## Smallest Spaceships Supporting Specific Speeds (5s) Project

For discussion of other cellular automata.
drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Smallest Spaceships Supporting Specific Speeds (5s) Project

Hello all, I have started a project that I think will attract a collaborative effort to find small spaceships of every speed across the vast isotropic rulespace. Here are some rules(? I don't know what to call them.)

1. Spaceships will be optimised by minimum population.
2. Speeds will be expressed unsimplified. (2c/6 is different than c/3)
3. Every ship will be oriented going to the east (orthogonal), southeast (diagonal), or in a position in which it lunges farthest to the right (knightships). No further optimization will be made for the orientation of asymmetric spaceships. Rule optimization will just be non-standard, for smaller spaceships I will try and shorten the rulestring, but for bigger ones I will leave the rulestring as-is in order to encourage further exploration in that rule.
4. Trivial flotillae don't count.

The format is currently: o#c#, d#c#, k#_#c# (with the largest number first in the case of knightships)

Maximum period is set to 1000 so far. Here's a link to the post with the current list of spaceships documented.
Last edited by drc on July 23rd, 2017, 5:50 am, edited 3 times in total.
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

toroidalet
Posts: 1024
Joined: August 7th, 2016, 1:48 pm
Location: my computer
Contact:

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

I'd recommend putting spaceships of simple speeds as well.
This 16c/44 has a smaller bounding box but same population.

Code: Select all

x = 24, y = 5, rule = B3-cky6ci/S23-ce4n7e
16b2o3bo$b2o12b5o2bo$o2bo10bo4bob3o$b2o12b5o2bo$16b2o3bo!

Here's a ridiculously large 12c/31

Code: Select all

x = 184, y = 63, rule = B35ce/S234t6c
129b2o$129bobo$131bo11b2o10b2o$92b2o35bobo11b2o11bo$89bo3bo35b2o10b2o
10bo$88bo4bo10b2o10b2o23b2o10b2o$88bo2b2o11b2o10b2o$92b2o37bo$92b2o36b
3o35b2o$89b3o11b3o8b2o13bo3bo34bo$85b2o15bo3bo23b2o2bo33bo2bo$84bo2bo 13bo5bo23b3o35b2o$84bo16b2o3b2o33b3o$90b3o8bobobobo32b2o2bo2bo$58b2ob
2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b 2ob3o3bo2bo30b4o$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bob
o$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$33bobo9bobo4b2o5b
ob2o21bo16b2o3b2o33b3o$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$16b
o2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$bo13b6o68b3o11b3o8b2o13bo3bo 34bo$obo11bobob2o72b2o36b3o35b2o$14bobobo12b2o35b2o22b2o37bo$3o12b3o
11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$bo14bo12bo36bo21bo4bo10b2o10b2o23b 2o10b2o$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$30bo3bo32bo3bo20b2o35bobo 11b2o11bo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$5bo8bo2bo24bobo34bob o47bobo$4b2o9b3o23bo5bobo28bo5bobo42b2o$41b2obobob2o28b2obobob2o$4b2o
9b3o23bo5bobo28bo5bobo42b2o$5bo8bo2bo24bobo34bobo47bobo$4bo9b2o15b3o9b
2o23b3o9b2o49bo11b2o10b2o$30bo3bo32bo3bo20b2o35bobo11b2o11bo$29bo5bo
30bo5bo16bo3bo35b2o10b2o10bo$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$14bobobo12b2o35b2o22b2o37bo$obo11bobob2o72b2o36b3o35b2o$bo13b6o68b3o11b3o8b2o13bo3bo34bo$16bo2b3o
31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$20b2o12bo11bo5bo5bo25bo2bo13bo5bo 23b3o35b2o$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$33bo2bo8bo2bo3b2ob 4o2bobo26b3o8bobobobo32b2o2bo2bo$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bo
b2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$
58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$90b3o8bobobobo32b2o2bo2bo$
84bo16b2o3b2o33b3o$84bo2bo13bo5bo23b3o35b2o$85b2o15bo3bo23b2o2bo33bo2b
o$89b3o11b3o8b2o13bo3bo34bo$92b2o36b3o35b2o$92b2o37bo$88bo2b2o11b2o10b
2o$88bo4bo10b2o10b2o23b2o10b2o$89bo3bo35b2o10b2o10bo$92b2o35bobo11b2o 11bo$131bo11b2o10b2o$129bobo$129b2o!

I optimized for bounding box, so a longer one might have a smaller minimum population.
7c/48 diagonal:

Code: Select all

x = 4, y = 4, rule = B3-cky8/S234n
bo$2b2o$obo$2o!  10c/27 Code: Select all x = 24, y = 27, rule = B3-cky8/S234n 2bo$2o2$12b2o$11bo2bo$12bobo$13bo3$18b3o$17bo3bo$17b2o3bo$23bo$20bo2bo$23bo$17b2o3bo$17bo3bo$18b3o3$13bo$12bobo$11bo2bo$12b2o2$2o$2bo!  c/5 diagonal Code: Select all x = 4, y = 4, rule = B3-cky4k/S23-c4cn b2o$o2bo$2bo$2o!

11c/37

Code: Select all

x = 35, y = 8, rule = B34n5y/S2-k34a
b3o16b3o$o2bo8b2o7b2o9bo$bo10b2o8b4obo4b2o$b3obo16bo2bo7b2o$b3obo16bo
2bo7b2o$bo10b2o8b4obo4b2o$o2bo8b2o7b2o9bo$b3o16b3o!  I guess it's too much work to search Catagolue as well as the forums. c/6 diagonal Code: Select all x = 3, y = 2, rule = B2-a/S12 2bo$2o!

4c/12

Code: Select all

x = 4, y = 4, rule = B2i3-y6ci/S23-e4t
2b2o$o2bo$o2bo$obo!  c/30 diagonal Code: Select all x = 4, y = 4, rule = B38/S234wz b2o$o2bo$o2bo$bobo!

4c/14 diagonal

Code: Select all

x = 15, y = 15, rule = B38/S234wz
2o$2obo$5bo$bo$4bo$2bo3$8b3o$8bo2bo$8bobo3bo$9bo4bo$14bo$13bo$10b3o!

8c/183

Code: Select all

x = 29, y = 5, rule = B2ei3aeiqr4-aiktz5aiqy6ac7c8/S12cin3i4cikwy5-ajr6ain7e
26bo$4bo13bobo5bo$2ob3o11bo2bo4b4o$4bo13bobo5bo$26bo!

2c/14 diagonal

Code: Select all

x = 3, y = 3, rule = B34n5y/S2-k34a
bo$2o$b2o!

