2o$4bo3$7b2o$7b2o!
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

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yujh
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Re: Rules with small adjustable spaceships

Post by yujh » December 1st, 2020, 5:14 am

AforAmpere wrote:
November 30th, 2020, 3:14 pm
silversmith wrote:
November 25th, 2020, 4:22 pm
Box ships:
Those are really nice!

True period glider based adjustable slope ships, an example at (3,1)c/156:

Code: Select all

x = 27, y = 28, rule = B2i3-ceqr4akt5cek6cn7e/S2aek3ajnr4inwz5n6a
17b2o$17b2o2$22bo$20bobo$21b2o$12b3o$14bo$13bo$25b2o$25b2o2$22bo$21bo$
21b3o4$2o$2o2$3bobo$4b2o$4bo3$7b2o$7b2o!
Impressive!
Is there any more examples?how did u find it
B34kz5e7c8/S23-a4ityz5k!!!

b2n3-q5y6cn7s23-k4c8

B3-kq6cn8/S2-i3-a4ciyz8

wiki

Spamming in sandbox is better than spamming in the OCA.

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

Re: Rules with small adjustable spaceships

Post by AforAmpere » December 1st, 2020, 2:52 pm

yujh wrote:
December 1st, 2020, 5:14 am
Impressive!
Is there any more examples?how did u find it
Do you mean examples in this rule? You can shift the edges to create higher period versions, like this (3,1)c/172:

Code: Select all

x = 30, y = 31, rule = B2i3-ceqr4akt5cek6cn7e/S2aek3ajnr4inwz5n6a
19b2o$19b2o2$24bo$22bobo$23b2o$14b3o$16bo$15bo2$28b2o$28b2o2$25bo$24bo
$24b3o5$2o$2o2$3bobo$4b2o$4bo4$8b2o$8b2o!
This rule was found with EnumPattEvo, a search program I wrote. Link.

Adjustable period knightships of the form (2,1)c/(4n+3), n>=9:

Code: Select all

x = 18, y = 9, rule = B2e3aijr4eiknqtw5cn6ac7/S012-ai3eijny4nqtwy5-ackr6ai7c
3bo13bo3$obo11bobo$bo13bo3$17bo$3bo!
(2,1)c/(4n+1), n>=9:

Code: Select all

x = 4, y = 9, rule = B2e3aij4eiknqty5aceky6ac7/S012cek3ejn4ejnqry5ik6ck
o3$bobo$2bo4$o!
(2,1)c/(4n+2), n>=10:

Code: Select all

x = 4, y = 8, rule = B2e3aijry4eknqt5cen6ck7/S012-ai3eijn4enqw5ceqry6-ik
3bo4$obo$bo2$3bo!
(2,1)c/4n, n>=9:

Code: Select all

x = 4, y = 8, rule = B2ei3-eknq4eiknqy5ny6k7/S012-ai3eijn4nw5-eikr6ace7c
3bo4$obo$bo2$3bo!
EDIT: 5 cell (3,1)c/(4n+3), n>=15:

Code: Select all

x = 13, y = 9, rule = B2e3acij4ekqtwy5ceny6ac7/S012cek3-aciq4acjqr5-ainq6ack7c
o$o9bo$10bo$obo$10bobo4$bo9bo!
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

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yujh
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Re: Rules with adjustable puffers?

Post by yujh » December 25th, 2020, 8:19 pm

Code: Select all

x = 601, y = 3, rule = B2cei3j4c5i6c7e/S1e2i3-ckq4air5i6ci8
2b318o$3ob3o4bob4ob3o2bo5b2o2b2obob4o4bob2o3bo3b4o2b4o4b3ob2obo5bobobo
2bob2ob3o3b7o3b4ob2obo2bob2o2b2o2b2obobo5bo4bo3b4obobo2bo6b2ob2obob2o
2b4obobo2bo2b2ob3o5b2o2b5o2b2ob2obo2b2obobob2o2bobo3b2obo3bo2bo2bob2o
2bo3bo5bobobo2bo2b4o2bo3bobo3bobob3o5b3o$2b599o!
B34kz5e7c8/S23-a4ityz5k!!!

b2n3-q5y6cn7s23-k4c8

B3-kq6cn8/S2-i3-a4ciyz8

wiki

Spamming in sandbox is better than spamming in the OCA.

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

Re: Rules with small adjustable spaceships

Post by AforAmpere » January 1st, 2021, 2:57 am

Beautiful adjustable ships:

Code: Select all

x = 40, y = 22, rule = B2-ae3aeq4ajrt5y6ci7/S012in3ejnr4aikr5aiqry6c7e8
33bo$32bo6bo$o32bo17$33bo$32bo6bo$27bo5bo!
Another strange one:

Code: Select all

x = 28, y = 3, rule = B2-ae3aekr4aikntw5a6cn/S012i3ejnr4aijr5ijqy6n7e
24bo$23bo3bo$o23bo!
Adjustable diagonals with some weird horizontal wick shenanigans:

Code: Select all

x = 32, y = 3, rule = B2-ae3ae4akqt5n6c/S012in3ejnr4air5iqy6aik7e8
28bo$27bo3bo$o27bo!
3c/(4n+3), n>=7:

Code: Select all

x = 10, y = 3, rule = B2-an3-cikn4eikt5ai6k8/S012ck3jnqry4ij5any6c7e
4bo$o4bo$4bo4bo!
3c/(12n+2), n>=6:

Code: Select all

x = 12, y = 3, rule = B2-an3aery4jknr5ijn6ik7e8/S01c2-en3ejnry4eiz5nqr6-ae8
4bo$o4bo$4bo6bo!
3c/(12n+4), n>=7:

Code: Select all

x = 14, y = 3, rule = B2-a3aeqy4qr5ijnq6ik7e/S01c2-en3-acik4iqt5n6ci
4bo$o4bo$4bo8bo!
3c/(12n+9), n>=4:

Code: Select all

x = 10, y = 3, rule = B2-a3aeqr4r5aijry6aik7e8/S01c2-en3-acik4ei6c7e8
4bo$o4bo$4bo4bo!
3c/(12n+11), n>=6:

Code: Select all

x = 13, y = 3, rule = B2-an3aer4knz5i6ikn7e/S01c2-en3ejnry4ei5jn6aci
4bo$o4bo$4bo7bo!
8c/(24n+18) n>=10:

Code: Select all

x = 17, y = 3, rule = B2-a3aeq4nr5ijqy6aik7e8/S01c2-en3-aci4eiqt5jq6c7e
4bo$o4bo$4bo11bo!
Last edited by AforAmpere on January 1st, 2021, 5:17 am, edited 6 times in total.
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

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GUYTU6J
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Re: Rules with small adjustable spaceships

