Smallest Spaceships Supporting Specific Speeds (5s) Project

For discussion of other cellular automata.

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

I found a smaller 2c/6 with average population 3.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...:
x = 2, y = 3, rule = B2-a3cinq4nw/S1bo2$2o! Compare this with the old 2c/6 with an average population of 7: x = 2, y = 3, rule = B2ce3ejnr4ceinwy5acn6an7e/S01e3j4cejkrtyo$bo$o! In the new rule, this happens to the old spaceship: x = 2, y = 3, rule = B2-a3cinq4nw/S1o$bo$o! It can be stabilized into a 12c/24, but suboptimal... 10c/56: x = 7, y = 7, rule = B2-a3cinq4enw/S1e2bo$o2b2o$2b2o$o5bo$bo2b3o$4bo$6bo! The rule also supports the c/7 I mentioned earlier. 8c/16: x = 13, y = 11, rule = B2-a3cinq4enw/S123b3o$b2o2bo$6b3o$o$bo9bo$2bo9bo$bo9bo$o$6b3o$b2o2bo$3b3o! Spaceship, anyone? It's a 16c/32 gone wrong: x = 3, y = 2, rule = B2-a3cinq4nw/S12bo$obo!
Replicator!
x = 3, y = 3, rule = B3/S234y2bo$3o$bo!

wwei23

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

wwei23 wrote:I found a smaller 2c/6 with average population
3.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...:

ship

This is legit, but do not spam 3s. It causes code tags to be shifted over. There is also a 3-cell 8c/16. The collection exists for a reason, and check it before posting. You don't need to post evolutions of patterns in rules.
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toroidalet

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

toroidalet wrote:
wwei23 wrote:I found a smaller 2c/6 with average population
3.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...:

ship

This is legit, but do not spam 3s. It causes code tags to be shifted over. There is also a 3-cell 8c/16. The collection exists for a reason, and check it before posting. You don't need to post evolutions of patterns in rules.

I checked the wrong file, it seems.
Replicator!
x = 3, y = 3, rule = B3/S234y2bo$3o$bo!

wwei23

Posts: 642
Joined: May 22nd, 2017, 6:14 pm
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Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

36c/84:
x = 70, y = 33, rule = B36n/S234y5y7e12bo$11bobo$11bob2o$13bo$9bo3bo51b3o$8bobobo50bo4b2o$9b3o51bo5bo$63bo5bo$62b2o4bo$13bo48b2o3bo$8bo2b2ob2o47b3o$7b4o2bo50bo$6bo$5bo3b2o48b2o$6b4obo47b2o$10b2o$54b2o$15bobo33b3o2bo$14b2o34bo3b2o7bo$14bo47b3o$19b2o26b2o3b2o7b2o3bo$16bo2b2o26b2o2b2o3bo4b2o4bo$2o14bo7b2o21bobo6bo5bo5bo$2o46bo7bo5bo5bo$48bo13bo4b2o$5bo24bo33b3o$4b3o22bobo$3b2o3bo19b2ob2o$3b2o4bo19bobo$4bo5bo19bo$4bo5bo$4bo4b2o$6b3o!

