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

For discussion of other cellular automata.

### 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

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'd recommend putting spaceships of simple speeds as well.
This 16c/44 has a smaller bounding box but same population.
x = 24, y = 5, rule = B3-cky6ci/S23-ce4n7e16b2o3bo$b2o12b5o2bo$o2bo10bo4bob3o$b2o12b5o2bo$16b2o3bo!

Here's a ridiculously large 12c/31
x = 184, y = 63, rule = B35ce/S234t6c129b2o$129bobo$131bo11b2o10b2o$92b2o35bobo11b2o11bo$89bo3bo35b2o10b2o10bo$88bo4bo10b2o10b2o23b2o10b2o$88bo2b2o11b2o10b2o$92b2o37bo$92b2o36b3o35b2o$89b3o11b3o8b2o13bo3bo34bo$85b2o15bo3bo23b2o2bo33bo2bo$84bo2bo13bo5bo23b3o35b2o$84bo16b2o3b2o33b3o$90b3o8bobobobo32b2o2bo2bo$58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bobo$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$16bo2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$bo13b6o68b3o11b3o8b2o13bo3bo34bo$obo11bobob2o72b2o36b3o35b2o$14bobobo12b2o35b2o22b2o37bo$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$30bo3bo32bo3bo20b2o35bobo11b2o11bo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$5bo8bo2bo24bobo34bobo47bobo$4b2o9b3o23bo5bobo28bo5bobo42b2o$41b2obobob2o28b2obobob2o$4b2o9b3o23bo5bobo28bo5bobo42b2o$5bo8bo2bo24bobo34bobo47bobo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$30bo3bo32bo3bo20b2o35bobo11b2o11bo$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$14bobobo12b2o35b2o22b2o37bo$obo11bobob2o72b2o36b3o35b2o$bo13b6o68b3o11b3o8b2o13bo3bo34bo$16bo2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$90b3o8bobobobo32b2o2bo2bo$84bo16b2o3b2o33b3o$84bo2bo13bo5bo23b3o35b2o$85b2o15bo3bo23b2o2bo33bo2bo$89b3o11b3o8b2o13bo3bo34bo$92b2o36b3o35b2o$92b2o37bo$88bo2b2o11b2o10b2o$88bo4bo10b2o10b2o23b2o10b2o$89bo3bo35b2o10b2o10bo$92b2o35bobo11b2o11bo$131bo11b2o10b2o$129bobo$129b2o!

I optimized for bounding box, so a longer one might have a smaller minimum population.
7c/48 diagonal:
x = 4, y = 4, rule = B3-cky8/S234nbo$2b2o$obo$2o! 10c/27 x = 24, y = 27, rule = B3-cky8/S234n2bo$2o2$12b2o$11bo2bo$12bobo$13bo3$18b3o$17bo3bo$17b2o3bo$23bo$20bo2bo$23bo$17b2o3bo$17bo3bo$18b3o3$13bo$12bobo$11bo2bo$12b2o2$2o$2bo! c/5 diagonal x = 4, y = 4, rule = B3-cky4k/S23-c4cnb2o$o2bo$2bo$2o!

11c/37
x = 35, y = 8, rule = B34n5y/S2-k34ab3o16b3o$o2bo8b2o7b2o9bo$bo10b2o8b4obo4b2o$b3obo16bo2bo7b2o$b3obo16bo2bo7b2o$bo10b2o8b4obo4b2o$o2bo8b2o7b2o9bo$b3o16b3o! I guess it's too much work to search Catagolue as well as the forums. c/6 diagonal x = 3, y = 2, rule = B2-a/S122bo$2o!

4c/12
x = 4, y = 4, rule = B2i3-y6ci/S23-e4t2b2o$o2bo$o2bo$obo! c/30 diagonal x = 4, y = 4, rule = B38/S234wzb2o$o2bo$o2bo$bobo!

4c/14 diagonal
x = 15, y = 15, rule = B38/S234wz2o$2obo$5bo$bo$4bo$2bo3$8b3o$8bo2bo$8bobo3bo$9bo4bo$14bo$13bo$10b3o!

8c/183
x = 29, y = 5, rule = B2ei3aeiqr4-aiktz5aiqy6ac7c8/S12cin3i4cikwy5-ajr6ain7e26bo$4bo13bobo5bo$2ob3o11bo2bo4b4o$4bo13bobo5bo$26bo!

2c/14 diagonal
x = 3, y = 3, rule = B34n5y/S2-k34abo$2o$b2o!