Post by GUYTU6J » January 1st, 2021, 5:07 am

A quick, random note that does not quite fit in the topic but responds an earlier post:
muzik wrote:
October 8th, 2017, 12:40 pm
Here's a rule with adjustable-speed wickstretchers and adjustable-direction spacefillers:
[B2i3ainqr4ai5ainy6-i78/S2-a3a4r5ain6-i78]
Said features can be realized in the outer-totalistic rule Plow World:

Code: Select all

x = 70, y = 20, rule = B378/S012345678
38bobo8bobo$36b7o4b7o$5bobobobobobobobobobobobobobobob8o4b8obobobobobo
$3b41o2b21o$3b40o4b20o$2b42o2b22o$3b40o4b20o$2b42o2b22o$3b40o4b20o$2b
42o2b22o$3b40o4b20o$2b42o2b22o$b42o4b22o$b43o2b23o$43o4b23o$b43o2b23o$
43o4b23o$b43o2b23o$b42o4b22o$3bobobobobobobobobobobobobobobobobobobob
2o4b2obobobobobobobobobo!
It works in the following rulespace, but I don't think there are any adjustable spaceships based on it here.

Code: Select all

|isorulemin       = B3aijn7c/S3ain4anr5acijn6ac78
|isorulemax       = B2ikn34-a5-ai6-a78/S012345678
Besides, there is a natural LWoD-like ladder that can be stopped with a single dot:

Code: Select all

x = 21, y = 8, rule = B378/S012345678
12bobobobo$10b11o$o9b10o$7b13o$7b14o$8b12o$8b13o$10bobobobobo!
Lifequote:
In the drama The Peony Pavilion, Tang Xianzu wrote: 原来姹紫嫣红开遍,似这般都付与断井颓垣。
(Here multiflorate splendour blooms forlorn
Midst broken fountains, mouldering walls.)
I'm afraid there's arrival but no departure.
Stop Japan from pouring nuclear waste!

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

Re: Rules with small adjustable spaceships

Post by AforAmpere » January 1st, 2021, 5:00 pm

10c/(120n+104), n>=2:

Code: Select all

x = 16, y = 3, rule = B2-an3aeqry4knr5ijqy6ikn7e8/S01c2-en3-acik4itz5jn6cn7e
3bo11bo$o3bo$3bo!
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

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Macbi
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Joined: March 29th, 2009, 4:58 am

Re: Rules with small adjustable spaceships

Post by Macbi » January 2nd, 2021, 10:36 am

Here are the two adjustable ships with just 3 cells (the smallest possible population) that I discovered in August 2020 and posted on the Discord but not here until now. (Posting since lemon41625 wanted to nominate them for DOTY.)

Code: Select all

x = 10, y = 1, rule = B2ce3kry4ackqry5ciry6ack/S02-c3-akqr4-ajnqy5aejqr6ei7
obo6bo!

Code: Select all

x = 8, y = 3, rule = B2cek3ejnqr4iky5ejkny6aik8/S02ei3akqry4cijqrz5cqry6ai78
o$7bo$o!
EDIT Found using the script from here.
Last edited by Macbi on January 4th, 2021, 3:14 am, edited 1 time in total.

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LaundryPizza03
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Re: Rules with small adjustable spaceships

Post by LaundryPizza03 » January 2nd, 2021, 11:35 pm

Not only that, the first rule is apgsearchable and has a period-tripling mechanism for the adjustable spaceships:

Code: Select all

x = 13, y = 1, rule = B2ce3kry4ackqry5ciry6ack/S02-c3-akqr4-ajnqy5aejqr6ei7
o2bo6bobo!
There is even a parabolic sawtooth:

Code: Select all

x = 3, y = 17, rule = B2ce3kry4ackqry5ciry6ack/S02-c3-akqr4-ajnqy5aejqr6ei7
bo7$bo$obo$bo7$bo!

Code: Select all

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

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

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GUYTU6J
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Re: Rules with small adjustable spaceships

Post by GUYTU6J » January 3rd, 2021, 3:26 am

AforAmpere wrote:
December 1st, 2020, 2:52 pm
[An adjustable glider+block collision based spaceship]
This rule was found with EnumPattEvo, a search program I wrote.
Not quite understand how to enter the RLEs. For example, I'd like to find a Harvest Moon relative where the following G+checkerboard collision evolves in a suitable manner:

Code: Select all

x = 11, y = 11, rule = B3-ckr5y/S2-i3-aek4ci5c
bbo$obo$boo$$bbbbbbbo$bbbbbbobo$bbbbbobobo$bbbbobobobo$bbbbbobobo$bbbbbbobo$bbbbbbbo!
Then how do I enter the rulespace, offset of the checkerboard (since it has to be diagonal and perpendicular to the glider lane) and displacement of the glider (since it has to turn 180 degrees on a different lane forward)?
Lifequote:
In the drama The Peony Pavilion, Tang Xianzu wrote: 原来姹紫嫣红开遍,似这般都付与断井颓垣。
(Here multiflorate splendour blooms forlorn
Midst broken fountains, mouldering walls.)
I'm afraid there's arrival but no departure.
Stop Japan from pouring nuclear waste!

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silversmith
Posts: 80
Joined: June 15th, 2020, 6:20 pm

Re: Rules with small adjustable spaceships

Post by silversmith » January 22nd, 2021, 10:57 am

Here is a box ship I posted on discord with adjustable speed and period multiplying capabilities.

Code: Select all

x = 27, y = 26, rule = B2cen3ajn4acty5aiy6cei7e/S2aci3aejy4ant5ikqr6-ci78
26o$26o$26o$26o$10ob15o$12ob14o$10ob16o$27o$27o$21ob5o$23ob3o$21ob5o$
27o$27o$23ob3o$23o2b2o$23ob3o$27o$27o$10ob16o$10o2b15o$10ob16o$27o$
27o$27o$27o!
Last edited by silversmith on March 21st, 2021, 12:36 pm, edited 1 time in total.

kiho park
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Joined: September 24th, 2010, 12:16 am

Re: Rules with small adjustable spaceships

Post by kiho park » February 6th, 2021, 4:06 am

Here is some adjustable ships I found before.