8c/128 diagonal

Code: Select all

x = 4, y = 4, rule = B36in/S234cw
3o$3bo$o2bo$b2o!  More coming soon! EDIT: 9c/56 diagonal Code: Select all x = 18, y = 14, rule = B2n3-ej4e6e/S234i 13b2o$13b2o2$7bo$2b2o3bo$2b2obobo5b2o$4bo8bob2o$2b2o$16b2o$16bo$17bo$2obo$o2bo6b2o$b3o6b2o!  3c/10 Code: Select all x = 4, y = 5, rule = B3-y4e6ci/S2-i3-ce b3o$3bo$2b2o$2o$o!  EDIT2: The 2c/8 is in a suboptimal phase. Code: Select all x = 3, y = 4, rule = B2-a3-i/S1e3 bo$2bo2$obo!  2c/6 diagonal Code: Select all x = 6, y = 7, rule = B3-j/S0234-r o$b2o$b2o$bobo$2bo2bo$5bo$3b3o!  9c/18 Code: Select all x = 7, y = 8, rule = B2-ai3-in4w/S1c2aei3-aj o4bo$6bo$o4bo$bo$bo$o4bo$6bo$o4bo!

4c/10

Code: Select all

x = 5, y = 5, rule = B3-q4n/S23-c
2b2o$bob2o$o2bo$obo$bo!

18c/156

Code: Select all

x = 18, y = 19, rule = B3-cky8/S23-c4n
3b3o2$4b2o$4b2o$3bo2bo$4b2o5$o$b2o3$16b2o$15b2o$12bobo$12b3o$13bo!  c/3 diagonal Code: Select all x = 3, y = 3, rule = B2-ai3-in4w/S1c2aei3-aj 2bo$bo$obo!  4c/8 Code: Select all x = 7, y = 5, rule = B3-cqy6i/S23-aeky4ai5i 3b2o$o4bo$o4b2o$o4bo$3b2o!  2c/16 Code: Select all x = 4, y = 3, rule = B3-j4nwz5c7/S1c2-ik34i5ac bobo$o2bo$bobo!  EDIT3: 16c/52 Code: Select all x = 26, y = 15, rule = B3-y6-a/S23-e 3bo$2bobo$bo2bo$o2bo9bobo$bobo7b3obo$5b2o4b4o6bo2bo$5b2o4bo9bo3bo$4bo
15bobo2bo$5b2o4bo9bo3bo$5b2o4b4o6bo2bo$bobo7b3obo$o2bo9bobo$bo2bo$2bob
o$3bo!  8c/22 Code: Select all x = 15, y = 11, rule = B3-cky6ci/S23-ce4n7e8 12bo$7bobobobo$7bo2bo3bo$7bobobobo$12bo$3o$12bo$7bobobobo$7bo2bo3bo$7b
obobobo$12bo!  8c/16 Code: Select all x = 6, y = 16, rule = B3-j/S234i 2b3o$obo2bo$o4bo$2ob3o$2bo7$2bo$2ob3o$o4bo$obo2bo$2b3o!

c/25 diagonal

Code: Select all

x = 6, y = 6, rule = B2-a3-ik4-aik/S23
3bo$4b2o$4b2o$o2bo$b2o$b2o!  17c/34 Code: Select all x = 14, y = 7, rule = B2e3-a4/S23-a4-a7e 9bo$8b3obo$b2o5b2o3bo$2obo4b2o3bo$b2o5b2o3bo$8b3obo$9bo!  14c/28 Code: Select all x = 5, y = 13, rule = B34et/S23-a4eit6 bo$2bo$3b2o$2o2bo$bo2bo$2b2o2$2b2o$bo2bo$2o2bo$3b2o$2bo$bo!

EDIT4:
6c/12

Code: Select all

x = 6, y = 7, rule = B2ce3-a/S2
o$bo$bo3bo$bob3o$bo3bo$bo$o!

10c/36

Code: Select all

x = 38, y = 19, rule = B3/S2-k34k6c
12b2o$12b2o$7b2o$9bo7bo10bo8bo$6bo2bo7bo10b2o6b2o$9bo7bo10bo8bo$o6b2o$o$o2$o$o$o6b2o$9bo7bo10bo8bo$6bo2bo7bo10b2o6b2o$9bo7bo10bo8bo$7b2o$12b
2o$12b2o!  20c/72 Code: Select all x = 44, y = 13, rule = B3/S2-k34k6c 34bo8bo$34b2o6b2o$34bo8bo2$18bo$18b2o$14bo25bobo$13b2o20bo4bobo$13b2o
7b3o8b2o8bo$2o11b2o20bo4bobo$2o12bo25bobo$18b2o$18bo!

4c/11

Code: Select all

x = 9, y = 13, rule = B34t6k/S2-i35a
2bo$bobo$o$o4bo$b2o3bo$5bobo$8bo$5bobo$b2o3bo$o4bo$o$bobo$2bo!

16c/92 diagonal

Code: Select all

x = 7, y = 4, rule = B34i5eiy/S234qy
4bo$2bobo$2o3bo$4b3o!  18c/72 Code: Select all x = 46, y = 30, rule = B356/S23 21b3ob3o2$2bo$bobo$o3bo11bo23b2o$o3bo10bo2bo21bob2o$bobo10bo3bo22bo2bo
$2bo12b2obo14bo11bo$16bo14b4o6bo3bo$31bob3o7bo$31bo2b2o$32bobo$33bo5$33bo$32bobo$31bo2b2o$31bob3o7bo$16bo14b4o6bo3bo$2bo12b2obo14bo11bo$bob o10bo3bo22bo2bo$o3bo10bo2bo21bob2o$o3bo11bo23b2o$bobo$2bo2$21b3ob3o!

11c/22

Code: Select all

x = 25, y = 15, rule = B3-ky/S23-aiy4anq6n
bo2bo$5o14b3o$o4bo13b2ob2o$2o3bobo13bo2bo$2bo5bo15bo$5b2o17bo$22b3o2$22b3o$5b2o17bo$2bo5bo15bo$2o3bobo13bo2bo$o4bo13b2ob2o$5o14b3o$bo2bo!  18c/87, optimized for bounding box like the 12c/31 Code: Select all x = 37, y = 20, rule = B2i3-ck/S02-i3-ck 33b2o$33b2o$21bobo11bo$21bo2bo8b2o$33b2o$22b2o$11bobo7bo5b2o$2bo9b2o
13b2o$2bo10bo8bo$2bo9b2o$o2bo7bobo$obo$bo5b2o20b2o$7b2o20b2o$2bo20b2o$
23bobo9bo$23b3o9b2o$23bobo10bo$35b2o$35bo!

9c/50 diagonal

Code: Select all

x = 23, y = 19, rule = B34-iqr7c/S23-a4i
14bo$14bo$14bo3$b2o$o2bo$4bo11b2o$bo2bo10b2o4bo$2bobo10bo6bo$2b2o11b2o
5bo$15bo6bo$15b2o4bo$16b2o3$7bo$7bo$7bo!

(3,4)c/20

Code: Select all

x = 10, y = 8, rule = B3/S234w7c
b3o3bo$2obo$2b2o$5bo$8b2o$9bo$7b2o$7bo!  EDIT5: Ships from the oblique ships thread (plus the previous one) (5,16)c/74 Code: Select all x = 5, y = 4, rule = B3/S23-e4e 2b2o$bob2o$o$2o!