8c/128 diagonal
x = 4, y = 4, rule = B36in/S234cw3o$3bo$o2bo$b2o! More coming soon! EDIT: 9c/56 diagonal x = 18, y = 14, rule = B2n3-ej4e6e/S234i13b2o$13b2o2$7bo$2b2o3bo$2b2obobo5b2o$4bo8bob2o$2b2o$16b2o$16bo$17bo$2obo$o2bo6b2o$b3o6b2o! 3c/10 x = 4, y = 5, rule = B3-y4e6ci/S2-i3-ceb3o$3bo$2b2o$2o$o! EDIT2: The 2c/8 is in a suboptimal phase. x = 3, y = 4, rule = B2-a3-i/S1e3bo$2bo2$obo! 2c/6 diagonal x = 6, y = 7, rule = B3-j/S0234-ro$b2o$b2o$bobo$2bo2bo$5bo$3b3o! 9c/18 x = 7, y = 8, rule = B2-ai3-in4w/S1c2aei3-ajo4bo$6bo$o4bo$bo$bo$o4bo$6bo$o4bo!

4c/10
x = 5, y = 5, rule = B3-q4n/S23-c2b2o$bob2o$o2bo$obo$bo!

18c/156
x = 18, y = 19, rule = B3-cky8/S23-c4n3b3o2$4b2o$4b2o$3bo2bo$4b2o5$o$b2o3$16b2o$15b2o$12bobo$12b3o$13bo! c/3 diagonal x = 3, y = 3, rule = B2-ai3-in4w/S1c2aei3-aj2bo$bo$obo! 4c/8 x = 7, y = 5, rule = B3-cqy6i/S23-aeky4ai5i3b2o$o4bo$o4b2o$o4bo$3b2o! 2c/16 x = 4, y = 3, rule = B3-j4nwz5c7/S1c2-ik34i5acbobo$o2bo$bobo! EDIT3: 16c/52 x = 26, y = 15, rule = B3-y6-a/S23-e3bo$2bobo$bo2bo$o2bo9bobo$bobo7b3obo$5b2o4b4o6bo2bo$5b2o4bo9bo3bo$4bo15bobo2bo$5b2o4bo9bo3bo$5b2o4b4o6bo2bo$bobo7b3obo$o2bo9bobo$bo2bo$2bobo$3bo! 8c/22 x = 15, y = 11, rule = B3-cky6ci/S23-ce4n7e812bo$7bobobobo$7bo2bo3bo$7bobobobo$12bo$3o$12bo$7bobobobo$7bo2bo3bo$7bobobobo$12bo! 8c/16 x = 6, y = 16, rule = B3-j/S234i2b3o$obo2bo$o4bo$2ob3o$2bo7$2bo$2ob3o$o4bo$obo2bo$2b3o!

c/25 diagonal
x = 6, y = 6, rule = B2-a3-ik4-aik/S233bo$4b2o$4b2o$o2bo$b2o$b2o! 17c/34 x = 14, y = 7, rule = B2e3-a4/S23-a4-a7e9bo$8b3obo$b2o5b2o3bo$2obo4b2o3bo$b2o5b2o3bo$8b3obo$9bo! 14c/28 x = 5, y = 13, rule = B34et/S23-a4eit6bo$2bo$3b2o$2o2bo$bo2bo$2b2o2$2b2o$bo2bo$2o2bo$3b2o$2bo$bo!

EDIT4:
6c/12
x = 6, y = 7, rule = B2ce3-a/S2o$bo$bo3bo$bob3o$bo3bo$bo$o!

10c/36
x = 38, y = 19, rule = B3/S2-k34k6c12b2o$12b2o$7b2o$9bo7bo10bo8bo$6bo2bo7bo10b2o6b2o$9bo7bo10bo8bo$o6b2o$o$o2$o$o$o6b2o$9bo7bo10bo8bo$6bo2bo7bo10b2o6b2o$9bo7bo10bo8bo$7b2o$12b2o$12b2o! 20c/72 x = 44, y = 13, rule = B3/S2-k34k6c34bo8bo$34b2o6b2o$34bo8bo2$18bo$18b2o$14bo25bobo$13b2o20bo4bobo$13b2o7b3o8b2o8bo$2o11b2o20bo4bobo$2o12bo25bobo$18b2o$18bo!

4c/11
x = 9, y = 13, rule = B34t6k/S2-i35a2bo$bobo$o$o4bo$b2o3bo$5bobo$8bo$5bobo$b2o3bo$o4bo$o$bobo$2bo!

16c/92 diagonal
x = 7, y = 4, rule = B34i5eiy/S234qy4bo$2bobo$2o3bo$4b3o! 18c/72 x = 46, y = 30, rule = B356/S2321b3ob3o2$2bo$bobo$o3bo11bo23b2o$o3bo10bo2bo21bob2o$bobo10bo3bo22bo2bo$2bo12b2obo14bo11bo$16bo14b4o6bo3bo$31bob3o7bo$31bo2b2o$32bobo$33bo5$33bo$32bobo$31bo2b2o$31bob3o7bo$16bo14b4o6bo3bo$2bo12b2obo14bo11bo$bobo10bo3bo22bo2bo$o3bo10bo2bo21bob2o$o3bo11bo23b2o$bobo$2bo2$21b3ob3o!