○ (2n, 0)c/(4n+4), n=[2,+Inf)

Code: Select all

x = 16, y = 37, rule = B1e2ce3jkq4-ajknw5-acek6-ck8/S12-ek3-a4knz5-in6ein7
5bobo$obo4bo$bo2b4o5bobo$3obob2o6bo$13b3o12$5bobo$obo4bo$bo2b4o4bobo$
3obob2o5bo$12b3o12$5bobo$obo4bo$bo2b4o3bobo$3obob2o4bo$11b3o!
○ (2n, 0)c/(4n+4), n=[2,+Inf), B0 Version

Code: Select all

x = 66, y = 5, rule = B01e2aik3ckqy4acenwyz5-cery6a/S01c2-ei3cjq4cn5cy6an
6b2o22b2o22b2o$5b2o22b2o22b2o$3obo2bo16b3obo2bo16b3obo2bo$obo10b3o8bob
o11b3o7bobo12b3o$4bo8bobo12bo9bobo11bo10bobo!
○ (2n, 0)c/(4n), n=[4,+Inf)

Code: Select all

x = 68, y = 9, rule = B1e2cik3cjkqy4-ajt5ej6eik7e/S01e2kn3ejkq4ceijqz5jnr6-ac8
bobo10bobo8bobo11bobo7bobo12bobo$2bo4b4o4bo10bo4b4o5bo9bo4b4o6bo$obob
2o3bo3bobobo6bobob2o3bo4bobobo5bobob2o3bo5bobobo$ob2ob2o3bo2bobobo6bob
2ob2o3bo3bobobo5bob2ob2o3bo4bobobo$5b4o20b4o20b4o$2bo3bo19bo3bo19bo3bo
$2b2o2bo19b2o2bo19b2o2bo$2b2o2bo19b2o2bo19b2o2bo$2b3o21b3o21b3o!
○ (2n, 0)c/(4n), n=[4,+Inf), B0 Version

Code: Select all

x = 19, y = 31, rule = B01c2ein3-nr4cjknqy5aijnq6a/S012-ce3eknqr4-cjk5acny6ck
obo4bo6bobo$obob3o7bobo$2b6o6bo$2bob3o7bo$5bo$4bo$6bo6$obo4bo7bobo$obo
b3o8bobo$2b6o7bo$2bob3o8bo$5bo$4bo$6bo6$obo4bo8bobo$obob3o9bobo$2b6o8b
o$2bob3o9bo$5bo$4bo$6bo!
○ (2n+4, 0)c/(4n+4), n=[2,+Inf), B0 Version

Code: Select all

x = 102, y = 4, rule = B02aek3jknr4aceirty5acijk6c/S1c2cek3-ajkr4cknw5en6i7e
4b2o6bobo17b2o7bobo16b2o8bobo15b2o9bobo$obo4bo5bo14bobo4bo6bo13bobo4bo
7bo12bobo4bo8bo$bo4bo22bo4bo22bo4bo22bo4bo$4bo27bo27bo27bo!
○ (2n, 2n)c/(4n+4), n=[1,+Inf), B0 Version

Code: Select all

x = 43, y = 41, rule = B012-an3ijnqy4inqw5nry6an/S02ei3er4y5anr6ce7e
42bo$39bob2o2$40bo$38bobo$35bo$34b2o10$26bo$23bob2o2$24bo$22bobo2$18bo
$17b2o9$10bo$7bob2o2$8bo$6bobo3$bo$2o!
○ (4n+2, 0)c/(12n+5), n=[2,+Inf)

Code: Select all

x = 28, y = 68, rule = B2ce3ae4aeijqrt5-r6ekn7c8/S01e2-ei3ejkry4-aiy5aejnq6ace7e
16b2o3bo3b2o$16b3ob2o3b3o$16b2o3bo3b2o6$16b4o5b2o$15bo3bo5b3o$16b4o5b
2o6$13b2obo8b2o$13b2o10b3o$13b2obo8b2o5$13bo$14bo10b2o$13bobo9b3o$14bo
10b2o$13bo4$12bo$10b2obo11b2o$11b3o11b3o$10b2obo11b2o$12bo4$10b2o$8b2o
15b2o$7b2o2bo13b3o$8b2o15b2o$10b2o4$8b2o$5b2o3bo14b2o$7bobo15b3o$5b2o
3bo14b2o$8b2o4$6b3o$3b2o2b2o16b2o$2b4ob3o15b3o$3b2o2b2o16b2o$6b3o4$4b
2o$o2b5o17b2o$b2obobo18b3o$o2b5o17b2o$4b2o!
○ (4n+3, 0)c/(12n+8), n=[4,+Inf)

Code: Select all

x = 18, y = 27, rule = B2cen3aceny4-cknqt5-ckr6cen8/S1e2-e3-aiky4cejknt5cjny6cn
3b2o3bo8bo$3b3ob2o7bo$3b2o3bo8bo6$3b4o10bo$2bo3bo9bo$3b4o10bo6$4o13bo$
2o14bo$4o13bo6$2o15bo$b2o13bo$2o15bo!
○ (4n+4, 0)c/(12n+10), n=[4,+Inf)

Code: Select all

x = 21, y = 67, rule = B2ce3-cijr4aeiz5ijkqr6/S1e2-ek3ejr4jntw5acq6ac78
6b2o7bo2b2o$6b3o6b2ob3o$6b2o7bo2b2o14$6bo8bo2b2o$5bo9b2ob3o$6bo8bo2b2o
14$3bo11bo2b2o$3b3o9b2ob3o$3bo11bo2b2o14$b2o12bo2b2o$b3o11b2ob3o$b2o
12bo2b2o14$bo13bo2b2o$o14b2ob3o$bo13bo2b2o!
○ (4n+4, 0)c/(12n+11), n=[2,+Inf)

Code: Select all

x = 15, y = 19, rule = B2ce3-cijn4acijny5-acjk6in8/S01e2-en3ejqry4jqrtwz5cky6cin
3b2o3bo3b2o$3b3ob2o3b3o$3b2o3bo3b2o6$3b4o5b2o$2bo3bo5b3o$3b4o5b2o6$4o
8b2o$3o9b3o$4o8b2o!

The existing RwSAS was a method of shifting objects from their original place after collision. The idea I came up with is to switch the direction or speed instead of shifting the components from their original position with each collision.
I placed two c2o spaceships both pattern's front and back, then c1o photon between them. After that, I designed it to turn 180 degree for every collision, but I couldn't get any satisfactory results. So, I rewrited the blueprint from start to finish.
the entire design was rewritten to move one or more c1o signals to the side of the expandable tube-shaped c2o spaceship. And then.. I finally got following perfect results.