152 cells
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toroidalet

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c/32:
x = 3, y = 4, rule = B2ei3aijnq4nrtyz5knq6ak7e/S1c2-ei3kq4anrwy5ackry6ck2bo$2o$bo$bo! Rhombic Posts: 768 Joined: June 1st, 2013, 5:41 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I have a page for the first 7 periods, that will eventually have the first ten, with all known and unknown, but theoretically possible speeds. Feel free to add in the rest from the uploaded files. I will try to add in some of it. Things to work on: - An Isotropic version of All_Speeds - Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y - Find a (3,1)c/5 ship in a Non-totalistic rule (someone please search the rules) AforAmpere Posts: 267 Joined: July 1st, 2016, 3:58 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project AforAmpere wrote:I have a page for the first 7 periods, that will eventually have the first ten, with all known and unknown, but theoretically possible speeds. Feel free to add in the rest from the uploaded files. I will try to add in some of it. Looks nice so far! Still rooting for the Niemiec-style table idea but let's get the fundamentals out of the way first. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1470 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Will LtL rules be allowed in the collection? There's some pretty exotic speeds in said rules. 2c/n spaceships project Current priorities: see here muzik Posts: 2595 Joined: January 28th, 2016, 2:47 pm Location: Scotland Re: Smallest Spaceships Supporting Specific Speeds (5s) Project muzik wrote:Will LtL rules be allowed in the collection? There's some pretty exotic speeds in said rules. If we allow LtL rules, then we have to allow faster-than-light speeds, which is just going to make the database ten times as big. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1470 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Smallest Spaceships Supporting Specific Speeds (5s) Project BlinkerSpawn wrote: muzik wrote:Will LtL rules be allowed in the collection? There's some pretty exotic speeds in said rules. If we allow LtL rules, then we have to allow faster-than-light speeds, which is just going to make the database ten times as big. Gotta catch em all. Although, if it does become a major enough problem, we could restrict the database to c or slower. 2c/n spaceships project Current priorities: see here muzik Posts: 2595 Joined: January 28th, 2016, 2:47 pm Location: Scotland Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Let's not include LTL or Generations, that would be too much. Things to work on: - An Isotropic version of All_Speeds - Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y - Find a (3,1)c/5 ship in a Non-totalistic rule (someone please search the rules) AforAmpere Posts: 267 Joined: July 1st, 2016, 3:58 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project muzik wrote:Gotta catch em all. Can I poke you now? Replicator! x = 3, y = 3, rule = B3/S234y2bo$3o$bo! wwei23 Posts: 642 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Three cell knightship (p7): x = 3, y = 5, rule = B2-ac3ijn5y/S02co2$2bo2$2bo! 13c/125 x = 5, y = 3, rule = B2n34cqy5acik6ace7c/S023-cjnr4n5eo3bo$3b2o$o3bo! Last edited by Rhombic on August 25th, 2017, 8:35 am, edited 1 time in total. Rhombic Posts: 768 Joined: June 1st, 2013, 5:41 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I found a marginally better c/4 orthogonal, by average population, beating the previous record holder by 3/4 of a cell: x = 3, y = 2, rule = B3aei4i/S12acobo$bo!

EDIT:
That's a little better:
x = 2, y = 3, rule = B3aei4i/S12aco$bo$o!

A 3 cell c/3 with same average population as the best known, but with smaller maximum population:
x = 2, y = 3, rule = B2ce3e4a/S2ac4to$bo$o!
Last edited by wwei23 on August 24th, 2017, 3:30 pm, edited 1 time in total.
Replicator!
x = 3, y = 3, rule = B3/S234y2bo$3o$bo!

wwei23

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

Rhombic wrote:Three cell knightship (p7):
x = 3, y = 5, rule = B2-ac3ijn5y/S02co2$2bo2$2bo!

Is this the first three-cell knightship?
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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

Rhombic wrote:Three cell knightship (p7):
x = 3, y = 5, rule = B2-ac3ijn5y/S02co2$2bo2$2bo!

Is this the first three-cell knightship?

Obviously not, since there's already plenty in the collection.
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2595
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Beware xqN_2a

c/7
x = 4, y = 2, rule = B2cei3enqy4acqr5-ekr6ein7/S01c2-ek3aei4aqt5ijn6nbo$o2bo! c/11 x = 4, y = 2, rule = B2-ai3ajnr4ert5ajkq6k7c8/S2aek3cj4jnqtz5aky6ci7cbo$o2bo!

c/12
x = 4, y = 2, rule = B2-an3-ikqy4ainqr5cjk6ain7e/S2ae3jr5kry6e8bo$o2bo! 3c/12 x = 4, y = 2, rule = B2cei3ae4iqwz5cek8/S03ny4enw5i6ak7cbo$o2bo!

c/9
x = 4, y = 2, rule = B2-an3aj4crty5ijy/S2aek3aejky4nqtwz5any6-ck8bo$o2bo! c/14 x = 4, y = 2, rule = B2ce3r4artyz6eik/S01c2a3aciry4ijq5acn7cbo$o2bo!
4c/14
x = 4, y = 2, rule = B2cei3ckn4-ekr5cjqry6-ci7e8/S01c2kn3aj4jnqr5iy6acbo$o2bo! 2c/10 x = 4, y = 2, rule = B2-an3acej4aijqryz5-acej6in78/S2ae3jbo$o2bo!

c/16
x = 4, y = 2, rule = B2cen3ry4a5aknr6ain8/S01c2-ek3-eky4cijw5cry6cek7cbo$o2bo! c/20 x = 4, y = 2, rule = B2-ai3aj4er5aeqy6n/S2aen3-cinq4acjqwy5kn6aci7cbo$o2bo!