11c/22
x = 25, y = 15, rule = B3-ky/S23-aiy4anq6nbo2bo$5o14b3o$o4bo13b2ob2o$2o3bobo13bo2bo$2bo5bo15bo$5b2o17bo$22b3o2$22b3o$5b2o17bo$2bo5bo15bo$2o3bobo13bo2bo$o4bo13b2ob2o$5o14b3o$bo2bo! 18c/87, optimized for bounding box like the 12c/31 x = 37, y = 20, rule = B2i3-ck/S02-i3-ck33b2o$33b2o$21bobo11bo$21bo2bo8b2o$33b2o$22b2o$11bobo7bo5b2o$2bo9b2o13b2o$2bo10bo8bo$2bo9b2o$o2bo7bobo$obo$bo5b2o20b2o$7b2o20b2o$2bo20b2o$23bobo9bo$23b3o9b2o$23bobo10bo$35b2o$35bo!

9c/50 diagonal
x = 23, y = 19, rule = B34-iqr7c/S23-a4i14bo$14bo$14bo3$b2o$o2bo$4bo11b2o$bo2bo10b2o4bo$2bobo10bo6bo$2b2o11b2o5bo$15bo6bo$15b2o4bo$16b2o3$7bo$7bo$7bo!

(3,4)c/20
x = 10, y = 8, rule = B3/S234w7cb3o3bo$2obo$2b2o$5bo$8b2o$9bo$7b2o$7bo! EDIT5: Ships from the oblique ships thread (plus the previous one) (5,16)c/74 x = 5, y = 4, rule = B3/S23-e4e2b2o$bob2o$o$2o!

(5,2)c/190
x = 22, y = 39, rule = B38/S23bo$obo$b2o7$18bo$17b2o2$18bo$16b2o4$20b2o$20b2o11$9bo$8b2o2$9bo$7b2o4$11b2o$11b2o!

(2,6)c/21
x = 16, y = 19, rule = B37/S2-i34q7b5o$6b2o2b2o$6bo2bo2b3o$6b2ob2ob2obo$6b2o2bo4bo$13b2o$11bobo$10bo5$3b3o$bo2bo$2bo5b2o$obo3bo3bob2o$obo9bobo$bo5b3obobo$12bo!

(3,1)c/13
x = 4, y = 5, rule = B2-ak3/S25aib3o$2b2o$3bo$obo$b2o!

(7,8)c/168
x = 7, y = 4, rule = B013568/S012obobo$2bo2b2o$2bo$4b2o! (5,7)c/330 x = 6, y = 11, rule = B015/S14o$o7$4b2o$4b2o$3bo! (3,2)c/23 x = 5, y = 6, rule = B345/S126o2$3bo$obobo$obo$ob3o! (2,3)c/10 x = 5, y = 3, rule = B2en3/S25678o2bo$bo2bo$3bo! (2,29)c/89 x = 126, y = 58, rule = B3-k4c/S2345b2o27bo$41bo3b2o27bo$41bo32bo$41bo$70b3o3b3o$2bobo$3ob2o68bo$2bo2b2o43bobo21bo$2b2obo44bo2bob2o17bo$3bobo46b2o2b2o$52b2obo$43bo31b2o$43bo6b2o23b2o$43bo5b3o$50b2o25bo25b3o$39b3o3b3o8b2o18b3o23bo$75b2ob2o22bo2bo$43bo30bo25b2ob2o3b3o$43bo55bo2bo5b2obo$43bo55bo2bo3bo4bo$101bobo2b2o3bo$74bobo25b3ob2o2bo$74b3o28bo3b2o7b2o$74b3o27bo4b2o7b2o$100b2o3b2o2b2o11b2o$100b2o4bo15bobo$123b3o$81bo41b2o$80bobo$38b2o40bobo$38b2o41bo$67b2o19bo13b2o$67b2o8b2o10b2o11bobo$77b2o9b2o14bo$102b3o$101bo$101bo5bo$108bo$106b3o7$101bo$100bobo$100b2o3bo$105b2o$92bo4bo4bo$91bo9bo5bo5bo$92bo14bo4b5o$94b2obobo3b3obo3bo5bo$94b2o5bobo6b3o2bob2o$100bo10b2o2bobo$97b2o13bo$113b3o$114bo!

(1,4)c/25
x = 6, y = 3, rule = B2e3/S2a36o$bo2bo$3b3o!