○ (2b)/(13+4b+4a), a = [0,+Inf), b = [0,+Inf)

Code: Select all

x = 74, y = 39, rule = B2cek3aeqy4-jknrz5eikry6-ei7c/S1e2cik3-iy4ijqrt5-cnry6aen8
9bo31bo27bo$8bo31bo27bo$2b12o22b10o19b9o$35b2o$2b12o22b10o19b9o$10bo
31bo27bo$9bo31bo27bo10$9bo31bo27bo$8bo31bo27bo$b13o21b11o18b10o$34b2o$
b13o21b11o18b10o$9bo31bo27bo$8bo31bo27bo10$9bo31bo27bo$8bo31bo27bo$14o
20b12o17b11o$33b2o$14o20b12o17b11o$8bo31bo27bo$7bo31bo27bo!
○ (2b)/(14+4a+4b), a = [0,+Inf), b = [0,+Inf)

Code: Select all

x = 95, y = 31, rule = B2ce3ajkry4aeiqz5ejkqy6c/S1e2-an3-aikq4ikqty5ejk67e8
11bo27bo27bo23bo$10bo27bo27bo23bo$2b12o18b10o19b9o17b7o$13b2o16b2o8b2o
26b2o15b2o5b2o$2b12o18b10o19b9o17b7o$10bo27bo27bo23bo$9bo27bo27bo23bo
6$11bo27bo27bo23bo$10bo27bo27bo23bo$b13o17b11o18b10o16b8o$13b2o15b2o9b
2o26b2o14b2o6b2o$b13o17b11o18b10o16b8o$9bo27bo27bo23bo$8bo27bo27bo23bo
6$11bo27bo27bo23bo$10bo27bo27bo23bo$14o16b12o17b11o15b9o$13b2o14b2o10b
2o26b2o13b2o7b2o$14o16b12o17b11o15b9o$8bo27bo27bo23bo$7bo27bo27bo23bo!
○ (2b)/(15+4b+4a), a = [0,+Inf), b = [0,+Inf)

Code: Select all

x = 62, y = 31, rule = B2-an3acqry4-nqwz5akqry6an/S1e2ik3cejkr4aeijry5-aeiy6-i
9bo23bo23bo$8bo23bo23bo$2b12o14b10o15b9o$27b2o$2b12o14b10o15b9o$10bo
23bo23bo$9bo23bo23bo6$9bo23bo23bo$8bo23bo23bo$b13o13b11o14b10o$26b2o$b
13o13b11o14b10o$9bo23bo23bo$8bo23bo23bo6$9bo23bo23bo$8bo23bo23bo$14o
12b12o13b11o$25b2o$14o12b12o13b11o$8bo23bo23bo$7bo23bo23bo!
○ (2b)/(16+4b+4a), a = [0,+Inf), b = [0,+Inf)

Code: Select all

x = 72, y = 31, rule = B2cek3aenqy4-eijny5-aknr6a/S1e2-e3-aikn4cijky5acny6ekn7
10bo27bo27bo$9bo27bo27bo$3b12o17b11o19b9o$2b2o10b2o17bo8b2o17b2o7b2o$
3b12o17b11o19b9o$11bo27bo27bo$10bo27bo27bo6$10bo27bo27bo$9bo27bo27bo$
2b13o16b12o18b10o$b2o11b2o16bo9b2o16b2o8b2o$2b13o16b12o18b10o$10bo27bo
27bo$9bo27bo27bo6$10bo27bo27bo$9bo27bo27bo$b14o15b13o17b11o$2o12b2o15b
o10b2o15b2o9b2o$b14o15b13o17b11o$9bo27bo27bo$8bo27bo27bo!

Next time, I'll do a search using something other faster than c2o to make it have more wider speed range.
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

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

Re: Rules with small adjustable spaceships

Post by wildmyron » February 18th, 2021, 9:35 am

silversmith wrote:
January 22nd, 2021, 10:57 am
Here is kind of box ship with adjustable speed and period multiplying capabilities.

Code: Select all

x = 27, y = 26, rule = B2cen3ajn4acty5aiy6cei7e/S2aci3aejy4ant5ikqr6-ci78
26o$26o$26o$26o$10ob15o$12ob14o$10ob16o$27o$27o$21ob5o$23ob3o$21ob5o$
27o$27o$23ob3o$23o2b2o$23ob3o$27o$27o$10ob16o$10o2b15o$10ob16o$27o$
27o$27o$27o!
Fantastic to see some more adjustable spaceships with this kind of design that allows an adjustable step as well as adjustable period. This has (in part) prompted me to finally post the anti-photon in a box spaceship I found last year. In some sense yours is even nicer because it allows any number of internal anti-spaceships whereas mine is limited to an odd number (because they travel at 2c/2 and the bounce reaction is determined by the phase, while in the design above there are two different c/2 anti-spaceships).

I was inspired to try this design by Saka's box spaceships which were posted here and in the ConwayLife Lounge Discord server in the first half of last year. I actually posted the initial search result to the Discord server on 2020-05-18 (and it made a brief appearance here on the forum too). The principle is that a p2 anti-photon in a rectangular region of On cells can be reflected by a boundary, and when it does it creates a wave which either grows or shrinks the rectangle by one cell - which wave is created is determined by antiphoton's parity (which phase the antiphoton is in when it is reflected). The nice thing about the reflection creating a wave is that the width of the spaceship need not be fixed like it is in many of the other similar spaceships, so these spaceships have separately adjustable period and population.

Code: Select all

x = 55, y = 107, rule = B2c3-cikn4-eijn5-akn6ein7c8/S01e2ei3-cen4-iqy5iknqr6ai7c8
3b11o11b9o13b8o$3b11o11b9o12bo2b6o$3b6o2b3o11b4o2b3o13bo4b3o$3b6obob2o
11b4obob2o15bobob2o$3b6ob2obo11b4ob2obo14b2ob2obo$3b6obob2o11b4obob2o
15bobob2o$3b6o2b3o11b4o2b3o13bo4b3o$3b11o11b9o12bo2b6o$3b11o11b9o13b8o
11$3b11o11b9o13b8o$3b11o11b9o12bo2b6o$3b6o2b3o11b4o2b3o13bo4b3o$3b6obo
b2o11b4obob2o15bobob2o$3b6ob2obo11b4ob2obo14b2ob2obo$3b6obob2o11b4obob
2o15bobob2o$3b6o2b3o11b4o2b3o13bo4b3o$3b11o11b9o12bo2b6o$3b11o11b9o13b
8o$3b11o9bob9o13b8o$3b11o10b10o13b8o$bob11o10b10o13b8o$2b12o10b10o13b
8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o
$2b12o10b10o13b8o$2b12o10b10o13b7o$2b12o10b10o13b7o$2b12o10b10o13b7o$
2b12o10b10o13b7o$2b12o10b9o12bob7o$2b12o10b9o13b8o$2b12o10b9o13b8o$2b
12o10b9o13b8o$2b11o11b9o13b8o$2b11o11b9o13b8o$2b11o9bob9o13b8o$2b11o
10b10o13b8o$2b11o10b10o13b8o$2b11o10b10o13b8o$2b11o10b10o13b8o$2b11o
10b10o13b7o$ob11o10b10o13b7o$b12o10b10o13b7o$b12o10b10o13b7o$b12o10b
10o11bob7o$b12o10b10o12b8o11$2b12o10b9o13b8o$2b12o10b9o12bob7o$2b12o
10b10o13b7o$2b12o10b10o13b7o$2b12o10b10o13b7o$2b12o10b10o13b7o$2b12o
10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b12o
10b10o13b8o$2b12o10b10o13b8o$bob11o10b10o13b8o$3b11o10b10o13b8o$3b11o
9bob9o13b8o$3b11o11b9o13b8o$3b11o11b9o12bo2b6o$3b6o2b3o11b4o2b3o13bo4b
3o$3b6obob2o11b4obob2o15bobob2o$3b6ob2obo11b4ob2obo14b2ob2obo$3b6obob
2o11b4obob2o15bobob2o$3b6o2b3o11b4o2b3o13bo4b3o$3b11o11b9o12bo2b6o$3b
11o11b9o13b8o$3b11o9bob9o13b8o$3b11o10b10o13b8o$bob11o10b10o13b8o$2b
12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b8o$2b
12o10b10o13b8o$2b12o10b10o13b8o$2b12o10b10o13b7o$2b12o10b10o13b7o$2b
12o10b10o13b7o$2b12o10b10o13b7o$2b12o10b9o12bob7o$2b12o10b9o13b8o!
Macbi mentioned that the speed of spaceships based on this mechanism could be adjusted by changing the number of antiphotons. Despite expecting it wouldn't work, I got stuck on the idea of having two antiphotons inside the spaceship - and as suspected it didn't work out because of parity restrictions. I went to sleep and during my slumber there was a flurry of activity on the Discord server.