(5,2)c/190

Code: Select all

x = 22, y = 39, rule = B38/S23
bo$obo$b2o7$18bo$17b2o2$18bo$16b2o4$20b2o$20b2o11$9bo$8b2o2$9bo$7b2o4$11b2o$11b2o!

(2,6)c/21

Code: Select all

x = 16, y = 19, rule = B37/S2-i34q
7b5o$6b2o2b2o$6bo2bo2b3o$6b2ob2ob2obo$6b2o2bo4bo$13b2o$11bobo$10bo5$3b
3o$bo2bo$2bo5b2o$obo3bo3bob2o$obo9bobo$bo5b3obobo$12bo!

(3,1)c/13

Code: Select all

x = 4, y = 5, rule = B2-ak3/S25ai
b3o$2b2o$3bo$obo$b2o!

(7,8)c/168

Code: Select all

x = 7, y = 4, rule = B013568/S01
2obobo$2bo2b2o$2bo$4b2o!  (5,7)c/330 Code: Select all x = 6, y = 11, rule = B015/S14 o$o7$4b2o$4b2o$3bo!  (3,2)c/23 Code: Select all x = 5, y = 6, rule = B345/S126 o2$3bo$obobo$obo$ob3o!  (2,3)c/10 Code: Select all x = 5, y = 3, rule = B2en3/S25678 o2bo$bo2bo$3bo!  (2,29)c/89 Code: Select all x = 126, y = 58, rule = B3-k4c/S23 45b2o27bo$41bo3b2o27bo$41bo32bo$41bo$70b3o3b3o$2bobo$3ob2o68bo$2bo2b2o
43bobo21bo$2b2obo44bo2bob2o17bo$3bobo46b2o2b2o$52b2obo$43bo31b2o$43bo 6b2o23b2o$43bo5b3o$50b2o25bo25b3o$39b3o3b3o8b2o18b3o23bo$75b2ob2o22bo 2bo$43bo30bo25b2ob2o3b3o$43bo55bo2bo5b2obo$43bo55bo2bo3bo4bo$101bobo2b 2o3bo$74bobo25b3ob2o2bo$74b3o28bo3b2o7b2o$74b3o27bo4b2o7b2o$100b2o3b2o 2b2o11b2o$100b2o4bo15bobo$123b3o$81bo41b2o$80bobo$38b2o40bobo$38b2o41b o$67b2o19bo13b2o$67b2o8b2o10b2o11bobo$77b2o9b2o14bo$102b3o$101bo$101bo 5bo$108bo$106b3o7$101bo$100bobo$100b2o3bo$105b2o$92bo4bo4bo$91bo9bo5bo 5bo$92bo14bo4b5o$94b2obobo3b3obo3bo5bo$94b2o5bobo6b3o2bob2o$100bo10b2o 2bobo$97b2o13bo$113b3o$114bo!

(1,4)c/25

Code: Select all

x = 6, y = 3, rule = B2e3/S2a36
o$bo2bo$3b3o!

(2,15)c/35

Code: Select all

x = 51, y = 25, rule = B3aijnq5ce/S23-y4ik5j
5bobo11b2o$18bo2bo$6bo12b2o13b2o$23b2o8bo2bo$23b2o9b2o$38b2o$6bo31b2o
5b2o$45bob2o$5bo39bobobo$17b2o30b2o$17bobo25b2ob2o$2bo16bo10bo12b2o3bo$4bo11bob2o23b5o$2ob2o11b2o27bo2$bo28bo$bobo3bo21b3o$2bo3bo21b2obob2o$3b2o26bo2bo7b2o$2bo2bo26b3o7bobo$2bo2bo6bo31b2o$2b3o7b3o26bob2o$14bo 26b3o$2o10b3o$2o!  (1,11)c/30 Code: Select all x = 15, y = 7, rule = B3/S23-c4w7 12bo$11bobo$b2o8bo2bo$2o12bo$o2bo8b3o$o2bo$bobo!  (1,6)c/21 Code: Select all x = 5, y = 3, rule = B367/S023-a4i5i o2b2o$b3o$2bo!  "Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life." -Terry Pratchett drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Just updated, 45 new, 8 improved This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y AbhpzTa Posts: 475 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project toroidalet wrote:Here's a ridiculously large 12c/31 Code: Select all x = 184, y = 63, rule = B35ce/S234t6c 129b2o$129bobo$131bo11b2o10b2o$92b2o35bobo11b2o11bo$89bo3bo35b2o10b2o 10bo$88bo4bo10b2o10b2o23b2o10b2o$88bo2b2o11b2o10b2o$92b2o37bo$92b2o36b 3o35b2o$89b3o11b3o8b2o13bo3bo34bo$85b2o15bo3bo23b2o2bo33bo2bo$84bo2bo
13bo5bo23b3o35b2o$84bo16b2o3b2o33b3o$90b3o8bobobobo32b2o2bo2bo$58b2ob 2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b
2ob3o3bo2bo30b4o$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bob o$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$33bobo9bobo4b2o5b ob2o21bo16b2o3b2o33b3o$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$16b o2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$bo13b6o68b3o11b3o8b2o13bo3bo
34bo$obo11bobob2o72b2o36b3o35b2o$14bobobo12b2o35b2o22b2o37bo$3o12b3o 11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$bo14bo12bo36bo21bo4bo10b2o10b2o23b
2o10b2o$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$30bo3bo32bo3bo20b2o35bobo
11b2o11bo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$5bo8bo2bo24bobo34bob
o47bobo$4b2o9b3o23bo5bobo28bo5bobo42b2o$41b2obobob2o28b2obobob2o$4b2o 9b3o23bo5bobo28bo5bobo42b2o$5bo8bo2bo24bobo34bobo47bobo$4bo9b2o15b3o9b 2o23b3o9b2o49bo11b2o10b2o$30bo3bo32bo3bo20b2o35bobo11b2o11bo$29bo5bo 30bo5bo16bo3bo35b2o10b2o10bo$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o
$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$14bobobo12b2o35b2o22b2o37bo
$obo11bobob2o72b2o36b3o35b2o$bo13b6o68b3o11b3o8b2o13bo3bo34bo$16bo2b3o 31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$20b2o12bo11bo5bo5bo25bo2bo13bo5bo
23b3o35b2o$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$33bo2bo8bo2bo3b2ob
4o2bobo26b3o8bobobobo32b2o2bo2bo$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bo b2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$90b3o8bobobobo32b2o2bo2bo$84bo16b2o3b2o33b3o$84bo2bo13bo5bo23b3o35b2o$85b2o15bo3bo23b2o2bo33bo2b o$89b3o11b3o8b2o13bo3bo34bo$92b2o36b3o35b2o$92b2o37bo$88bo2b2o11b2o10b 2o$88bo4bo10b2o10b2o23b2o10b2o$89bo3bo35b2o10b2o10bo$92b2o35bobo11b2o
11bo$131bo11b2o10b2o$129bobo$129b2o!  Smaller: Code: Select all x = 68, y = 56, rule = B35ce/S234t6c 14b2o10b2o10b2o$14b2o11bo10b2o$12b2o10bo11b2o$12b2o10b2o10b2o2$50b2o$
18bo30bo2bo$17b2o30bo2bo$16bo32bo3bo$17b2obo29bo2bo$18b3o30b2o10b2o$62bo3bo$30b3o28bo5bo$29bo2b2o27bo5bo$28bo5bo26bo5bo$29bo2b2o28bo3bo$
30b3o18b2o10b2o$50bo2bo$18b3o28bo3bo$17b2obo28bo2bo$16bo32bo2bo$17b2o 31b2o$18bo4$39bobo$40b2o$40b2o$35bo5$16bo32bo$16b2o30b2o$17b3o27bo$18b
obo27b2obo$49b3o$o27bo$27bo2bo30b3o$29b2o29bo2b2o$27bo2bo28bo5bo$o27bo
31bo2b2o$61b3o$18bobo$17b3o29b3o$16b2o30b2obo$16bo30bo$48b2o$49bo2$10b
2o10b2o10b2o$10b2o10bo11b2o$12b2o11bo10b2o$12b2o10b2o10b2o! 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). drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Accidentally forgot to mention I found a very small 12c/31 that let its exhaust die out, so I put that in the project folder right after I found it, which was when I was reading the post and adding the spaceships. This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y 83bismuth38 Posts: 453 Joined: March 2nd, 2017, 4:23 pm Location: Still sitting around in Sagittarius A... Contact: ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project (3,2)c/9: Code: Select all x = 3, y = 4, rule = B34-air5/S234-ai b2o$2bo$b2o$3o!