(2,15)c/35
x = 51, y = 25, rule = B3aijnq5ce/S23-y4ik5j5bobo11b2o$18bo2bo$6bo12b2o13b2o$23b2o8bo2bo$23b2o9b2o$38b2o$6bo31b2o5b2o$45bob2o$5bo39bobobo$17b2o30b2o$17bobo25b2ob2o$2bo16bo10bo12b2o3bo$4bo11bob2o23b5o$2ob2o11b2o27bo2$bo28bo$bobo3bo21b3o$2bo3bo21b2obob2o$3b2o26bo2bo7b2o$2bo2bo26b3o7bobo$2bo2bo6bo31b2o$2b3o7b3o26bob2o$14bo26b3o$2o10b3o$2o! (1,11)c/30 x = 15, y = 7, rule = B3/S23-c4w712bo$11bobo$b2o8bo2bo$2o12bo$o2bo8b3o$o2bo$bobo! (1,6)c/21 x = 5, y = 3, rule = B367/S023-a4i5io2b2o$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 toroidalet Posts: 1002 Joined: August 7th, 2016, 1:48 pm Location: my computer ### 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 drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project toroidalet wrote:Here's a ridiculously large 12c/31 x = 184, y = 63, rule = B35ce/S234t6c129b2o$129bobo$131bo11b2o10b2o$92b2o35bobo11b2o11bo$89bo3bo35b2o10b2o10bo$88bo4bo10b2o10b2o23b2o10b2o$88bo2b2o11b2o10b2o$92b2o37bo$92b2o36b3o35b2o$89b3o11b3o8b2o13bo3bo34bo$85b2o15bo3bo23b2o2bo33bo2bo$84bo2bo13bo5bo23b3o35b2o$84bo16b2o3b2o33b3o$90b3o8bobobobo32b2o2bo2bo$58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bobo$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$16bo2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$bo13b6o68b3o11b3o8b2o13bo3bo34bo$obo11bobob2o72b2o36b3o35b2o$14bobobo12b2o35b2o22b2o37bo$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$30bo3bo32bo3bo20b2o35bobo11b2o11bo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$5bo8bo2bo24bobo34bobo47bobo$4b2o9b3o23bo5bobo28bo5bobo42b2o$41b2obobob2o28b2obobob2o$4b2o9b3o23bo5bobo28bo5bobo42b2o$5bo8bo2bo24bobo34bobo47bobo$4bo9b2o15b3o9b2o23b3o9b2o49bo11b2o10b2o$30bo3bo32bo3bo20b2o35bobo11b2o11bo$29bo5bo30bo5bo16bo3bo35b2o10b2o10bo$bo14bo12bo36bo21bo4bo10b2o10b2o23b2o10b2o$3o12b3o11bo3b2o31bo3b2o16bo2b2o11b2o10b2o$14bobobo12b2o35b2o22b2o37bo$obo11bobob2o72b2o36b3o35b2o$bo13b6o68b3o11b3o8b2o13bo3bo34bo$16bo2b3o31bo4bo26b2o15bo3bo23b2o2bo33bo2bo$20b2o12bo11bo5bo5bo25bo2bo13bo5bo23b3o35b2o$33bobo9bobo4b2o5bob2o21bo16b2o3b2o33b3o$33bo2bo8bo2bo3b2ob4o2bobo26b3o8bobobobo32b2o2bo2bo$34b2o10b2o4b2obo6b2o18bo2bo3bo2bo17bob2o26b2o6bo31bobo$53bo4b6o5b3o10bo3bo2bo19b2o2bo23b2ob3o3bo2bo30b4o$58b2ob2o19bo2bo3bo2bo17bob2o26b2o6bo31bobo$90b3o8bobobobo32b2o2bo2bo$84bo16b2o3b2o33b3o$84bo2bo13bo5bo23b3o35b2o$85b2o15bo3bo23b2o2bo33bo2bo$89b3o11b3o8b2o13bo3bo34bo$92b2o36b3o35b2o$92b2o37bo$88bo2b2o11b2o10b2o$88bo4bo10b2o10b2o23b2o10b2o$89bo3bo35b2o10b2o10bo$92b2o35bobo11b2o11bo$131bo11b2o10b2o$129bobo$129b2o! Smaller: x = 68, y = 56, rule = B35ce/S234t6c14b2o10b2o10b2o$14b2o11bo10b2o$12b2o10bo11b2o$12b2o10b2o10b2o2$50b2o$18bo30bo2bo$17b2o30bo2bo$16bo32bo3bo$17b2obo29bo2bo$18b3o30b2o10b2o$62bo3bo$30b3o28bo5bo$29bo2b2o27bo5bo$28bo5bo26bo5bo$29bo2b2o28bo3bo$30b3o18b2o10b2o$50bo2bo$18b3o28bo3bo$17b2obo28bo2bo$16bo32bo2bo$17b2o31b2o$18bo4$39bobo$40b2o$40b2o$35bo5$16bo32bo$16b2o30b2o$17b3o27bo$18bobo27b2obo$49b3o$o27bo$27bo2bo30b3o$29b2o29bo2b2o$27bo2bo28bo5bo$o27bo31bo2b2o$61b3o$18bobo$17b3o29b3o$16b2o30b2obo$16bo30bo$48b2o$49bo2$10b2o10b2o10b2o$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). AbhpzTa Posts: 473 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### 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 drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project (3,2)c/9: x = 3, y = 4, rule = B34-air5/S234-aib2o$2bo$b2o$3o!
(I hope I got that right, I've never discovered an oblique before)