A for Awesome posted the first spaceship with three antiphotos and a subsequent discussion and posting of results (involving AforAmpere, A for Awesome, Blinkerspawn, bubblegum, Macbi, and sarp) found the following range of spaceship speeds:

4n+1/80n+7+4m, n>=0 and m>=0 (except if n=0 then m>=2) and 4n+3/80n+49+4m, n>=0 and m>=0

Code: Select all

x = 186, y = 224, rule = B2c3-cikn4-eijn5-akn6ein7c8/S01e2ei3-cen4-iqy5iknqr6ai7c8
155b11o11b9o$155b11o11b9o$155b6o2b3o11b4o2b3o$155b6obob2o11b4obob2o$
155b6ob2obo11b4ob2obo$155b6obob2o11b4obob2o$155b6o2b3o11b4o2b3o$155b
11o11b9o$155b11o11b9o11$119b27o15b25o$118bob26o15b25o$120b21o2b3o15b
20o2b3o$120b21obob2o14bob19obob2o$120b21ob2obo16b19ob2obo$120b21obob2o
16b19obob2o$120b21o2b3o16b19o2b3o$120b26o16b24o$120b26o16b24o$120b9o2b
15o16b7o2b15o$120b9obob14o16b7obob14o$120b9o4b13o16b7o4b13o$120b9obob
14o16b7obob14o$120b9o2b15o16b7o2b15o$120b26o16b24o$120b26o16b24o$120bo
2b23o16b3o2b19o$121bob23o16b2obob19o$119b2o2b23o16bo4b19o$121bob23o14b
ob2obob19o$120bo2b23o15b4o2b19o$118bob26o15b25o$119b27o15b25o11$80b46o
16b44o$79bob45o16b44o$81b40o2b3o16b39o2b3o$81b40obob2o15bob38obob2o$
81b40ob2obo17b38ob2obo$81b40obob2o17b38obob2o$81b40o2b3o17b38o2b3o$81b
45o17b43o$81b45o17b43o$81b28o2b15o17b26o2b15o$81b28obob14o17b26obob14o
$81b28o4b13o17b26o4b13o$81b28obob14o17b26obob14o$81b28o2b15o17b26o2b
15o$81b45o17b43o$81b45o17b43o$81b16o2b27o17b14o2b27o$81b16obob26o17b
14obob26o$81b16ob2ob25o17b14ob2ob25o$81b16obob26o17b14obob26o$81b16o2b
27o17b14o2b27o$80bob44o17b43o$82b44o17b43o$82b3o2b39o16bobo2b39o$82bo
3bob38o16b2ob2ob38o$82bobo4b37o16bobo4b37o$82bo3bob38o16b2ob2ob38o$82b
3o2b39o16bobo2b39o$82b44o17b43o$80bob44o17b43o$81b8o2b35o17b10o2b31o$
81b7obob35o17b9obob31o$81b6o4b35o17b8o4b31o$81b7obob35o15bob9obob31o$
81b8o2b35o16b11o2b31o$79bob45o16b44o$80b46o16b44o11$40b66o15b65o$40b
66o14bob64o$40b61o2b3o16b59o2b3o$40b61obob2o16b59obob2o$40b61ob2obo16b
59ob2obo$40b61obob2o16b59obob2o$40b61o2b3o16b59o2b3o$40b66o16b64o$40b
66o16b64o$40b49o2b15o16b47o2b15o$40b49obob14o16b47obob14o$40b49o4b13o
16b47o4b13o$40b49obob14o16b47obob14o$40b49o2b15o16b47o2b15o$40b66o16b
64o$40b66o16b64o$40b37o2b27o16b35o2b27o$40b37obob26o16b35obob26o$40b
37ob2ob25o16b35ob2ob25o$39bob36obob26o16b35obob26o$41b36o2b27o16b35o2b
27o$41b65o15bob63o$41b65o17b63o$41b24o2b39o17b22o2b39o$41b24obob38o17b
22obob38o$41b24o4b37o17b22o4b37o$41b24obob38o17b22obob38o$41b24o2b39o
17b22o2b39o$41b65o17b63o$41b65o17b63o$41b12o2b51o17b10o2b51o$41b12obob
50o17b10obob50o$41b12ob2ob49o17b10ob2ob49o$41b12obob50o17b10obob50o$
41b12o2b51o17b10o2b51o$41b65o17b63o$41b65o17b63o$43b63o19b61o$42bob62o
19b61o$40b3o2b61o16b64o$42bob62o19b61o$43b63o19b61o$41b65o17b63o$41b
65o15bob63o$41b12o2b51o16b15o2b47o$39bob11obob51o16b14obob47o$40b11o4b
51o16b13o4b47o$40b12obob51o16b14obob47o$40b13o2b51o16b15o2b47o$40b66o
14bob64o$40b66o15b65o10$b85o16b84o$b85o15bob83o$b80o2b3o17b78o2b3o$b
80obob2o17b78obob2o$b80ob2obo17b78ob2obo$b80obob2o17b78obob2o$b80o2b3o
17b78o2b3o$b85o17b83o$b85o17b83o$b68o2b15o17b66o2b15o$b68obob14o17b66o
bob14o$b68o4b13o17b66o4b13o$b68obob14o17b66obob14o$b68o2b15o17b66o2b
15o$b85o17b83o$b85o17b83o$b56o2b27o17b54o2b27o$b56obob26o17b54obob26o$
b56ob2ob25o17b54ob2ob25o$ob55obob26o17b54obob26o$2b55o2b27o17b54o2b27o
$2b84o16bob82o$2b84o18b82o$2b43o2b39o18b41o2b39o$2b43obob38o18b41obob
38o$2b43o4b37o18b41o4b37o$2b43obob38o18b41obob38o$2b43o2b39o18b41o2b
39o$2b84o18b82o$2b84o18b82o$2b31o2b51o18b29o2b51o$2b31obob50o18b29obob
50o$2b31ob2ob49o18b29ob2ob49o$2b31obob50o18b29obob50o$2b31o2b51o18b29o
2b51o$2b84o18b82o$2b84o18b82o$2b19o2b63o18b17o2b63o$2b19obob62o18b17ob
ob62o$bob18o4b61o18b17o4b61o$3b18obob62o18b17obob62o$3b18o2b63o17bob
16o2b63o$3b83o19b81o$3b83o19b81o$3b6o2b75o19b4o2b75o$3b6obob74o19b4obo
b74o$3b6ob2ob73o19b4ob2ob73o$3b6obob74o19b4obob74o$3b6o2b75o19b4o2b75o
$3b83o19b81o$3b83o19b81o$3b4o2b77o17bob6o2b73o$3b3obob77o18b6obob73o$b
ob2ob2ob77o18b5ob2ob73o$2b4obob77o18b6obob73o$2b5o2b77o18b7o2b73o$2b
84o18b82o$2b84o16bob82o$2b19o2b63o17b22o2b59o$ob18obob63o17b21obob59o$
b18o4b63o17b20o4b59o$b19obob63o17b21obob59o$b20o2b63o17b22o2b59o$b85o
15bob83o$b85o16b84o!
So these spaceships are actually adjustable in three separate (but slightly dependent) ways: the step, the period, and the population.