(I hope I got that right, I've never discovered an oblique before)

Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!  No football of any dui mauris said that. Rhombic Posts: 1056 Joined: June 1st, 2013, 5:41 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project 10c/88 Code: Select all x = 6, y = 10, rule = B3-e4c5e6a/S2-i3-c7 2b3o$2bo2bo$bo2b2o$3bo$o2bo$2obo$3bo2$b2ob2o$3b2o!  SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI what is “sesame oil”? bprentice Posts: 626 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project An excellent collection of small ships! You may find some of the bullets fired by the gun collections in this thread: viewtopic.php?f=11&t=2792#p41832 useful. Some sample bullets follow: Code: Select all x = 11, y = 71, rule = b2cea3n4ek5ceyqj7e/s2ea3knj4yz5eayq6ea 9.A$10.A$10.A$9.A9$10.A$8.A.A10$10.A$10.A$7.A.A9$8.A.A$10.A$7.A.A$8. A7$9.A$10.A$10.A$9.A$8.A$6.A6$4.A.A$4.A.A.A.A$4.A.A.A.A$4.A.A7$A.A.
A.A2$A.A.A.A3.A$A.A.A.A3.A2$A.A.A.A!  Code: Select all x = 200, y = 46, rule = b2eai3knq4enqj5yqj6ek8/s2a3kqj4nqz5eyj8 99.A5.A$104.A.A53.A$29.A.A19.A.A49.A.A.A51.A.A15.A.A$30.A.A3.A16.A36.
A7.A3.A3.A.A51.A.A16.A18.A$29.A.A.A.A.A13.A3.A17.A17.A15.A.A15.A.A17. A17.A15.A.A17.A$35.A.A17.A17.A15.A.A15.A.A17.A17.A17.A15.A.A17.A$54. A15.A.A17.A7.A3.A3.A.A17.A13.A.A.A15.A.A16.A18.A$51.A.A15.A.A17.A13.
A.A.A33.A17.A.A15.A.A$70.A15.A.A15.A.A53.A$99.A5.A9$192.A.A.A$189.A
7.A$50.A3.A121.A.A.A11.A.A.A.A$35.A.A9.A.A3.A.A17.A17.A17.A15.A.A17.
A15.A.A17.A17.A$37.A15.A.A17.A17.A17.A17.A17.A17.A15.A.A13.A3.A$36.
A9.A.A.A3.A11.A.A3.A11.A.A3.A11.A.A3.A17.A17.A49.A.A.A$32.A.A32.A3. A13.A3.A13.A3.A15.A.A15.A.A$34.A33.A.A15.A.A15.A.A$67.A.A15.A.A15.A .A$66.A.A15.A.A17.A$65.A.A17.A$66.A6$136.A3.A.A$112.A.A3.A.A.A14.A3.
A.A$54.A17.A15.A.A15.A.A6.A7.A2.A9.A5.A.A15.A.A17.A$5.A31.A17.A14.A
2.A17.A15.A.A4.A.A.A.A.A.A2.A17.A17.A4.A.A3.A.A.A2.A15.A.A$5.A31.A13. A.A.A13.A.A.A17.A17.A5.A3.A.A.A.A.A11.A.A3.A17.A7.A3.A.A.A.A15.A.A$
A3.A15.A5.A.A3.A3.A17.A15.A.A33.A.A5.A.A.A3.A3.A13.A.A.A17.A9.A3.A.
A.A15.A.A$3.A13.A7.A5.A.A.A123.A.A9.A.A3.A.A$2.A21.A.A.A.A.A.A$5.A15. A7.A.A.A$6.A15.A5.A.A.A$31.A!  Code: Select all x = 220, y = 94, rule = b2ea3nr4kiyz5kin/s3r4i5kiny6n 27.A$26.A.A$25.A.A.A36.A$24.A.A.A.A34.A.A36.A$25.A.A.A.A32.A.A.A34. A.A$26.A.A.A.A30.A.A.A.A32.A.A.A73.A$27.A3.A.A30.A3.A.A30.A3.A.A71. A.A36.A$34.A36.A36.A73.A36.A$34.A36.A36.A73.A36.A$27.A3.A.A30.A3.A.
A30.A3.A.A73.A36.A$28.A.A.A30.A.A.A.A32.A.A.A$29.A.A32.A.A.A34.A.A$30.A34.A.A36.A$66.A$17.A$16.A.A$15.A.A.A$14.A.A.A.A$13.A.A.A.A.A157. A36.A$12.A.A.A.A.A.A157.A.A34.A.A$11.A.A.A.A.A.A.A156.A.A34.A.A$10.
A.A.A.A.A.A.A.A152.A3.A34.A$9.A.A.A.A.A.A.A.A.A$8.A.A.A.A.A.A.A.A.A
.A$7.A.A3.A.A.A.A.A.A.A.A36.A36.A$6.A.A5.A.A.A.A.A.A.A.A34.A.A34.A.
A$5.A.A7.A.A.A.A.A.A.A.A32.A.A.A32.A.A.A$4.A.A9.A.A.A.A.A.A.A.A30.A
.A.A.A30.A.A.A.A$3.A.A11.A.A.A3.A.A.A.A30.A.A.A.A30.A.A.A.A$2.A.A13.
A.A5.A.A.A.A30.A.A.A.A30.A.A.A.A$3.A15.A7.A3.A.A30.A3.A.A30.A3.A.A20. A42.A40.A$34.A36.A36.A20.A.A.A.A.A.A.A.A.A26.A.A.A.A.A.A30.A.A.A.A$34.A36.A36.A20.A.A.A.A.A.A.A.A.A26.A.A.A.A.A.A30.A.A.A.A$3.A15.A7.A
3.A.A22.A7.A3.A.A30.A3.A.A20.A42.A40.A$2.A.A13.A.A5.A.A.A.A22.A.A5. A.A.A.A30.A.A.A.A$3.A.A11.A.A.A3.A.A.A.A24.A.A3.A.A.A.A30.A.A.A.A$4. A.A9.A.A.A.A.A.A.A.A26.A.A.A.A.A.A30.A.A.A.A$5.A.A7.A.A.A.A.A.A.A.A
28.A.A.A.A.A32.A.A.A$6.A.A5.A.A.A.A.A.A.A.A30.A.A.A.A34.A.A$7.A.A3.
A.A.A.A.A.A.A.A32.A.A.A36.A$8.A.A.A.A.A.A.A.A.A.A34.A.A$9.A.A.A.A.A
.A.A.A.A36.A148.A.A$10.A.A.A.A.A.A.A.A189.A$11.A.A.A.A.A.A.A107.A.A
.A.A.A.A.A.A32.A.A.A32.A.A.A$12.A.A.A.A.A.A112.A.A.A.A.A.A36.A32.A. A.A$13.A.A.A.A.A112.A38.A.A.A3.A32.A$14.A.A.A.A110.A.A46.A30.A.A$15.
A.A.A153.A5.A$16.A.A155.A3.A$17.A157.A.A4$207.A.A$179.A.A28.A$178.A 3.A28.A.A.A.A.A$180.A.A28.A.A.A.A.A$173.A3.A.A30.A$99.A72.A.A.A.A28.
A.A$26.A36.A34.A.A70.A.A.A.A$25.A.A34.A.A32.A.A.A68.A.A.A.A$24.A.A. A32.A.A.A30.A.A.A.A68.A.A.A$23.A.A.A.A30.A.A.A.A28.A.A.A.A.A68.A.A$22.A.A.A.A.A28.A.A.A.A.A26.A.A.A.A.A.A68.A$21.A3.A.A.A.A26.A3.A.A.A
.A24.A.A3.A.A.A.A$20.A5.A.A.A.A24.A5.A.A.A.A22.A.A5.A.A.A.A110.A$19.
A7.A3.A.A22.A7.A3.A.A22.A7.A3.A.A69.A38.A.A$34.A36.A36.A69.A.A.A36. A$34.A36.A36.A69.A.A.A36.A$19.A7.A3.A.A22.A7.A3.A.A22.A7.A3.A.A67.A .A38.A.A$20.A5.A.A.A.A22.A.A5.A.A.A.A22.A.A5.A.A.A.A69.A40.A$21.A3. A.A.A.A24.A.A3.A.A.A.A24.A.A3.A.A.A.A$22.A.A.A.A.A26.A.A.A.A.A.A26.
A.A.A.A.A.A$23.A.A.A.A28.A.A.A.A.A28.A.A.A.A.A$24.A.A.A30.A.A.A.A30.
A.A.A.A$25.A.A32.A.A.A32.A.A.A$26.A34.A.A34.A.A76.A38.A$62.A36.A76. A.A36.A.A$177.A.A36.A.A$180.A.A36.A$180.A.A36.A$177.A.A36.A.A$176.A
.A36.A.A$177.A38.A7$A$.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A. A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A .A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A. A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A$.A.A.A.A.A.A.A.A.A.A.A.A.
A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A
.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.
A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A$A!  There are many more small ships featured there but unfortunately you will have to run the guns to find them. Some errors, the original file name is on the left and the correct file name is on the right. errors.png (73.3 KiB) Viewed 26718 times The asterisk indicates that the pattern is not a ship but does evolve into one. o6c50 is not a ship. Brian Prentice drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Fixed all the errors, thanks. The most curious of them all was, of course, the o6c50.rle case, where that rule DOES have a ship, but it's o12c122. I have no idea what happened in all honesty. Plus I was up at 02:00 one night. I'm not including B0 rules for now because I feel like those rules aren't as 'genuine' , in the sense that they are really strobing rules and don't have any real spaceships. Feel free to argue this cause with me,though. This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y toroidalet Posts: 1024 Joined: August 7th, 2016, 1:48 pm Location: my computer Contact: ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project c/14 diagonal Code: Select all x = 3, y = 3, rule = B2ek3-qy6cik/S2aein3inr4ai5i bo$o$2bo!  c/12 diagonal Code: Select all x = 4, y = 4, rule = B2cek3acijr5c6cik/S2-ck3inr 3bo2$3bo$obo!  We should devise a modified apgcode for these so they will be dc14_214, and dc12_8085. oc3_1101 Code: Select all x = 4, y = 1, rule = B2ci3ai6c/S02ac3-en 2obo!  6k1c88_ec23 (yes, it's a bit awkward.) Code: Select all x = 4, y = 4, rule = B2in3/S2-in3-jr4ajr 3bo$ob2o$2o$2o!