2k3c30_2li
x = 3, y = 5, rule = B2e3-cey/S1c2ace3ajnrbo$obo$bo2$b2o! 1k7c71_699azwccw4aa4 x = 10, y = 9, rule = B3/S2-n34z6cb2o$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 x = 3, y = 3, rule = B2-ae3aijy4t/S02ack3inobo$2bo$b2o! EDIT2: d4c14_28092 x = 5, y = 4, rule = B2-ai/S02i3j3bo$o3bo2$bobo! Can someone help? I'm running out of steam (ships) here! EDIT3: o6c12_44y1ewh4 x = 12, y = 5, rule = B2ikn3ainqy4int5r67/S010bo$7bo$2o5bo3bo$7bo$10bo! dc8_215 x = 3, y = 3, rule = B2-ae3-i4e/S02b2o$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: 1002 Joined: August 7th, 2016, 1:48 pm Location: my computer ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project bumped also d8c28_o88f1t4z103111 x = 7, y = 7, rule = B2ek3ai6a/S2-i3-a4eijktz3b3o$3bo$3bob2o$4obo$o4bo$ob4o$2bo! d5c28_31ck8 x = 5, y = 5, rule = B2ek3ai6a/S2-i3-a4eijktz2o$o$2b2o$2bobo$3bo! d12c42_o88f1i8z010211 x = 7, y = 7, rule = B2ek3ai6i/S2-i3-a4eijkt3b2o$3bobo$3bo$4o2bo$o4bo$bo2b2o$3bo! d18c63_7d72zy15kngeqzy210111 x = 11, y = 11, rule = B2ek3ai/S2-i3-a4ijk3o$ob2o$3o$bo2$5bobo$7bob2o$5b3obo$9b2o$6b3obo$6bob3o!

EDIT:d2c14_1w5
x = 4, y = 3, rule = B2cek3k4c5y/S02i3jo2bo2$3bo! 3k17c41_33033z0gggy9gggz1443y81443 x = 20, y = 13, rule = B3-ej4e/S234i2ob2o$2ob2o8$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

toroidalet

Posts: 1002
Joined: August 7th, 2016, 1:48 pm
Location: my computer

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

A lot of strange speeds that I have found

6c/66 orthogonal:
x = 4, y = 5, rule = B2-ac3-jnqr67e8/S1c23-akny4obo$obo$obo$o2bo$o!

3c/25 diagonal:
x = 3, y = 3, rule = B34eqyz5/S233o$o$o!

c/2 diagonal:
x = 5, y = 5, rule = B2a3an4i5r/S2ae3a4a2b3o$bo$o$o2b2o$o2bo!

c/64 orthogonal:
x = 5, y = 5, rule = B2-ac3-jnqr/S1c23-akny42o$b4o$4bo$b4o$2o!

Smaller 3c/10 diagonal:
x = 4, y = 6, rule = B2-ac3-jnqr/S1c23-akny4b2o$2bo$2b2o$obo$obo$3o! 3c/212 diagonal: x = 6, y = 11, rule = B2-ac3-jnqr/S1c23-akny44bo$3b3o$3bobo$3bo$3b2o$bo$2b4o$b2ob2o$4bo$o3bo$3o! Smaller 3c/10 orthogonal: x = 2, y = 8, rule = B2en3-ckqy5akqy68/S12ei3an578bo$o2$bo$bo2$o$bo!

2c/46 diagonal:
x = 5, y = 5, rule = B2en3-ckqy5akqy68/S12ei3an578obo$bo2$3b2o$3b2o! 4c/14 orthogonal: x = 6, y = 6, rule = B2n34ckqz/S23bo$o3bo$bo3bo$3bobo$2bo2bo$3bobo!

2c/18 diagonal:
x = 5, y = 3, rule = B34eqyz5-k/S23ob3o$ob2o$2bo!

Smaller c/16 diagonal:
x = 3, y = 4, rule = B2ek3-ajny4aw/S02-ei3n4aqo2$2bo$o!

16c/38 orthogonal based repship:
x = 48, y = 15, rule = B2i34cejqwyz/S2314bo$12b4o$10b2o$11b2o17bo$29bobo11bo$28bo2bo10b2ob2o$b2o14b2o8b5o3b2o6bo3bo$o2bo13b2o7b3o7bo6bo3bo$b2o14b2o8b5o3b2o6bo3bo$28bo2bo10b2ob2o$29bobo11bo$11b2o17bo$10b2o$12b4o$14bo!