It seems that the parity constraints prevent construction of oscillators but I don't think this restriction applies to silversmith's design above. However, A for Awesome did post this interesting linear growth spacefiller:

Code: Select all

x = 29, y = 29, rule = B2c3-cikn4-eijn5-akn6ein7c8/S01e2ei3-cen4-iqy5iknqr6ai7c8
29o$5ob23o$4obob22o$3ob3ob15o2b4o$3o5b15obob3o$23o4b2o$23obob3o$23o2b
4o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$3o2b24o$2obob24o
$o4b16o5b3o$2obob16ob3ob3o$3o2b17obob4o$23ob5o$29o$29o!
kiho park wrote:
February 6th, 2021, 4:06 am
Here is some adjustable ships I found before.

<snip>

The existing RwSAS was a method of shifting objects from their original place after collision. The idea I came up with is to switch the direction or speed instead of shifting the components from their original position with each collision.
I placed two c2o spaceships both pattern's front and back, then c1o photon between them. After that, I designed it to turn 180 degree for every collision, but I couldn't get any satisfactory results. So, I rewrited the blueprint from start to finish.
the entire design was rewritten to move one or more c1o signals to the side of the expandable tube-shaped c2o spaceship. And then.. I finally got following perfect results.

○ (2b)/(13+4b+4a), a = [0,+Inf), b = [0,+Inf)

Code: Select all

x = 74, y = 39, rule = B2cek3aeqy4-jknrz5eikry6-ei7c/S1e2cik3-iy4ijqrt5-cnry6aen8
9bo31bo27bo$8bo31bo27bo$2b12o22b10o19b9o$35b2o$2b12o22b10o19b9o$10bo
31bo27bo$9bo31bo27bo10$9bo31bo27bo$8bo31bo27bo$b13o21b11o18b10o$34b2o$
b13o21b11o18b10o$9bo31bo27bo$8bo31bo27bo10$9bo31bo27bo$8bo31bo27bo$14o
20b12o17b11o$33b2o$14o20b12o17b11o$8bo31bo27bo$7bo31bo27bo!
<snip>

Next time, I'll do a search using something other faster than c2o to make it have more wider speed range.
That is a beautiful design. I look forward to seeing your further results.
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: 1518
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Rules with small adjustable spaceships

Post by wildmyron » February 19th, 2021, 12:16 am

silversmith wrote:
January 22nd, 2021, 10:57 am
Here is kind of box ship with adjustable speed and period multiplying capabilities.

Code: Select all

x = 27, y = 26, rule = B2cen3ajn4acty5aiy6cei7e/S2aci3aejy4ant5ikqr6-ci78
26o$26o$26o$26o$10ob15o$12ob14o$10ob16o$27o$27o$21ob5o$23ob3o$21ob5o$
27o$27o$23ob3o$23o2b2o$23ob3o$27o$27o$10ob16o$10o2b15o$10ob16o$27o$
27o$27o$27o!
wildmyron wrote:
February 18th, 2021, 9:35 am
<snip p2 antiphoton in a box spaceships>

It seems that the parity constraints prevent construction of oscillators but I don't think this restriction applies to silversmith's design above.
For the record - adjustable oscillators in silversmith's rule:

p(4n+1), n>9

Code: Select all

x = 51, y = 16, rule = B2cen3ajn4acty5aiy6cei7e/S2aci3aejy4ant5ikqr6-ci78
9o10b10o11b11o$9o10b10o11b11o$9o10b10o11b11o$9o10b10o11b11o$3ob5o10b3o
b6o11b4ob6o$5ob3o10b5ob4o11b6ob4o$3ob5o10b3ob6o11b4ob6o$9o10b10o11b11o
$9o10b10o11b11o$5ob3o10b6ob3o11b6ob4o$3ob5o10b4ob5o11b4ob6o$5ob3o10b6o
b3o11b6ob4o$9o10b10o11b11o$9o10b10o11b11o$9o10b10o11b11o$9o10b10o11b
11o!
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.

User avatar
wwei47
Posts: 417
Joined: February 18th, 2021, 11:18 am

Re: Rules with small adjustable spaceships

Post by wwei47 » March 4th, 2021, 7:48 pm

And to think that this wasn't even actually searched for. c/(41+9n):
Moosey wrote:
March 4th, 2021, 6:21 pm
the c/41d and c/50d are part of an infinite family (first five members below)