2k3c30_2li

Code: Select all

x = 3, y = 5, rule = B2e3-cey/S1c2ace3ajnr
bo$obo$bo2$b2o!  1k7c71_699azwccw4aa4 Code: Select all x = 10, y = 9, rule = B3/S2-n34z6c b2o$o2bo$o$b3o3$7b2o$2b2o2bo2bo$2b2o3b2o!  EDIT: Just to make things clear, these are the codes for the ship in the optimal phase (lowest bounding box of all phases with minimum population, heading east or southeast or moving most to the right) o4c12_147 Code: Select all x = 3, y = 3, rule = B2-ae3aijy4t/S02ack3in obo$2bo$b2o!  EDIT2: d4c14_28092 Code: Select all x = 5, y = 4, rule = B2-ai/S02i3j 3bo$o3bo2$bobo!  Can someone help? I'm running out of steam (ships) here! EDIT3: o6c12_44y1ewh4 Code: Select all x = 12, y = 5, rule = B2ikn3ainqy4int5r67/S0 10bo$7bo$2o5bo3bo$7bo$10bo!  dc8_215 Code: Select all x = 3, y = 3, rule = B2-ae3-i4e/S02 b2o$o$2bo!  "Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life." -Terry Pratchett toroidalet Posts: 1024 Joined: August 7th, 2016, 1:48 pm Location: my computer Contact: ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project bumped also d8c28_o88f1t4z103111 Code: Select all x = 7, y = 7, rule = B2ek3ai6a/S2-i3-a4eijktz 3b3o$3bo$3bob2o$4obo$o4bo$ob4o$2bo!  d5c28_31ck8 Code: Select all x = 5, y = 5, rule = B2ek3ai6a/S2-i3-a4eijktz 2o$o$2b2o$2bobo$3bo!  d12c42_o88f1i8z010211 Code: Select all x = 7, y = 7, rule = B2ek3ai6i/S2-i3-a4eijkt 3b2o$3bobo$3bo$4o2bo$o4bo$bo2b2o$3bo!  d18c63_7d72zy15kngeqzy210111 Code: Select all x = 11, y = 11, rule = B2ek3ai/S2-i3-a4ijk 3o$ob2o$3o$bo2$5bobo$7bob2o$5b3obo$9b2o$6b3obo$6bob3o!