2c/18
x = 4, y = 2, rule = B2-an3-einr4ciknqrt5aky6aei7/S2-cn3jq4ej5qy6ckbo$o2bo! 2c/22 x = 4, y = 2, rule = B2cek3aj4ikrz5ceiq6n7e/S2ae3jky4j5r6inbo$o2bo!

2c/24
x = 4, y = 2, rule = B2-ai3ajr4cirt5n6k/S2ae3jkqr4ejqrwz5cjr6ikn7cbo$o2bo! 2c/70 x = 4, y = 2, rule = B2cek3ajn4jr/S2ae3jk4-aikr5ajk6-in7cbo$o2bo!

2c/32
x = 4, y = 2, rule = B2-ai3ajk4rty7c/S1e2ae3jkq4cjtz5-ekqr6cnbo$o2bo! 2c/54 x = 4, y = 2, rule = B2-an3aj4ackryz5anry/S2-ci3cj4w5ci6ce7bo$o2bo!

c/30
x = 4, y = 2, rule = B2cek3aj4nr6en7c/S2ae3ijk4a5cey6k8bo$o2bo! c/34 x = 4, y = 2, rule = B2-an3ajqr4eikqrwz5cij6aen78/S2aen3j4az6kbo$o2bo!

c/26
x = 4, y = 2, rule = B2cek3ajkr4cinrz5jknqy6ik7e/S2aei3ijky4eqrz5aciq6-ck7cbo$o2bo! 3c/26 x = 4, y = 2, rule = B2-an3-ikn4ejqrtwz5-cknq6ikn7e8/S2ae3cej4wy5enr6ebo$o2bo!

c/42
x = 4, y = 2, rule = B2-ai3aej4enrtz5y8/S2aen3j4wz5jrbo$o2bo! 8c/100 x = 4, y = 2, rule = B2cek3ajnq4kr5an6n7c/S2-cn3cjkq4eqy5ijq6i7bo$o2bo!

4c/32
x = 4, y = 2, rule = B2cek3ajq4-ijnt5-cy6eik7/S2aen3jk4nr5ek6c8bo$o2bo! 2c/38 x = 4, y = 2, rule = B2-an3-eikq4aiknqrz5eijkr6aek/S2aei3jk4atwz5jnr6n7ebo$o2bo!

3c/24
x = 4, y = 2, rule = B2-ai3-ciq4-aeijq5jky6an7/S2ae3j4czbo$o2bo! 2c/18 x = 4, y = 2, rule = B2cek3acij4ckr5cr6-ak7/S2aei3ijy4iqrtwyz5acnqy6cen7e2bo$o2bo!

c/10d
x = 4, y = 2, rule = B2-an3-acjq4cejnqry5ajr6-kn7c/S1e2ae3ckq4jqwy5cqy6cn2bo$o2bo! More 3-cell knightships (2,1)c/12 x = 4, y = 2, rule = B2cek3-cinr4jnry5aejn6aik/S2ae3ijqy4nry5ijny6-ak7e8bo$o2bo!

(2,1)c/19
x = 4, y = 2, rule = B2-ai3ajr4qrtw5qr6e7c/S2aen3eij4r5nrbo$o2bo! (2,1)c/22 x = 4, y = 2, rule = B2cek3aj4r/S2aei3ejk4cwy5ceqy6i7cbo$o2bo!