Code: Select all

x = 187, y = 33, rule = B2cei3-i4z5-a6-a78/S1c2ik3y4q5-a678
165b2o7b2o8b2o$164bo2bob8ob6o2bo$164bob19obo$123b2o8b2o30b21o$118b8ob
6o2bo30b20o$117b17obo29b21o$72bo3b2o8b2o29b18o30b21o$73b6ob6o2bo28b18o
30b21o$73b14obo28b18o30b21o$35b2o8b2o26b15o29b18o30b20o$34bo2bob6o2bo
24b16o28b19o29b22o$34bob10obo24b16o28b19o29b23o$8b2o25b12o26b15o29b17o
31b22o$2b6o2bo25b11o27b14o30b17o31b20o$b8obo24b12o26b15o29b19o29b21o$b
9o25b12o26b14o30b19o29b21o$b9o25b12o26b15o29b18o30b21o$b9o25b12o26b16o
28b18o30b21o$b9o25b11o27b16o28b18o30b20o$b9o25b12o26b15o29b18o30b21o$
10o24b12obo24b16o28b19o29b21obo$b8o26b8obo2bo25b8ob6o29b8ob8o31b8ob8ob
o2bo$obo31bobo8b2o25bobo8b2o3bo27bobo8b2o35bobo8b2o7b2o8$2b3o3bobobob
2o2b2o14b3o3bo2b2ob3ob2o20b3o3bo2b2ob2ob2o27b3o3bobo2b2o2b2o33b3o3bob
3ob3ob2o$2bo4bo2b3o2bo2bobo13bo4bo3bo2bobobobo19bo4bo3bo2b2obobo26bo4b
o2b2ob3obobo32bo4bo4bo3bobobo$2b3obo5bob3ob2o14b3obo3b2o2b3ob2o20b3obo
3b2o3bob2o27b3obo3b2o2b2ob2o33b3obo5bo3bob2o!

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

kiho park
Posts: 65
Joined: September 24th, 2010, 12:16 am

Re: Rules with small adjustable spaceships

Post by kiho park » March 13th, 2021, 9:52 am

Here is some adjustable spaceships by modifying recent discovery.

○ 4n+2/16n+18, n>=1

Code: Select all

x = 13, y = 43, rule = B2ce3ajkry4aeiqz5ejkqy6c/S1e2-an3-aikq4ikqty5ejk67e8
9bo$10bo$b12o$2o9b2o$b12o4$9bo$10bo$2b11o$11b2o$2b11o4$9bo$10bo$4b9o$
3b2o6b2o$4b9o4$9bo$10bo$5b8o$11b2o$5b8o4$9bo$10bo$7b6o$6b2o3b2o$7b6o5$
12bo$12bo!
○ 4n+2/16n+22, n>=1

Code: Select all

x = 10, y = 30, rule = B2cen3-cikn4-cknyz5-ainr6ck8/S1e2-a3cejry4ceijyz5enr6ack7
6bo$7bo$b9o$2o6b2o$b9o4$6bo$7bo$2b8o$8b2o$2b8o4$6bo$7bo$4b6o$3b2o3b2o$
4b6o8$9bo$9bo!
○ 4n+2/16n+26, n>=4

Code: Select all

x = 12, y = 29, rule = B2cin3aceky4aiknqrt5-aijn6ce8/S12ik3aejnr4acijrwy5-einy6ck7c8
9bo$9b2o$b9o$2o9bo$b10o4$9bo$9b2o$2b8o$11bo$2b9o4$9bo$9b2o$4b6o$3b2o6b
o$4b7o7$11bo$11bo!


○ 4n+3/16n+17, n>=2

Code: Select all

x = 11, y = 29, rule = B2-ai3ae4-ejntz5-aknr6ac/S01e2-e3-aikn4cijkty5ackny6cn7e
8bo$9bo$b8o$2o8bo$b9o4$8bo$9bo$2b7o$3bo6bo$2b8o4$8bo$9bo$4b5o$3b2o5bo$
4b6o7$10bo$10bo!
○ 4n+3/16n+21, n>=0

Code: Select all

x = 13, y = 45, rule = B2ce3acq4-eknr5eikry6e/S1e2ikn3ejknr4ceijknr5-jnry6-i78
9bo$9b2o$10o$10bobo$11o4$9bo$9b2o$2b8o$b2o7bobo$2b9o4$9bo$9b2o$3b7o$
10bobo$3b8o4$9bo$9b2o$5b5o$4b2o4bobo$5b6o4$9bo$9b2o$6b4o$10bobo$6b5o7$
12bo$12bo!
○ 4n+3/16n+25, n>=2

Code: Select all

x = 14, y = 65, rule = B2-an3aekny4-knry5ajqr7c/S1e2eik3ejkqr4cijky5acijk6-in7c
10bo$11bo$11o$13bo$12o8$10bo$11bo$2b9o$b2o10bo$2b10o8$10bo$11bo$3b8o$
13bo$3b9o8$10bo$11bo$5b6o$4b2o7bo$5b7o8$10bo$11bo$6b5o$13bo$6b6o11$13b
o$13bo!
○ 4n+3/16n+29, n>=1

Code: Select all

x = 12, y = 33, rule = B2-an3acqry4-nqwz5akqry6an/S1e2ik3cejkr4aeijry5-aeiy6-i
7bo$8bo$10o$10b2o$10o4$7bo$8bo$2b8o$b2o7b2o$2b8o4$7bo$8bo$3b7o$10b2o$
3b7o4$7bo$8bo$5b5o$4b2o4b2o$5b5o3$11bo$11bo!


○ 4n/16n+4, n>=3

Code: Select all

x = 11, y = 29, rule = B2cek3aenqy4-eijny5-aknr6a/S1e2-e3-aikn4cijky5acny6ekn7
8bo$9bo$b8o$2o8bo$b9o4$8bo$9bo$2b7o$3bo6bo$2b8o4$8bo$9bo$4b5o$3b2o5bo$
4b6o7$10bo$10bo!
○ 4n/16n+8, n>=3

Code: Select all

x = 11, y = 29, rule = B2-ai3-ijkn4-nqr5cjry6ack7c/S1e2in3-ai4eijtwy5ainq6aek7c
7bo$8bo$8o$10bo$9o4$7bo$8bo$2b6o$b2o7bo$2b7o4$7bo$8bo$3b5o$10bo$3b6o7$
10bo$10bo!
○ 4n/16n+12, n>=3

Code: Select all

x = 15, y = 43, rule = B2ck3ar4-cj5-akq6-in7c8/S012eik3acjry4-ceitz5-ceny6-in8
10bo$10b2o$13o$14bo$13o4$10bo$10b2o$2b11o$b2o11bo$2b11o4$10bo$10b2o$3b
10o$14bo$3b10o4$10bo$10b2o$5b8o$4b2o8bo$5b8o4$10bo$10b2o$6b7o$14bo$6b
7o5$14bo$14bo!
○ 4n/16n+16, n>=2

Code: Select all

x = 12, y = 37, rule = B2cei3acek4-en5eijr6-ci/S02-cn3ejqr4-ntyz5-ack7e
8bo$9bo$b11o$2o$b11o4$8bo$9bo$2b10o$3bo$2b10o4$8bo$9bo$4b8o$3b2o$4b8o
4$8bo$9bo$5b7o$6bo$5b7o7$11bo$11bo!