EDIT:d2c14_1w5

Code: Select all

x = 4, y = 3, rule = B2cek3k4c5y/S02i3j
o2bo2$3bo!  3k17c41_33033z0gggy9gggz1443y81443 Code: Select all x = 20, y = 13, rule = B3-ej4e/S234i 2ob2o$2ob2o8$b3o13b3o$o2bo12bo2bo$3bo15bo$b2o14b2o!

Last edited by toroidalet on June 21st, 2017, 3:50 pm, edited 1 time in total.
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

AforAmpere
Posts: 1050
Joined: July 1st, 2016, 3:58 pm

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

A lot of strange speeds that I have found

6c/66 orthogonal:

Code: Select all

x = 4, y = 5, rule = B2-ac3-jnqr67e8/S1c23-akny4
obo$obo$obo$o2bo$o!

3c/25 diagonal:

Code: Select all

x = 3, y = 3, rule = B34eqyz5/S23
3o$o$o!

c/2 diagonal:

Code: Select all

x = 5, y = 5, rule = B2a3an4i5r/S2ae3a4a
2b3o$bo$o$o2b2o$o2bo!

c/64 orthogonal:

Code: Select all

x = 5, y = 5, rule = B2-ac3-jnqr/S1c23-akny4
2o$b4o$4bo$b4o$2o!

Smaller 3c/10 diagonal:

Code: Select all

x = 4, y = 6, rule = B2-ac3-jnqr/S1c23-akny4
b2o$2bo$2b2o$obo$obo$3o!  3c/212 diagonal: Code: Select all x = 6, y = 11, rule = B2-ac3-jnqr/S1c23-akny4 4bo$3b3o$3bobo$3bo$3b2o$bo$2b4o$b2ob2o$4bo$o3bo$3o!  Smaller 3c/10 orthogonal: Code: Select all x = 2, y = 8, rule = B2en3-ckqy5akqy68/S12ei3an578 bo$o2$bo$bo2$o$bo!

2c/46 diagonal:

Code: Select all

x = 5, y = 5, rule = B2en3-ckqy5akqy68/S12ei3an578
obo$bo2$3b2o$3b2o!  4c/14 orthogonal: Code: Select all x = 6, y = 6, rule = B2n34ckqz/S23 bo$o3bo$bo3bo$3bobo$2bo2bo$3bobo!

2c/18 diagonal:

Code: Select all

x = 5, y = 3, rule = B34eqyz5-k/S23
ob3o$ob2o$2bo!

Smaller c/16 diagonal:

Code: Select all

x = 3, y = 4, rule = B2ek3-ajny4aw/S02-ei3n4aq
o2$2bo$o!

16c/38 orthogonal based repship:

Code: Select all

x = 48, y = 15, rule = B2i34cejqwyz/S23
14bo$12b4o$10b2o$11b2o17bo$29bobo11bo$28bo2bo10b2ob2o$b2o14b2o8b5o3b2o
6bo3bo$o2bo13b2o7b3o7bo6bo3bo$b2o14b2o8b5o3b2o6bo3bo$28bo2bo10b2ob2o$
29bobo11bo$11b2o17bo$10b2o$12b4o$14bo!

(2,1)c/105:

Code: Select all

x = 4, y = 7, rule = B2n34cqz5ckny/S23
3o$bo4$2b2o$2b2o!  EDIT 1, ones not found by me, in the glider database, I have a huge list of totalistic ships: 4c/6 orthogonal: Code: Select all x = 4, y = 5, rule = B256/S03 2bo2$o2bo2$2bo!  26c/60 orthogonal: Code: Select all x = 132, y = 22, rule = B38/S02456 79b3o$29bobo45bob3o$28b2obo19bobo23bo17b2o18bo$28bo2bo16b3ob3o20b2o17b
obo8bo13b3o6bo$16bo12b2o18bo2b2o21bo2b2o10bo4b2o7b3o3bo6b3ob3o4bobo$6b
o7b3o4bo7b2o9b3o5bob2obo12b3o5bo6b2o7b2ob2obo6bo3bobobo5bobo4bo4b3o$5b o9b2o23b3o4b3o4b2o10b3o5bo6b2o7b2ob2obo6bo3bobobo5bobo4bo4b3o$8bo8bo3b
o9bo17b2o2b3o2bo16bo2b2o10bo4b2o7b3o3bo6b3ob3o4bobo$6b3o39b4o3b3obo15b 2o17bobo8bo13b3o6bo$7b2o19b2o18bo2b6obo18bo17b2o18bo$bo46b3ob3o22bob3o$obo24bobo21bobo2bo22b3o3bo22bo$bo2bobo21bobobo2bo13bob2o3b3o26bo18bo 4b2o$2b3obo19bo2b2ob3o14b4ob2o2bo6b2o13bo3bo24bobo4b2o$3bo2bo14bobo2bo b6obobo12bobo4b2o6b4obo9bo5bob2o4bo4bo7bo5b2o3bo$2b2o18bobo3bob2o5bo
11bo5bo13bobo8b5o7b2ob2obobo4b3o3b2o5b2o$b3o16bo3bo4bobo4bo13bo2bo14bo bo9b5o7b2ob2obobo4b3o3b2o5b2o$2b2o18bo4b2obobobo16bob2o10bo2bo11bo5bob
2o4bo4bo7bo5b2o3bo$29bob4o17b3o13b2o14bo24bobo4b2o$30bobo20bo13bobo15b
o18bo4b2o$66b3o16bo22bo$66bobobo!

Same pop and smaller bounding box for 3c/7:

Code: Select all

x = 4, y = 5, rule = B34/S12567
2bo$3bo$o2bo$3bo$2bo!

11c/38 orthogonal:

Code: Select all

x = 12, y = 15, rule = B3/S2378
9bo$8bobo$7b2ob2o$3o5bo2bo$o8b2o$o4$o$o8b2o$3o5bo2bo$7b2ob2o$8bobo$9bo!  2c/9 orthogonal: Code: Select all x = 3, y = 7, rule = B3/S246 o$bo$2bo$2bo$2bo$bo$o!  4c/30 orthogonal: Code: Select all x = 3, y = 5, rule = B346/S013 o$bo2$2bo$2o!

2c/19 orthogonal:

Code: Select all

x = 5, y = 5, rule = B347/S02567
bobo$o$2b3o$bo$3bo!