(2,1)c/105:
x = 4, y = 7, rule = B2n34cqz5ckny/S233o$bo4$2b2o$2b2o! EDIT 1, ones not found by me, in the glider database, I have a huge list of totalistic ships: 4c/6 orthogonal: x = 4, y = 5, rule = B256/S032bo2$o2bo2$2bo! 26c/60 orthogonal: x = 132, y = 22, rule = B38/S0245679b3o$29bobo45bob3o$28b2obo19bobo23bo17b2o18bo$28bo2bo16b3ob3o20b2o17bobo8bo13b3o6bo$16bo12b2o18bo2b2o21bo2b2o10bo4b2o7b3o3bo6b3ob3o4bobo$6bo7b3o4bo7b2o9b3o5bob2obo12b3o5bo6b2o7b2ob2obo6bo3bobobo5bobo4bo4b3o$5bo9b2o23b3o4b3o4b2o10b3o5bo6b2o7b2ob2obo6bo3bobobo5bobo4bo4b3o$8bo8bo3bo9bo17b2o2b3o2bo16bo2b2o10bo4b2o7b3o3bo6b3ob3o4bobo$6b3o39b4o3b3obo15b2o17bobo8bo13b3o6bo$7b2o19b2o18bo2b6obo18bo17b2o18bo$bo46b3ob3o22bob3o$obo24bobo21bobo2bo22b3o3bo22bo$bo2bobo21bobobo2bo13bob2o3b3o26bo18bo4b2o$2b3obo19bo2b2ob3o14b4ob2o2bo6b2o13bo3bo24bobo4b2o$3bo2bo14bobo2bob6obobo12bobo4b2o6b4obo9bo5bob2o4bo4bo7bo5b2o3bo$2b2o18bobo3bob2o5bo11bo5bo13bobo8b5o7b2ob2obobo4b3o3b2o5b2o$b3o16bo3bo4bobo4bo13bo2bo14bobo9b5o7b2ob2obobo4b3o3b2o5b2o$2b2o18bo4b2obobobo16bob2o10bo2bo11bo5bob2o4bo4bo7bo5b2o3bo$29bob4o17b3o13b2o14bo24bobo4b2o$30bobo20bo13bobo15bo18bo4b2o$66b3o16bo22bo$66bobobo!

Same pop and smaller bounding box for 3c/7:
x = 4, y = 5, rule = B34/S125672bo$3bo$o2bo$3bo$2bo!

11c/38 orthogonal:
x = 12, y = 15, rule = B3/S23789bo$8bobo$7b2ob2o$3o5bo2bo$o8b2o$o4$o$o8b2o$3o5bo2bo$7b2ob2o$8bobo$9bo! 2c/9 orthogonal: x = 3, y = 7, rule = B3/S246o$bo$2bo$2bo$2bo$bo$o! 4c/30 orthogonal: x = 3, y = 5, rule = B346/S013o$bo2$2bo$2o!

2c/19 orthogonal:
x = 5, y = 5, rule = B347/S02567bobo$o$2b3o$bo$3bo!

2c/25 orthogonal:
x = 5, y = 16, rule = B36/S2372o$2o4$2b2o$bo2bo$bo2bo$bo2bo$bo2bo$2b2o4$2o$2o! 2c/26 orthogonal: x = 5, y = 4, rule = B34/S025674bo$3b2o$3o$bobo!

2c/27 orthogonal:
x = 6, y = 9, rule = B347/S0372bo$o$4bo$o$obo2bo$o$4bo$o$2bo!

2c/31 orthogonal:
x = 3, y = 10, rule = B36/S0135672bo$o$bo$2o$bo$bo$2o$bo$o$2bo! c/18 orthogonal: x = 6, y = 9, rule = B3567/S01455bo$2bo$3bo2$o2b2o2$3bo$2bo$5bo! 2c/35 orthogonal: x = 8, y = 10, rule = B346/S045785bo$3b2o$4b2o$o3b2o$obo2b3o$obo2b3o$o3b2o$4b2o$3b2o$5bo!

2c/43 orthogonal:
x = 5, y = 9, rule = B346/S14682o$2bo$2bo$2bobo$obobo$2bobo$2bo$2bo$2o!

2c/15 diagonal:
x = 7, y = 7, rule = B347/S2473b2o$5bo$6bo$o3b2o$o2b3o$bob2o$2bo!

2c/21 diagonal:
x = 9, y = 9, rule = B3567/S13576bo$5bo$6b2o$7bo$8bo$bo4bo$obo2bo2bo$2b2o$4bobo!

2c/25 diagonal:
x = 5, y = 5, rule = B34/S02562b2o$b2o$2obo$obobo$3bo!

smaller c/14 diagonal:
x = 4, y = 3, rule = B3/S01243bo$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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

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

dc2_e1d5
x = 4, y = 4, rule = B2a3a4i/S2ae3ab3o$o$ob2o$obo! o4c8_1w1011 x = 7, y = 1, rule = B2ac3nr4ci5y/S0o2bob2o! d4c8_80gps x = 5, y = 5, rule = B2a3acr4ai/S2ae3a3bo2$4bo$o2b2o$2b3o!

d8c16_xg1024z12036062
x = 8, y = 8, rule = B2ae3acr4ai/S2ae3a4bo$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

toroidalet

Posts: 1002
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### 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.

x = 76, y = 76, rule = B3/S2359b2o$59b2o7$67b2o$67b2o4$56bo$55b3o$55bob2o$54b2o$54b2o$54b2o$58bo13bo$57b2o10b2o$55bobo11b2ob2o$54bo2bo13bo$55b2o12b2o2$56bo13b2o$56bo$46b2ob2o5bo16bo$46bo2bo20bobo$48b2o21bo2b2o$47bo$46bobo4$48b4o$48bo10$27b2o2bo$27bo2bo$29bobo3b2o$27b3o5bo$27bo7bo$35bo3$16b3o3bo$14b5o2bobo$13b2o8bob3o$14b2o4b3o$15bo3b2o$2o$2o7$8b2o$8b2o$20b2obo$20b2obobo2bo$22bo2bo3bo$19bobo6bo$21bo5bo$29bo$29bo! More ships: x = 41, y = 48, rule = B358/S23816$15bo$14bobo$14bobo$16bo$14bo$13b3o4b3o$19bob2o$19bobob2o$19bob2o$13b3o4b3o$14bo$16bo$14bobo$14bobo$15bo!

x = 8, y = 8, rule = B3457/S4563b4o$b6o$b7o$5obo$4ob3o$3ob3o$7o$2bobo! Also, some soups that emit velocities that don't appear to be documented yet: x = 16, y = 16, rule = B2i3ai4/S23bboboooooobobbbb$obooobbboboobbbb$obobbboobboobobb$bobbooobboooobob$obbbobbbbbbooobo$bbooobobbbbobobb$boobbbbobbboboob$boobboboboooobbo$bbooobobbobboboo$bobboboboooobbob$boboboboboboobbo$oboooooooobooobo$booboooooboooooo$bbbooboboboooboo$boboobbbboobbbbb$obobboobbbbbbobb!

x = 16, y = 16, rule = B3678/S35678ooobobobbbboobob$bboobboboooobbbb$bobbboobbooboooo$oboobbbbbbbbobbb$bbobboobbobbobbo$booooooboooboobb$bbobbbbooooobobb$bbooooobbooobboo$obbobbooboobbbbb$ooobbbbbbooboobo$bobboboobbobobbo$obbbbbbbboooobbo$bbbooooooooboboo$bbboobbobobbbooo$obobooooboboobbo$boobobboobbbbooo! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3466 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I am just trying to fill in the gaps in the list, so these are probably not optimal, unfortunately a lot of my minimum size ships for totalistic rules are B0 rules. Do you want to see the list, drc? C/21 diagonal: x = 10, y = 10, rule = B345/S055bobobo$bo3bo$5bo3bo$5bo3bo$5bo3bo$6o$7bobo$o5b2o2$ob3obo! C/23 diagonal: x = 4, y = 4, rule = B3567/S024672o$o2bo2$bo! C/24 diagonal: x = 6, y = 3, rule = B36/S013562bo2bo$4obo$4bo! C/27 diagonal: x = 8, y = 8, rule = B356/S134bob2o$3b2o$5bo$bo$2o$2bo$o$o!

C/29 diagonal:
x = 11, y = 11, rule = B3678/S13489b2o$9b2o2$6bobo$6bo$7bo$3b2o2bo$5b3o$3bo$2o$2o! Smaller c/30 diagonal: x = 4, y = 3, rule = B3567/S1256ob2o$o2bo$bobo! c/33 diagonal: x = 17, y = 17, rule = B36/S0356783bo$b4o2bo$b8o$12o$b11o$2b11o$2b11o$b12o$2b11o$3b12o$3b11o$3b12o$5b12o$9b8o$9bob4o$12b2o$12b2o! 2c/68 diagonal: x = 6, y = 4, rule = B35/S01352bo$2bobo$4o$3bobo!

c/37 diagonal:
x = 12, y = 12, rule = B345/S056bo$11bo$4b2ob3obo$11bo$2bo5b4o$2bo$o6b4o$2bo3b2o$2bobobo$2bobobo$4bobo$b4o! c/38 diagonal: x = 4, y = 5, rule = B345/S0145b2o$3o$2bo$obo$3bo! c/45 diagonal: x = 8, y = 8, rule = B37/S0145674bo$2b2o$b5o$b6o$ob2ob2o$2b5o$3b5o$6bo!

2c/112 diagonal:
x = 6, y = 4, rule = B34/S0145obo$o$b2obo$2o3bo! c/59 diagonal: x = 8, y = 8, rule = B34/S01564bo$3bo$6bo$bo$o5b2o2$2bobobo$4bo! c/62 diagonal: x = 7, y = 7, rule = B345/S0457bobo$5bo$b2ob2o$o5bo$2bo$b2o2b2o$3bobo! c/86 diagonal: x = 7, y = 6, rule = B346/S01574bo$3o$o5bo$6bo$obo$4bo!

c/93 diagonal:
x = 7, y = 7, rule = B36/S24562bo2bo$2bob2o$7o$2bo$b2o$3o$2bo!

c/116 diagonal:
x = 6, y = 6, rule = B346/S014582bobo$bob2o$bo2b2o$2bob2o$o2bo$bo! c/118 diagonal: x = 8, y = 8, rule = B347/S3562bo2bo$b2obo$5ob2o$2bobobo$b3o2bo$o$2b3o$2bo!

EDIT 1:

12c/50 orthogonal:
x = 6, y = 8, rule = B2-ac3-jnqr/S1c23-akn43o$o2$4b2o$3ob2o$obobo$obobo$2b3o!

Better c/7 orthogonal:
x = 2, y = 5, rule = B345/S016o2$2o2$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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

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

C/2 diagonal:
x = 3, y = 4, rule = B2ac/S12bo2$b2o$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

A for awesome

Posts: 1879
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### 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:
, y = 6, rule = B3567/S0145o7bo$4bo$2bobobo$bo5bo2$4bo!!

c/21:
x = 5, y = 8, rule = B36/S0135bobo$2bo$2bo$bobo$bobo$o3bo2$2bo!

c/22:
x = 8, y = 6, rule = B3567/S1367b2o2b2o$obo2bobo$2bo2bo3$3b2o! c/24: x = 7, y = 12, rule = B2e3ai4arw5678/S3-an4ar5i6783bo$bobobo$2b3o$7o$b5o$7o$7o$2b3o$bobobo$2b3o$3bo$3bo!

c/29:
= 7, y = 4, rule = B345/S04782b3o$ob3obo$b5o$o5bo! c/30: x = 9, y = 5, rule = B346/S3578bo5bo$b2obob2o$3o3b3o$4bo$bo5bo! c/44: x = 7, y = 8, rule = B34568/S4582b3o$2obob2o2$o5bo$7o$7o$bobobo$bobobo! c/64: x = 5, y = 5, rule = B2-ac3-jnqr/S1c23-akny4b3o$bobo$bobo$2ob2o$o3bo! c/2068: (I'm surprised you forgot this one, unless you're excluding the ridiculous ships) x = 8, y = 8, rule = B34578/S456bobobo$2b4o$2ob2o2bo$4obobo$2ob3o$8o$2b4o$b3obo!

c/5648: (this one even more so)
x = 12, y = 14, rule = B3457/S45685b2o$3bo4bo$3b2o2b2o$b3o4b3o$b3o4b3o$2ob6ob2o$3ob4ob3o$ob3o2b3obo$2ob6ob2o$obobo2bobobo$2b2ob2ob2o$2b8o$4b4o$4bo2bo! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3466 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project The c/64 is only in this thread, found by me, so it is already been posted, I am not sure why it ended up in your post. I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I have added all of the discoveries, apologies for the wait. The only ship I contributed is this dc28: x = 4, y = 5, rule = B3-n4c8/S2-i34-ar6ci2o$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 drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Smallest Spaceships Supporting Specific Speeds (5s) Project c/20 orthogonal: x = 4, y = 5, rule = B35678/S1247obo$2bo$o2bo$2bo$obo! c/23 orthogonal: x = 4, y = 7, rule = B3/S0145678bo$bo2$2obo2$bo$bo! c/26 orthogonal: x = 7, y = 6, rule = B3457/S045782bobo$4ob2o$o5bo$o5bo$4ob2o$2bobo!

EDIT 1: 3c/30 diagonal
x = 5, y = 5, rule = B3-q4nrt5nr6i/S2-c3-q4r5cejno2bo$4bo$2o$bobo$2b3o!

EDIT 2: 13c/512 diagonal
x = 26, y = 27, rule = B2-ac3-jnqr5y67e8/S1c23-akny4o2bo$o2bo$4o$b2o13$18bo$8bobo5bob3o$10bo5bo3bo$7bo8b2o2bo$7b3o2bo4bobo2b2o$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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

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

Almost a p3 knightship:
x = 4, y = 3, rule = B2acn3r4at/S01e2ac3ir3o$bobo$obo!

Can anyone find a real one?
EDIT: 2c/3 orthogonal:
x = 3, y = 2, rule = B2ac3ae4t5e/S1c2i3ibo$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 A for awesome Posts: 1879 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### 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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### 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 A for awesome Posts: 1879 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### 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: x = 3, y = 3, rule = B2a/S1e2i3o2$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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

### 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

A for awesome

Posts: 1879
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

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