3-cell camelship
(3,1)c/13
x = 4, y = 2, rule = B2cek3aj4r5i/S2aen3jkqy4c5akn6ebo$o2bo! Last edited by Rhombic on August 25th, 2017, 6:10 am, edited 1 time in total. Rhombic Posts: 768 Joined: June 1st, 2013, 5:41 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project The other c/2 with average population 3.5: x = 2, y = 3, rule = B2c3ae/S1c3ebo$o$bo! Replicator! x = 3, y = 3, rule = B3/S234y2bo$3o$bo! wwei23 Posts: 642 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe Re: Smallest Spaceships Supporting Specific Speeds (5s) Project Smaller c/18 by minimum bounding box: x = 4, y = 1, rule = B2aci3a4ikqwy6in/S02en3cjny4eijkrw5acij7eob2o! 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: 1409 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Smallest Spaceships Supporting Specific Speeds (5s) Project I am not really focusing on bounding box or min population, but feel free to add it to the wiki version, I have up to period 8 on there, and it would be great if someone would add period 9 and 10, using the updated files. Things to work on: - An Isotropic version of All_Speeds - Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y - Find a (3,1)c/5 ship in a Non-totalistic rule (someone please search the rules) AforAmpere Posts: 267 Joined: July 1st, 2016, 3:58 pm Re: Smallest Spaceships Supporting Specific Speeds (5s) Project 10c/15: x = 2, y = 3, rule = B2acn3aey4aejrz5r6an7c/S1c2i3i4jt5qbo$o$bo! 8c/12: x = 2, y = 3, rule = B2acn3aen4ceiqtz5c6ei7/S1c2ei3cikr4cjknqwy5aiqy6ckn7e8bo$o$bo! 6c/9: x = 2, y = 3, rule = B2acn3aeqy4eqyz5aiknr6c7e/S1c2i3-cejq4aiknrz5eikry6ek7co$2o$o! EDIT: 3-cell 6c/9: x = 2, y = 3, rule = B2ack3ae4rw5er7e/S1c2eik3ikr4ceqty5cjkqy6-a7c8bo$o$bo! EDIT 2: Placed all of the ships in the correct orientation. 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: 1409 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Smallest Spaceships Supporting Specific Speeds (5s) Project 5c/10 diagonal: x = 3, y = 4, rule = B2acn3cen4qt5aik6cek7e/S12a3-knqr4ntwz5knr6c7e2bo2$b2o$o! 7c/14 diagonal: x = 3, y = 4, rule = B2ack3en4ckntyz5cr6ek8/S12bo2$b2o$o! EDIT: 6c/12, in a B1e rule: x = 4, y = 4, rule = B1e2cek3acry4jkqr5cjny6aei7e/S12-ce3ej4wy5cir6c7obo$o2bo2$2b2o! 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: 1409 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Smallest Spaceships Supporting Specific Speeds (5s) Project c/46 one cell reduction: x = 9, y = 10, rule = B34568/S04582bobo$3bob2o$obo3bo$4b2ob2o$6b2o$6b2o$4b2ob2o$obo3bo$3bob2o$2bobo!
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2595
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

Here are the perfect speeds below c/144 which do not currently appear in the collection, and seem to be unknown without the use of the infinite speed non-totalistic rules:

c/58 - nonec/62 - nonec/65 - nonec/71 - nonec/72 - nonec/76 - nonec/77 - nonec/78 - nonec/82 - nonec/84 - nonec/88 - nonec/91 - nonec/93 - nonec/94 - nonec/95 - nonec/96 - nonec/97 - nonec/99 - nonec/100 - nonec/101 - nonec/102 - nonec/103 - nonec/104 - nonec/105 - nonec/106 - nonec/107 - nonec/108 - nonec/109 - nonec/110 - nonec/111 - nonec/112 - nonec/113 - nonec/114 - nonec/115 - nonec/116 - nonec/117 - nonec/118 - nonec/119 - nonec/120 - nonec/121 - nonec/122 - nonec/123 - nonec/124 - nonec/125 - nonec/126 - nonec/127 - nonec/128 - nonec/129 - nonec/130 - nonec/131 - nonec/132 - nonec/133 - nonec/134 - nonec/135 - nonec/136 - nonec/137 - nonec/138 - nonec/139 - nonec/140 - nonec/142 - nonec/143 - nonec/144 - none

and here are the perfect speeds without 3-cell examples:
c/46 - 28 cellsc/59 - 34 cellsc/63 - 36 cellsc/64 - 13 cellsc/66 - 16 cellsc/70 - 18 cellsc/86 - 22 cellsc/89 - 34 cellsc/92 - 13 cellsc/98 - 24 cellsc/141 - 34 cells
2c/n spaceships project

Current priorities: see here
muzik

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

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

c/3 diagonal?
EDIT: Nope, it's 2c/7.

x = 5, y = 5, rule = B3/S234wbo2bo$o3bo$4bo$3bo$3o!
Last edited by Hdjensofjfnen on August 27th, 2017, 3:54 pm, edited 1 time in total.
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Pattern of the month (September 2017):
#C [[ AUTOFIT ]]x = 7, y = 9, rule = B34tw/S232o$2o$4b2o$6bo$3bo2bo$6bo$4b2o$2o$2o!

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