2c/25 orthogonal:

Code: Select all

x = 5, y = 16, rule = B36/S237
2o$2o4$2b2o$bo2bo$bo2bo$bo2bo$bo2bo$2b2o4$2o$2o!  2c/26 orthogonal: Code: Select all x = 5, y = 4, rule = B34/S02567 4bo$3b2o$3o$bobo!

2c/27 orthogonal:

Code: Select all

x = 6, y = 9, rule = B347/S037
2bo$o$4bo$o$obo2bo$o$4bo$o$2bo!

2c/31 orthogonal:

Code: Select all

x = 3, y = 10, rule = B36/S013567
2bo$o$bo$2o$bo$bo$2o$bo$o$2bo!  c/18 orthogonal: Code: Select all x = 6, y = 9, rule = B3567/S0145 5bo$2bo$3bo2$o2b2o2$3bo$2bo$5bo!  2c/35 orthogonal: Code: Select all x = 8, y = 10, rule = B346/S04578 5bo$3b2o$4b2o$o3b2o$obo2b3o$obo2b3o$o3b2o$4b2o$3b2o$5bo!

2c/43 orthogonal:

Code: Select all

x = 5, y = 9, rule = B346/S1468
2o$2bo$2bo$2bobo$obobo$2bobo$2bo$2bo$2o!

2c/15 diagonal:

Code: Select all

x = 7, y = 7, rule = B347/S247
3b2o$5bo$6bo$o3b2o$o2b3o$bob2o$2bo!

2c/21 diagonal:

Code: Select all

x = 9, y = 9, rule = B3567/S1357
6bo$5bo$6b2o$7bo$8bo$bo4bo$obo2bo2bo$2b2o$4bobo!

2c/25 diagonal:

Code: Select all

x = 5, y = 5, rule = B34/S0256
2b2o$b2o$2obo$obobo$3bo!

smaller c/14 diagonal:

Code: Select all

x = 4, y = 3, rule = B3/S0124
3bo$3bo$2o!

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)

toroidalet
Posts: 1024
Joined: August 7th, 2016, 1:48 pm
Location: my computer
Contact:

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

dc2_e1d5

Code: Select all

x = 4, y = 4, rule = B2a3a4i/S2ae3a
b3o$o$ob2o$obo!  o4c8_1w1011 Code: Select all x = 7, y = 1, rule = B2ac3nr4ci5y/S0 o2bob2o!  d4c8_80gps Code: Select all x = 5, y = 5, rule = B2a3acr4ai/S2ae3a 3bo2$4bo$o2b2o$2b3o!

d8c16_xg1024z12036062

Code: Select all

x = 8, y = 8, rule = B2ae3acr4ai/S2ae3a
4bo$6bo$7bo2$3bo$o2bo$bob2ob2o$4bobo!

"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

muzik
Posts: 3513
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

How about an 8c/96 diagonal? Pretty weird and exotic speed if I do say so myself.

Code: Select all

x = 76, y = 76, rule = B3/S23
59b2o$59b2o7$67b2o$67b2o4$56bo$55b3o$55bob2o$54b2o$54b2o$54b2o$58bo13b
o$57b2o10b2o$55bobo11b2ob2o$54bo2bo13bo$55b2o12b2o2$56bo13b2o$56bo$46b 2ob2o5bo16bo$46bo2bo20bobo$48b2o21bo2b2o$47bo$46bobo4$48b4o$48bo10$27b
2o2bo$27bo2bo$29bobo3b2o$27b3o5bo$27bo7bo$35bo3$16b3o3bo$14b5o2bobo$
13b2o8bob3o$14b2o4b3o$15bo3b2o$2o$2o7$8b2o$8b2o$20b2obo$20b2obobo2bo$22bo2bo3bo$19bobo6bo$21bo5bo$29bo$29bo!  More ships: Code: Select all x = 41, y = 48, rule = B358/S238 16$15bo$14bobo$14bobo$16bo$14bo$13b3o4b3o$19bob2o$19bobob2o$19bob2o$13b3o4b3o$14bo$16bo$14bobo$14bobo$15bo!

Code: Select all

x = 8, y = 8, rule = B3457/S456
3b4o$b6o$b7o$5obo$4ob3o$3ob3o$7o$2bobo!  Also, some soups that emit velocities that don't appear to be documented yet: Code: Select all x = 16, y = 16, rule = B2i3ai4/S23 bboboooooobobbbb$
obooobbboboobbbb$obobbboobboobobb$
bobbooobboooobob$obbbobbbbbbooobo$
bbooobobbbbobobb$boobbbbobbboboob$
boobboboboooobbo$bbooobobbobboboo$
bobboboboooobbob$boboboboboboobbo$
oboooooooobooobo$booboooooboooooo$
bbbooboboboooboo$boboobbbboobbbbb$
obobboobbbbbbobb!

Code: Select all

x = 16, y = 16, rule = B3678/S35678
ooobobobbbboobob$bboobboboooobbbb$
bobbboobbooboooo$oboobbbbbbbbobbb$
bbobboobbobbobbo$booooooboooboobb$
bbobbbbooooobobb$bbooooobbooobboo$
obbobbooboobbbbb$ooobbbbbbooboobo$
bobboboobbobobbo$obbbbbbbboooobbo$
bbbooooooooboboo$bbboobbobobbbooo$
obobooooboboobbo$boobobboobbbbooo! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I am just trying to fill in the gaps in the list, so these are probably not optimal, unfortunately a lot of my minimum size ships for totalistic rules are B0 rules. Do you want to see the list, drc? C/21 diagonal: Code: Select all x = 10, y = 10, rule = B345/S05 5bobobo$bo3bo$5bo3bo$5bo3bo$5bo3bo$6o$7bobo$o5b2o2$ob3obo!  C/23 diagonal: Code: Select all x = 4, y = 4, rule = B3567/S02467 2o$o2bo2$bo!  C/24 diagonal: Code: Select all x = 6, y = 3, rule = B36/S01356 2bo2bo$4obo$4bo!  C/27 diagonal: Code: Select all x = 8, y = 8, rule = B356/S13 4bob2o$3b2o$5bo$bo$2o$2bo$o$o!

C/29 diagonal:

Code: Select all

x = 11, y = 11, rule = B3678/S1348
9b2o$9b2o2$6bobo$6bo$7bo$3b2o2bo$5b3o$3bo$2o$2o!  Smaller c/30 diagonal: Code: Select all x = 4, y = 3, rule = B3567/S1256 ob2o$o2bo$bobo!  c/33 diagonal: Code: Select all x = 17, y = 17, rule = B36/S035678 3bo$b4o2bo$b8o$12o$b11o$2b11o$2b11o$b12o$2b11o$3b12o$3b11o$3b12o$5b12o$9b8o$9bob4o$12b2o$12b2o!  2c/68 diagonal: Code: Select all x = 6, y = 4, rule = B35/S0135 2bo$2bobo$4o$3bobo!

c/37 diagonal:

Code: Select all

x = 12, y = 12, rule = B345/S05
6bo$11bo$4b2ob3obo$11bo$2bo5b4o$2bo$o6b4o$2bo3b2o$2bobobo$2bobobo$4bob
o$b4o!  c/38 diagonal: Code: Select all x = 4, y = 5, rule = B345/S0145 b2o$3o$2bo$obo$3bo!  c/45 diagonal: Code: Select all x = 8, y = 8, rule = B37/S014567 4bo$2b2o$b5o$b6o$ob2ob2o$2b5o$3b5o$6bo!