○ 4n+1/16n+11, n>=1

Code: Select all

x = 13, y = 45, rule = B2cek3aeqy4-jknrz5eikry6-ei7c/S1e2cik3-iy4ijqrt5-cnry6aen8
9bo$10bo$b9o$2o9b2o$b10o4$9bo$10bo$2b8o$11b2o$2b9o4$9bo$10bo$4b6o$3b2o
6b2o$4b7o4$9bo$10bo$5b5o$11b2o$5b6o4$9bo$10bo$7b3o$6b2o3b2o$7b4o7$12bo
$12bo!
○ 4n+1/16n+15, n>=2

Code: Select all

x = 10, y = 29, rule = B2-ak3ejknq4acirtz5cjy6ae7c/S01e2-ce3acekr4eirwy5aciqr6cn78
6bo$7bo$10o$bo$10o4$6bo$7bo$2b8o$bo$2b8o4$6bo$7bo$3b7o$4bo$3b7o7$9bo$
9bo!
○ 4n+1/16n+19, n>=4

Code: Select all

x = 13, y = 29, rule = B2cei3-ijn4-knw5cry6-ei7c8/S1e2ik3ejnr4aikrwy5ijkq6cin8
9bo$10bo$b9o$2o9b2o$b10o4$9bo$10bo$2b8o$11b2o$2b9o4$9bo$10bo$4b6o$3b2o
6b2o$4b7o7$12bo$12bo!
○ 4n+1/16n+23, n>=2

Code: Select all

x = 11, y = 29, rule = B2ce3aekry4aceijtw5kqry6aen8/S1e2ikn3-ciqy4-ntz5cjkq6-an7c8
9bo$9bo$b7ob2o$2o7bo$b8o4$9bo$9bo$2b6ob2o$9bo$2b7o4$9bo$9bo$4b4ob2o$3b
2o4bo$4b5o7$10bo$10bo!

Edit : Ignore monominos and dominos.
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 417
Joined: February 18th, 2021, 11:18 am

Re: Rules with small adjustable spaceships

Post by wwei47 » March 13th, 2021, 10:16 am

kiho park wrote:
March 13th, 2021, 9:52 am
○ 4n/16n+4, n>=3

Code: Select all

x = 11, y = 29, rule = B2cek3aenqy4-eijny5-aknr6a/S1e2-e3-aikn4cijky5acny6ekn7
8bo$9bo$b8o$2o8bo$b9o4$8bo$9bo$2b7o$3bo6bo$2b8o4$8bo$9bo$4b5o$3b2o5bo$
4b6o7$10bo$10bo!
One of those explodes. Also, why not just say 17/4?

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
Macbi
Posts: 808
Joined: March 29th, 2009, 4:58 am

Re: Rules with small adjustable spaceships

Post by Macbi » March 13th, 2021, 10:20 am

wwei47 wrote:
March 13th, 2021, 10:16 am
kiho park wrote:
March 13th, 2021, 9:52 am
○ 4n/16n+4, n>=3

Code: Select all

x = 11, y = 29, rule = B2cek3aenqy4-eijny5-aknr6a/S1e2-e3-aikn4cijky5acny6ekn7
8bo$9bo$b8o$2o8bo$b9o4$8bo$9bo$2b7o$3bo6bo$2b8o4$8bo$9bo$4b5o$3b2o5bo$
4b6o7$10bo$10bo!
One of those explodes. Also, why not just say 17/4?
I think it's 4n/(16n+4).

User avatar
wwei47
Posts: 417
Joined: February 18th, 2021, 11:18 am

Re: Rules with small adjustable spaceships

Post by wwei47 » March 13th, 2021, 10:21 am

Macbi wrote:
March 13th, 2021, 10:20 am
I think it's 4n/(16n+4).
But they said 4n/16n+4, which simplifies to 17/4.
EDIT: I will retract my statement about some of the ships exploding. That's due to the ships hitting each other with sparks.

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
bubblegum
Posts: 860
Joined: August 25th, 2019, 11:59 pm
Location: click here to do nothing

Re: Rules with small adjustable spaceships

Post by bubblegum » March 13th, 2021, 1:51 pm

wwei47 wrote:
March 13th, 2021, 10:21 am
But they said 4n/16n+4, which simplifies to 17/4.
That's not how these formulae work (clearly, none of the ships move at 17c/4). Nobody applies maths to speeds. The correct simplification is 4n/4(4n+1) == n/4n+1 times c, and we don't like simplifying speeds around here.
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
sonata wrote:
July 2nd, 2020, 8:33 pm
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wwei47
Posts: 417
Joined: February 18th, 2021, 11:18 am

Re: Rules with small adjustable spaceships

Post by wwei47 » March 13th, 2021, 1:53 pm

bubblegum wrote:
March 13th, 2021, 1:51 pm
we don't like simplifying speeds around here.
I was simplifying it to show that it was "faster" than c.
bubblegum wrote:
March 13th, 2021, 1:51 pm
The correct simplification is 4n/4(4n+1) == n/4n+1 times c
But order of operations though...

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
bubblegum
Posts: 860
Joined: August 25th, 2019, 11:59 pm
Location: click here to do nothing

Re: Rules with small adjustable spaceships

Post by bubblegum » March 13th, 2021, 1:59 pm

wwei47 wrote:
March 13th, 2021, 1:53 pm
bubblegum wrote:
March 13th, 2021, 1:51 pm
we don't like simplifying speeds around here.
I was simplifying it to show that it was "faster" than c.
bubblegum wrote:
March 13th, 2021, 1:51 pm
The correct simplification is 4n/4(4n+1) == n/4n+1 times c
But order of operations though...
None of them are faster than c. (None of them are the same speed either.) A speed is a fraction, with everything on the left as the numerator and everything on the right as the denominator.
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
sonata wrote:
July 2nd, 2020, 8:33 pm
conwaylife signatures are amazing[citation needed]
anything

User avatar
wwei47
Posts: 417
Joined: February 18th, 2021, 11:18 am

Re: Rules with small adjustable spaceships

Post by wwei47 » March 13th, 2021, 2:01 pm

bubblegum wrote:
March 13th, 2021, 1:59 pm
A speed is a fraction, with everything on the left as the numerator and everything on the right as the denominator.
But you still need the parenthesis so that it complies with PEMDAS. (Can we take this to a different thread?)

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
bubblegum
Posts: 860
Joined: August 25th, 2019, 11:59 pm
Location: click here to do nothing

Re: Rules with small adjustable spaceships

Post by bubblegum » March 13th, 2021, 2:25 pm

wwei47 wrote:
March 13th, 2021, 2:01 pm
But you still need the parenthesis so that it complies with PEMDAS. (Can we take this to a different thread?)
You don't (unless you happen to write fractions like that, in which case what), it's just a convention, and let's go to Discord actually.
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
sonata wrote:
July 2nd, 2020, 8:33 pm
conwaylife signatures are amazing[citation needed]
anything

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