2c/112 diagonal:

Code: Select all

x = 6, y = 4, rule = B34/S0145
obo$o$b2obo$2o3bo!  c/59 diagonal: Code: Select all x = 8, y = 8, rule = B34/S0156 4bo$3bo$6bo$bo$o5b2o2$2bobobo$4bo!  c/62 diagonal: Code: Select all x = 7, y = 7, rule = B345/S0457 bobo$5bo$b2ob2o$o5bo$2bo$b2o2b2o$3bobo!  c/86 diagonal: Code: Select all x = 7, y = 6, rule = B346/S0157 4bo$3o$o5bo$6bo$obo$4bo!

c/93 diagonal:

Code: Select all

x = 7, y = 7, rule = B36/S2456
2bo2bo$2bob2o$7o$2bo$b2o$3o$2bo!

c/116 diagonal:

Code: Select all

x = 6, y = 6, rule = B346/S01458
2bobo$bob2o$bo2b2o$2bob2o$o2bo$bo!  c/118 diagonal: Code: Select all x = 8, y = 8, rule = B347/S356 2bo2bo$b2obo$5ob2o$2bobobo$b3o2bo$o$2b3o$2bo!

EDIT 1:

12c/50 orthogonal:

Code: Select all

x = 6, y = 8, rule = B2-ac3-jnqr/S1c23-akn4
3o$o2$4b2o$3ob2o$obobo$obobo$2b3o!

Better c/7 orthogonal:

Code: Select all

x = 2, y = 5, rule = B345/S016
o2$2o2$o!

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)

A for awesome
Posts: 1904
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

C/2 diagonal:

Code: Select all

x = 3, y = 4, rule = B2ac/S1
2bo2$b2o$o!

x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

muzik
Posts: 3513
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

I had a bunch of spaceships in this post, but the page refreshed, so excuse me while I type out this behemoth of a post again.

Some ships from my orthogonal ships thread that don't seem to be on here yet:

c/18:

Code: Select all

, y = 6, rule = B3567/S0145
o7bo$4bo$2bobobo$bo5bo2$4bo!
!
c/21:

Code: Select all

x = 5, y = 8, rule = B36/S0135
bobo$2bo$2bo$bobo$bobo$o3bo2$2bo!
c/22:

Code: Select all

x = 8, y = 6, rule = B3567/S1367
b2o2b2o$obo2bobo$2bo2bo3$3b2o! c/24: Code: Select all x = 7, y = 12, rule = B2e3ai4arw5678/S3-an4ar5i678 3bo$bobobo$2b3o$7o$b5o$7o$7o$2b3o$bobobo$2b3o$3bo$3bo!
c/29:

Code: Select all

= 7, y = 4, rule = B345/S0478
2b3o$ob3obo$b5o$o5bo! c/30: Code: Select all x = 9, y = 5, rule = B346/S3578 bo5bo$b2obob2o$3o3b3o$4bo$bo5bo! c/44: Code: Select all x = 7, y = 8, rule = B34568/S458 2b3o$2obob2o2$o5bo$7o$7o$bobobo$bobobo! c/64: Code: Select all x = 5, y = 5, rule = B2-ac3-jnqr/S1c23-akny4 b3o$bobo$bobo$2ob2o$o3bo! c/2068: (I'm surprised you forgot this one, unless you're excluding the ridiculous ships) Code: Select all x = 8, y = 8, rule = B34578/S456 bobobo$2b4o$2ob2o2bo$4obobo$2ob3o$8o$2b4o$b3obo!
c/5648: (this one even more so)

Code: Select all

x = 12, y = 14, rule = B3457/S4568
5b2o$3bo4bo$3b2o2b2o$b3o4b3o$b3o4b3o$2ob6ob2o$3ob4ob3o$ob3o2b3obo$2ob
6ob2o$obobo2bobobo$2b2ob2ob2o$2b8o$4b4o$4bo2bo! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project The c/64 is only in this thread, found by me, so it is already been posted, I am not sure why it ended up in your post. I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I have added all of the discoveries, apologies for the wait. The only ship I contributed is this dc28: Code: Select all x = 4, y = 5, rule = B3-n4c8/S2-i34-ar6ci 2o$b2o$3bo$2bo$3bo!  I promise I will have more next time. muzik wrote:(I'm surprised you forgot this one, unless you're excluding the ridiculous ships) I wrote:Maximum period is set to 1000 so far. I also wrote:*facepalm* This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project c/20 orthogonal: Code: Select all x = 4, y = 5, rule = B35678/S1247 obo$2bo$o2bo$2bo$obo!  c/23 orthogonal: Code: Select all x = 4, y = 7, rule = B3/S0145678 bo$bo2$2obo2$bo$bo!  c/26 orthogonal: Code: Select all x = 7, y = 6, rule = B3457/S04578 2bobo$4ob2o$o5bo$o5bo$4ob2o$2bobo!

EDIT 1: 3c/30 diagonal

Code: Select all

x = 5, y = 5, rule = B3-q4nrt5nr6i/S2-c3-q4r5cejn
o2bo$4bo$2o$bobo$2b3o!

EDIT 2: 13c/512 diagonal

Code: Select all

x = 26, y = 27, rule = B2-ac3-jnqr5y67e8/S1c23-akny4
o2bo$o2bo$4o$b2o13$18bo$8bobo5bob3o$10bo5bo3bo$7bo8b2o2bo$7b3o2bo4bobo
2b2o$5b2ob3ob2o4bo3bo$8bo9b5ob2o$7bobobo13bo$25bo$19bo4bo$21b2o!

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)

A for awesome
Posts: 1904
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

Almost a p3 knightship:

Code: Select all

x = 4, y = 3, rule = B2acn3r4at/S01e2ac3ir
3o$bobo$obo!

Can anyone find a real one?
EDIT: 2c/3 orthogonal:

Code: Select all

x = 3, y = 2, rule = B2ac3ae4t5e/S1c2i3i
bo$3o!  x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Are p3 knightships only possible in B2a rules? 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) A for awesome Posts: 1904 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project AforAmpere wrote:Are p3 knightships only possible in B2a rules? I believe so. I think the same goes for p4 knightships, although I don't know if those are possible in any rule. EDIT: Actually, they may be possible in B1e rules as well. Definitely nothing without either of those transistions, though. Last edited by A for awesome on June 19th, 2017, 3:47 pm, edited 1 time in total. x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project There is a p4 knightship in a B0 rule if that counts Here's a (3,1)c/3 close call: Code: Select all x = 3, y = 3, rule = B2a/S1e2i 3o2$2bo!

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)

A for awesome
Posts: 1904
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

See my edit, actually.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce