Difference between revisions of "LifeWiki:Spaceship Search Status Page"

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((2,0)c/5 asymmetric up to 35 cells and even-symmetric up to 70 cells)
(Add 2c/5 even census to pop 74)
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* All (2,0)c/5 ships up to a population of 35 cells (2 ships: [[30P5H2V0]] and [[34P5H2V0]])<ref name="post220821" />
* All (2,0)c/5 ships up to a population of 35 cells (2 ships: [[30P5H2V0]] and [[34P5H2V0]])<ref name="post220821" />
* All (2,0)c/5 odd-symmetric ships up to a population of 57 cells (2 ships: [[44P5H2V0]] and {{LinkCatagolue|xq5_ggg035d2sg0gs2d530gggz3sfcwc8r2o2r8cwcfs3|name=this ship|style=raw}})<ref name="post181755" />
* All (2,0)c/5 odd-symmetric ships up to a population of 57 cells (2 ships: [[44P5H2V0]] and {{LinkCatagolue|xq5_ggg035d2sg0gs2d530gggz3sfcwc8r2o2r8cwcfs3|name=this ship|style=raw}})<ref name="post181755" />
* All (2,0)c/5 even-symmetric ships up to a population of 70 cells ([[70P5H2V0|1 strict ship]])<ref name="post220821" />
* All (2,0)c/5 even-symmetric ships up to a population of 74 cells (3 strict ships: [[70P5H2V0]], {{LinkCatagolue|xq5_y4j55ewe55jzy1gqf46ay0a64fqgz7pvow4x11w11x4wovp7z01yi1|name=this ship|style=raw}}, and {{LinkCatagolue|xq5_y243hf33fh34z27fs0s3ooy0oo3s0sf72zx12d9fy2f9d21|name=this ship|style=raw}})<ref name="post221244" />
* All (2,0)c/5 ships up to width 12 ({{LinkCatagolue|xq5_rhlmggz3gggoar7zxpdm57zwmk8izw1ghe2zwmdb|name=1 width-10 ship|style=raw}}; infinitely many width-11 ships; infinitely many width-12 ships)<ref name="knightt-results" />
* All (2,0)c/5 ships up to width 12 ({{LinkCatagolue|xq5_rhlmggz3gggoar7zxpdm57zwmk8izw1ghe2zwmdb|name=1 width-10 ship|style=raw}}; infinitely many width-11 ships; infinitely many width-12 ships)<ref name="knightt-results" />
* All (2,0)c/5 odd-symmetric ships up to width 17 ([[44P5H2V0|1 width-15 ship]]; infinitely many width-17 ships)<ref name="knightt-results" />
* All (2,0)c/5 odd-symmetric ships up to width 17 ([[44P5H2V0|1 width-15 ship]]; infinitely many width-17 ships)<ref name="knightt-results" />
Line 1,389: Line 1,389:
|author = Keith Amling
|author = Keith Amling
|date  = November 1, 2025
|date  = November 1, 2025
}}</ref>
<ref name="post221244">{{LinkForumThread
|format = ref
|p      = 221244
|title  = Re: LLSSS min pop search results spam
|author = Keith Amling
|date  = November 10, 2025
}}</ref>
}}</ref>
</references>
</references>

Revision as of 19:38, 11 November 2025

Conventions

The tables below give the minimum orthogonal width and height of the envelope of a spaceship of the specified type. This is found by simulating a period-p spaceship for p iterations, with the initial phase chosen to minimise the width or height.

For types where the minimum is known, references point to the proof of minimality rather than the discovery of the ship possessing it. A stamp collection of minimum-width ships is given below the table.

Symmetry considered is in the line parallel to a spaceship's direction of motion.

Known spaceships by width

The width in the following table is the width of the envelope of the pattern after it has been run through every phase in its period and minimized over all starting phases. Further, the width is the direction perpendicular to the orthogonal direction of greatest displacement. For example, for a (2,1)c/6 ship the width is the dimension perpendicular to the direction in which the ship is displaced by 2 cells.

Note that symmetric diagonal spaceships always have an odd diagonal width (measured by half-diagonals), but since this table records the orthogonal width of the ship, the minimum width for such a ship might not be odd. The same applies to glide symmetric diagonal ships, although these ships can have odd or even width depending on whether their diagonal placement is even or odd respectively.

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 21 21 28 21 - -
(1,0)c/3 12 15 12 17 - -
(1,0)c/4 10 13 16 17 - -
(1,1)c/4 3 7[n 1] - 7[n 1] - 3
strict 18[1] 19[1]
(2,0)c/4 5 11 12[n 1] 11 5 12[n 1]
strict 20[2] 16[1]
(1,0)c/5 11 19 18 19 - -
(1,1)c/5 13[3] 19 < w ≤ 24 - 19 < w ≤ 24 - -
(2,0)c/5 10 15 18 15 - -
(1,0)c/6 12[4] 19 18 21 - -
(1,1)c/6 10 < w ≤ 35 13 < w ≤ 36 - 13 < w - 11 < w ≤ 35
(2,0)c/6 12[5] 17[2] 18[2][6] 19[2] 17 18[6]
(2,1)c/6 15[3] < w ≤ 31 - - - - -
(3,0)c/6 21[7] 21 28 21 - -
(1,0)c/7 10[8][9] 19[9] 22[10][n 1] 21[8][9][n 1] - -
(1,1)c/7 9 < w ≤ 27 11 < w ≤ 27 - 11 < w - -
(2,0)c/7 11[11][12] 23[2] 18 25[12][13] - -
(2,1)c/7 11[14] - - - - -
(3,0)c/7 14[15] 29[16] 28[15] 31[15][17] - -
(1,0)c/8 10[18] 19[19] 20[20] 21[18] - -
(1,1)c/8 7 < w ≤ 21 10 < w - 10 < w - 7 < w ≤ 21
(2,0)c/8 9[2] 15[2][21] 18[2][21] 17[2][21] 13 14
(2,1)c/8 8 - - - - -
(2,2)c/8 8 < w ≤ 24 8 - 8 8 -
(3,0)c/8 11[14] 21[14] 22[22] 23[14] - -
(3,1)c/8 12[14] - - - - -
(4,0)c/8 11[2] 17[2] 20[2] 19[2] 17 20[2]
(1,0)c/9 8[23] 15[23] 16[23] 17[24] - -
(1,1)c/9 6 8 - 8 - -
(2,0)c/9 9[24] 17[24] 18[24] 19[24] - -
(2,1)c/9 7 - - - - -
(2,2)c/9 8 11 - 11 - -
(3,0)c/9 11[25] 17[2] 16[5] 17[2] - -
(3,1)c/9 8 - - - - -
(4,0)c/9 11[15] 23[26] 24[27] 23[15] - -
(1,0)c/10 6[28] 11[28] 10 13[28] - -
(1,1)c/10 7 7 - 7 - 7
(2,0)c/10 7 < w ≤ 11 13 < w ≤ 19 14 < w ≤ 20 15 < w ≤ 19 13[29] < w ≤ 19 14[29] < w ≤ 20
(2,1)c/10 6 - - - - -
(2,2)c/10 6 6 - 6 6 -
(3,0)c/10 9[30] 17[31] 18[30] 19 - -
(3,1)c/10 7 - - - - -
(3,2)c/10 8 - - - - -
(4,0)c/10 10[5] 15[2] 22[32] 21[2] 15[33] 16[33]
(4,1)c/10 8 - - - - -
(5,0)c/10 11[5] 19[2] 22[5] 19[2] - -
(1,0)c/11 6[34] 11[35] 12[35] 11[34] - -
(1,1)c/11 ? ? - ? - -
(2,0)c/11 7 11[28] 12[28] 13[28] - -
(2,1)c/11 ? - - - - -
(2,2)c/11 ? ? - ? - -
(3,0)c/11 8 15[24] 16 17 - -
(3,1)c/11 ? - - - - -
(3,2)c/11 ? - - - - -
(4,0)c/11 9[36] 17[36] 18[36] 19[36] - -
(4,1)c/11 ? - - - - -
(5,0)c/11 10[36] 19[36] 20[36] 21[36] - -
(1,0)c/12 6[24] 11[24] 12[24] 13[24] - -
(2,0)c/12[37] 5 < w ≤ 63 9 10 11 9[38] 8
(3,0)c/12[37] 7 11 12 13 - -
(4,0)c/12[37] 7 13 < w ≤ 17 14 15 ? ?
(6,0)c/12[37] 8 11 16 15 ? ?
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2o$207bo275b2o4b3o4b2o398b2obobob2o31b2obobob2o$207bobo273b2o3bo3bo3b 2o396bobob2ob2obobo28b2o2bobo2b2o$206bo3bo271b3o4b3o4b3o394bo3bo5bo3bo 29bo5bo$205bo2b3o269b2o17b2o393b2o9b2o$205bo273bo5b2o2bobo2b2o5bo394bo 7bo$894bo11bo$209bob2o266bo2bob3ob2ob2ob3obo2bo390b2o13b2o$207b2o2b3o 271b3o5b3o396bo2bo9bo2bo$209b3o2bo272b3ob3o397bo17bo$209bo5bo266bo4b2o bob2o4bo393bo4b2o3b2o4bo$208b2o3b2o273bo3bo401b2ob2o3b2ob2o$209b2o687b 2ob2o$207bo3bo276b2ob2o$207bo4bo684b3ob3o$208bo3bo$208bo2bo2$207b2o2b 2o$207b2o2b2o$205b2o6b2o$204bob2o4b2obo$204bo10bo$205bo8bo$204b2o2b4o 2b2o$205bobo4bobo$206b2o4b2o$205bo3b2o3bo233bo3bo74bo5bo135b2o121bo14b o$205bo8bo231b9o71b3o3b3o133bo2bo119bobo12bobo$204bo10bo309b2o2bobo2b 2o132bo2bo118b2ob2o10b2ob2o$205bo8bo234b3o73b2o2bobo2b2o131bo4bo117b2o 2bo10bo2b2o$448b5o73bo2bobo2bo132bo4bo120bobo8bobo$208b2o2bo232b2o7b2o 69bo3bobo3bo132b4o121bobo8bobo$208bo3b2o230b3o7b3o68bo4bo4bo131b2o2b2o 117b2obob2o6b2obob2o$206bo3b2o231bo13bo67bo9bo131bo4bo118bobo12bobo$ 206bo3b2o313bo9bo131bo4bo119b2ob2o6b2ob2o$205bo6b2o232b3o3b3o70bo9bo 257bob2obo2bob2obo$204bo2bo2b4o229b2o11b2o67bo3b3o3bo260bobo2bobo93bo 5bo27bo17bo23b3o9b3o$205b2o2bo3bo229b2o4bobo4b2o69bo2bo2bo134b4o121b2o bobo2bobob2o89bobo3bobo26bo17bo23bo2bo7bo2bo$210bo235bobo3bobo72bobobo bo135b2o122b2o3b4o3b2o88bo2bo3bo2bo24bobo15bobo21b2o13b2o$445b2o7b2o 71bo5bo260bo3bo2bo3bo90b2o5b2o26bo17bo20b2obo3bo5bo3bob2o$446bobo3bobo 69bo2bo5bo2bo258bo2bo2bo2bo126bo17bo23b3ob2o3b2ob3o$445bo2bo3bo2bo67b 2o11b2o255b4o6b4o85bo5bo3bo5bo21bo4bo9bo4bo18bo21bo$445bobobobobobo70b 2o5b2o256b2o2bo8bo2b2o82bobo3bo5bo3bobo25b2o7b2o24bobob5o3b5obobo$444b 3o7b3o65bob2ob2o3b2ob2obo251bo3bo10bo3bo80bo2bo3b2o3b2o3bo2bo18b2o4bob 2o3b2obo4b2o18bo3bo2b2o3b2o2bo3bo$444b3o7b3o65bo5b2ob2o5bo251bo4bo8bo 4bo80bo2b2o3bo3bo3b2o2bo26b2o3b2o26bo3b3o7b3o3bo$444b3o7b3o70bo5bo256b o4b2o6b2o4bo129bobo28bo4bo9bo4bo$445b2o7b2o70bo2bobo2bo256b2o2bo8bo2b 2o122b3o3bobobobo3b3o24b3o7b3o$445b2o7b2o71bobobobo257b2obo10bob2o128b obobobo29bo2b2o5b2o2bo$446b3o3b3o73bo3bo398bobo4b2ob2o4bobo26b2o5b2o$ 446b3obob3o476bobo13bobo22b2o4bo3bo4b2o$449bobo339b2o14b2o123bo15bo22b o3bo3bobo3bo3bo$447bob3obo336bo2bo12bo2bo122bo15bo19b2ob3obobobobobobo b3ob2o$447bo5bo336bo2bo12bo2bo126bo7bo22bo5b2o4bobo4b2o5bo$447bo5bo 337b2o14b2o125b2obo5bob2o19bo4b2o15b2o4bo$444b3obo3bob3o477bo2bo5bo2bo 19b3o8bo5bo8b3o$444bo2bob3obo2bo476b2ob2o5b2ob2o27b2o7b2o$444bob2o5b2o bo477bob2o5b2obo29bo2bobo2bo$933bo2b2o5b2o2bo20bo8b2o3b2o8bo$933b2obo 7bob2o22bo6bo5bo6bo$935bo9bo20bo3b2o17b2o3bo$935bo9bo21bo25bo$934b3o7b 3o21b2o2bo15bo2b2o$967bo3bo17bo3bo$936bo7bo24b2obo15bob2o$934bo2bo5bo 2bo19bo2bo2b2o13b2o2bo2bo$936bobo3bobo22b2obo3b2o9b2o3bob2o$212bo722b 2obo3bob2o21b2o2b2ob2o9b2ob2o2b2o$211bobo722bo7bo28b3o9b3o$210bo2bo 719b2o11b2o25bo13bo$211b2o719b3o3bo3bo3b3o23bob2o9b2obo$974bo11bo$207b o5bo715b3o17b3o23bo9bo$206bobo3bo716bo5b2o7b2o5bo22bo11bo$205bo2bo3b2o 759b2ob2o5b2ob2o$205bo2b2o3bo762b2o5b2o$974bo2bo5bo2bo$490bo481bo15bo$ 489bobo484b2o5b2o$488bo3bo479bob2o9b2obo$489b3o$974b3o7b3o$487b2o3b2o 479b3o9b3o$484b2o3bobo3b2o475bo3b4ob4o3bo$484b2o3bobo3b2o477b4obobob4o $482b2o5bobo5b2o474b2obo2bobo2bob2o$486b2obobob2o478b2obo2bobo2bob2o$ 482bo6bobo6bo477bob2ob2obo$485b2o2bobo2b2o482bo3bo$483bo2bobo3bobo2bo 479bo5bo$483b2o11b2o$483b2o11b2o474b3o11b3o$486bo7bo478bo13bo$486b3o3b 3o478bo13bo$488bo3bo478bobo13bobo$485b2obo3bob2o476bo15bo$487b2o3b2o$ 487bobobobo2$487bo2bo2bo$488b2ob2o$487b2o3b2o2$486bo2b3o2bo$485b11o$ 485b2obo3bob2o$311bo5bo$310b3o3b3o$309b2obo2b2obo$309b3o3b3o$310b2o4b 2o$315bo$311bobob2obo$311bo2bobo$315bo$314b2o$312bo2bo$312bo625bo3bo 73b3o3b3o$312bo3bo621bo3bo73bo2bobo2bo$311b5obo619bobobobo71bo3bobo3bo $311bob2o2b2o698bobobobo$310bo5b3o617bo7bo72bo5bo$314bo618bob2o2bobo2b 2obo69b2o3b2o$311bo3bo617bobo2b2ob2o2bobo70b2ob2o$310bo3bo617bob2obobo bobob2obo69b2ob2o$310bo2b2o702bo5bo$309bo628bo3bo70b3o9b3o$310bo2bo 213bo5bo33b3ob3o438bo2b2o7b2o2bo$311bobo212b3o3b3o31bo2bobo2bo359b2ob 2o3b2ob2o65bo15bo$525bo2bo3bo2bo29bo3bobo3bo358b2o9b2o69bo7bo$311bo4b 3o205b3o7b3o28bo9bo361b2o3b2o69bo2bo7bo2bo$313bo2bo2bo205bobo5bobo31bo 5bo364bo3bo70bobo9bobo$310b2o4bo210b2o3b2o30bobo7bobo360bo5bo69b2o11b 2o$309bo3bo2bo206bo4bo3bo4bo25b2obob2ob2obob2o358bobo3bobo66bo3b3o5b3o 3bo$314bobo211bo3bo29bobobo2bobo2bobobo356b4o3b4o65bo5bo5bo5bo$309b2o 2bo209b2o3bo3bo3b2o23b2obo4bobo4bob2o354bo2bo5bo2bo69b2o5b2o$311b2o3b 3o206bo2bo3bo2bo24bo3bob2obobob2obo3bo353bob2o5b2obo66bo5bobo5bo$315b 3o209bo5bo30bob3o3b3obo359bo7bo71bob2ob2obo$314b2o244b2o3bo2b2ob2o2bo 3b2o355b2o5b2o70bo3bobo3bo$312bo5b2o210bo33b2o9b2o440b2o3b2o$312bobo3b 2o208b2ob2o31bo11bo361bo3bo73b3o3b3o$313bobo247bobo9bobo359bo5bo72bobo 3bobo$528b2ob2o29bo15bo358bo5bo71bo9bo$527bo2bo2bo30bo11bo439bobo3bobo $311b3o213bobobobo27b2obo11bob2o357b2o3b2o73bo5bo$525b2o3bo3b2o24bo3b 2o9b2o3bo356bobobobo74bo3bo$525b2ob5ob2o25bo2bo11bo2bo358b2ob2o73b4ob 4o$528b2ob2o33b2o5b2o364bobo74bo7bo$525bobo5bobo27b2ob2o5b2ob2o361bobo 75bo5bo$526bobo3bobo28b4o7b4o358b2obobob2o72bo5bo$528b2ob2o29b2o4b2ob 2o4b2o357b2obobob2o$528b2ob2o33bob2ob2obo360bo3bobo3bo68b3ob2ob2ob3o$ 565b5ob5o358b3ob2ob2ob3o66bo3b2o3b2o3bo$530bo34b2o7b2o358b2o9b2o65bo2b o2bo3bo2bo2bo$530bo38bobo362b3o7b3o65b2o3b2o3b2o3b2o$528bobobo35b2ob2o 361bo2bo5bo2bo65bob5o3b5obo$527b2o3b2o33bobobobo358b2o3b2o3b2o3b2o69b 2ob2o$566b2obobob2o358b2ob3o3b3ob2o64b5o7b5o$525bo9bo29bo3bobo3bo358bo 2bo5bo2bo64b4ob2o5b2ob4o$525bo9bo399bo2bo3bo2bo65b3o3b2o3b2o3b3o$526bo 7bo30b2ob2ob2ob2o359b2ob2ob2ob2o70bob2ob2obo$528bo3bo404bobobobo74b2ob 2o$566bo3bo3bo358bobo2bo3bo2bobo67bobo5bobo$565bo4bo4bo357bo2bo7bo2bo 66bob2o5b2obo$564bo11bo360bo5bo69b2o2bo5bo2b2o$563b2obo7bob2o434b2o13b 2o$562bobob2o5b2obobo357bobo3bobo70bo2b2ob2o2bo$561b2obobob2ob2obobob 2o358bo3bo69b2o4b2ob2o4b2o$560bo3bobo2bobo2bobo3bo355bobo3bobo73bo3bo$ 569bobo363bo2bo3bo2bo69b4o3b4o$560b2ob2ob2obobob2ob2ob2o355bo7bo69bo4b obo4bo$569bobo365bo5bo70bob2obobob2obo$561bo3bo9bo3bo433b2ob2obobob2ob 2o$932b2o2b2o5b2o2b2o63b3o11b3o$562b3o11b3o353b3o3bo3bo3b3o65bo11bo$ 935b4o3b4o68bo11bo$934bo4bobo4bo65b3o11b3o$564b2o9b2o358bo2bo3bo2bo69b 3o5b3o$564bob2o5b2obo358bo9bo70b2o5b2o$568bo3bo$563b2obob2ob2obob2o 437b3o5b3o$567bobobobo441b2o7b2o$569bobo445bo5bo$565b2o2bobo2b2o440b2o bobob2o$565b2o2bobo2b2o439bo9bo$564bo2bobobobo2bo438bo3bobo3bo$567bobo bobo$567bobobobo441b3o5b3o$567bobobobo440bo11bo$566bo2bobo2bo440bobo5b obo$562b2o2b3o3b3o2b2o434bo2bobo3bobo2bo$561bo2bo11bo2bo433b4obo3bob4o $562b2o13b2o433bo3bob2ob2obo3bo$1012bo2b2o7b2o2bo$1011b2obo3b2ob2o3bob 2o$561bo17bo434bob2obobob2obo$561bo17bo431b5obo5bob5o$1011bo6bo3bo6bo$ 1016bo7bo$1015bo2bo3bo2bo$1019bobo$1019bobo$1016b2obobob2o$1016bo2bobo 2bo$1016bo2bobo2bo2$1015b2o7b2o$1015b2o7b2o$1015b2o7b2o3$1014bo2bo5bo 2bo46$1016bo7bo32b3ob3o$1015b3o5b3o30bo2bobo2bo$1015bo2bo3bo2bo29bo3bo bo3bo$1016b2obobob2o30bo9bo$1012bo3b2obobob2o3bo28bo5bo$1011bobo5bobo 5bobo24bobo7bobo$1010b2ob2o3b2ob2o3b2ob2o22b2obob2ob2obob2o$1011bo7bob o7bo22bobobo2bobo2bobobo$1011bo7bobo7bo21b2obo4bobo4bob2o$1011bo2bo3b 2ob2o3bo2bo20bo3bob2obobob2obo3bo$1012bo15bo25bob3o3b3obo$1016b3o3b3o 25b2o3bo2b2ob2o2bo3b2o$1014b2obo5bob2o27b2o9b2o$1017bo5bo30bo11bo$ 1017b2o3b2o29bobo9bobo$1018b2ob2o29bo15bo$1054bo11bo$1015bo3bobo3bo25b 2obo11bob2o$1050bo3b2o9b2o3bo$1017bobobobo27bo2bo11bo2bo$1017bobobobo 32b2o5b2o$1018b2ob2o30b2ob2o5b2ob2o$1018bo3bo30b4obo3bob4o$1052b2o4bo 3bo4b2o$1056bo2bobo2bo$1057bobobobo$1054b2obobobobob2o$1054bo4bobo4bo$ 1056bo7bo$1053b2obob2ob2obob2o$1056bo7bo$1054bobobo3bobobo2$1055bobo5b obo$1055bobo5bobo$1054b2ob2o3b2ob2o2$1052b2obo2bo3bo2bob2o$1052b2obo9b ob2o$1052bob2ob2o3b2ob2obo$1051b2obo4bobo4bob2o$1056bo7bo$1051b3o4b2ob 2o4b3o3$1051b2o15b2o$1051bo2b2o9b2o2bo$1054bob2o5b2obo$1050b2o6bo3bo6b 2o$1053b2obob2ob2obob2o$1057bobobobo$1059bobo$1055b2o2bobo2b2o$1055b2o 2bobo2b2o$1054bo2bobobobo2bo$1057bobobobo$1057bobobobo$1057bobobobo$ 1056bo2bobo2bo$1052b2o2b3o3b3o2b2o$1051bo2bo11bo2bo$1052b2o13b2o3$ 1051bo17bo$1051bo17bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by width
(click above to open LifeViewer)
RLE: here Plaintext: here

Known spaceships by height

Velocity Asymmetric Odd-symmetric
(strict)		 Even-symmetric
(strict)		 Gutter
(strict)		 Odd glide-symmetric
(strict)		 Even glide-symmetric
(strict)
(1,0)c/2 8[39][40] 8 8 8 - -
(1,0)c/3 5[39][40] 6[41] 7[41] 6[41] - -
(1,0)c/4 8[39][40][41] 9[41] 10[42] 9[41] - -
(2,0)c/4 6[39][40] 7[41] 8[41] 7[41] 6 7[41]
(1,0)c/5 8[39][43] 8 8 8 - -
(2,0)c/5 11[44][45] 11 10 11 - -
(1,0)c/6 9[44] < h ≤ 12 9 9 9 - -
(2,0)c/6 7[46] < h ≤ 9 7 7 7 7 7
(3,0)c/6 9[39] < h ≤ 13 9 9 9 - -
(1,0)c/7 8[44] < h ≤ 10 8 8 8 - -
(2,0)c/7 8[39] < h ≤ 12 8 8 8 - -
(3,0)c/7 8[47] < h ≤ 42 8 8 8 - -
x = 65, y = 70, rule = B3/S23 6bo17bo$5b3o15b3o$3b2ob3o13b3ob2o$4bo2bob2o4bo4b2obo2bo$b2obo4bobob2ob 2obobo4bob2o$b2obobo2bobo7bobo2bobob2o$bo8b3obobob3o8bo$2o7b2o9b2o7b2o 13$15bo$8b2ob3ob3o$8b2o4bo2b2ob2o$7bo2bob2o3bo2b2o$19bo2bo16$3bo53bo$ 3bo7b3o11b3o28b3o$2bobo4b2o5b3o36b2obo$9b5ob5o4bo2bo27b3o$7bobo2bo2bo 3bo5bo30b2o$3b6o3bo2b2o4b6o$4b2o6bobo2b2o3bo$14bo6bo13$11bo7bo33bo$5b 2obobob2o3b2obobob2o26b3o$2b3obob3o9b3obob3o22bo3bo$2bo3bobo5bobo5bobo 3bo22b2ob2o5bo$6b2o6bobo6b2o36b2o$3b2o9bobo9b2o22b4obo5bob2o$3b2ob2o 15b2ob2o23bo2bo2b3o2bo$7bo15bo33b3o$61bo$61bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by height
(click above to open LifeViewer)
RLE: here Plaintext: here

Known diagonal spaceships by diagonal width and height

These are measured in half-diagonals, as the width of the intersection of a 1-cell-wide orthogonal ray with the cells that turn on during the spaceship's motion.

Minimum width
Velocity Asymmetric Symmetric Gutter Glide-symmetric
(1,1)c/4 4 11 11 4
strict 15[48] 15[48]
(1,1)c/5 15 27 27 -
(1,1)c/6 13 < w ≤ 26 25 < w ≤ 33 25 < w ≤ 55 26[48]
(1,1)c/7 11 < w ≤ 31 21 < w ≤ 31 21 < w ≤ 65 -
(1,1)c/8 11 < w ≤ 24 19 < w ≤ 51 19 < w ≤ 51 16 < w ≤ 24
(2,2)c/8 w ≤ 24 w ≤ 51 w ≤ 51 w ≤ 35
(1,1)c/9 9 15 15 -
(2,2)c/9 11 21 21 -
Minimum height
Velocity Asymmetric Symmetric (strict) Gutter (strict) Glide-symmetric (strict)
(1,1)c/4 5[42] 13[42] 14[42] 5[42]
(1,1)c/5 12[1] 12[1] 12[1] -
(1,1)c/6 12[49] 12[49] 11[49] 11[49]

Known spaceships by population

Herein, "strict" is used to refer to spaceships that cannot be decomposed into multiple smaller spaceships which still behave equivalently. (For instance, MWSS on MWSS 1's MWSSs would emit their side sparks in both phases if separated, so it is strict, where a LWSS pair is not.)

The evolution sequences of all patterns with up to 8 cells have been classified, so all stable objects of ≤ 8 cells (or with predecessors thereof) are known. As such, all negative results here have 8 as an additional lower bound.[50]

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 64[51] 64[51] 66[51] 70[51] - -
(1,0)c/3 25[52] 34[52] 44[52] 50[52] - -
strict 52[53]
(1,0)c/4 37[54] 46[55] 58[56] 46[55] - -
(1,1)c/4 5 10[57][58] - 10[57][58] - 5
strict 29[58] < p ≤ 37 29[58] < p ≤ 50
(2,0)c/4 9 18 18 18 9 18
strict 20[53][59] 48[60] 20[53][59] 32[61]
(1,0)c/5 p ≤ 58 p ≤ 58 p ≤ 116 p ≤ 58 - -
(1,1)c/5 p ≤ 58 p ≤ 58 - p ≤ 58 - -
(2,0)c/5 30[62] 44[63] 60[64] 44[63] - -
strict 70[65]
(1,0)c/6 p ≤ 56 p ≤ 112 p ≤ 56 p ≤ 112 - -
(1,1)c/6 p ≤ 77 p ≤ 77 - p ≤ 154 - p ≤ 170
(2,0)c/6 p ≤ 72 p ≤ 72 p ≤ 128 p ≤ 72 p ≤ 110 p ≤ 129
(2,1)c/6 p ≤ 282 - - - - -
(3,0)c/6 p ≤ 86 p ≤ 86 p ≤ 104 p ≤ 108 - -
(1,0)c/7 p ≤ 20 p ≤ 40 p ≤ 40 p ≤ 40 - -
strict p ≤ 90 p ≤ 684 p ≤ 90
(1,1)c/7 p ≤ 83 p ≤ 83 - p ≤ 166 - -
(2,0)c/7 p ≤ 36 p ≤ 72 p ≤ 36 p ≤ 72 - -
(3,0)c/7 p ≤ 232 p ≤ 232 ? p ≤ 232 - -
(1,1)c/8 p ≤ 68 ? - ? - p ≤ 68
(2,0)c/8 p ≤ 74 p ≤ 121 p ≤ 148 p ≤ 148 p ≤ 74 p ≤ 148
(2,2)c/8 p ≤ 89 ? - ? ? -
(4,0)c/8 p ≤ 31 p ≤ 58 p ≤ 62 p ≤ 58 p ≤ 62 p ≤ 62

Full Censuses

This section contains details on searches that completely cover all ships in a particular search space. For example, all c/4 orthogonal ships of width 10. There are infinitely many such ships, but a finite collection can be made that includes all possible rows present in a width-10 c/4 orthogonal ship. This section only includes census containing at least one ship.

c/2 orthogonal

c/3 orthogonal

  • All (1,0)c/3 ships up to a population of 50 cells[52][72]
  • All (1,0)c/3 odd-symmetric ships up to a population of 67 cells (26 strict ships)[73]
  • All (1,0)c/3 even-symmetric ships up to a population of 86 cells (29 strict ships)[74]
  • All (1,0)c/3 ships up to width 13[75]
  • All (1,0)c/3 ships up to height 6 (5 ships)[41]
  • All (1,0)c/3 odd-symmetric ships up to width 19 (1 width-15 ship; infinitely many width-17+ ships)[75]
  • All (1,0)c/3 even-symmetric ships up to width 20 (1 width-12 ship; infinitely many width-14+ ships)[75]
  • All (1,0)c/3 gutter-symmetric ships up to width 21 (1 width-17 ship; infinitely many width-19+ ships)[75]
  • All (2,0)c/6 even-symmetric ships up to width 18[6]
  • All (2,0)c/6 even-glide-symmetric ships up to width 18[6]

c/4 orthogonal

c/4 diagonal

  • All (1,1)c/4 ships up to a population of 27 cells (3 ships: glider, crab, and wings)[77]
  • All (1,1)c/4 symmetric ships in an 18 × 18 bounding box (1 strict ship)[1]
  • All (1,1)c/4 gutter-symmetric ships in a 19 × 19 bounding box (1 strict ship)[1]
  • All (1,1)c/4 ships up to diagonal height 12 (1 ship)[42]
  • All (1,1)c/4 ships up to diagonal width 13 (4 ships)[48]
  • All (1,1)c/4 ships up to orthogonal width 10 (5 ships)[48]
  • All (1,1)c/4 ships up to single-phase orthogonal width 9 (15 ships)[48]

c/5 orthogonal

  • All (1,0)c/5 ships up to height 8[78]
  • All (1,0)c/5 even-symmetric ships up to width 18[75]
  • All (1,0)c/5 gutter-symmetric ships up to width 19[75]

c/5 diagonal

  • All (1,1)c/5 ships up to diagonal height 12 (1 ship)[1]
  • All (1,1)c/5 ships up to diagonal width 16 (1 ship)[41]
  • All (1,1)c/5 symmetric ships up to diagonal width 27 (2 ships: 86P5H1V1 and this ship)[79]
  • All (1,1)c/5 gutter-symmetric ships up to diagonal width 29 (1 ship)[41]

2c/5 orthogonal

  • All (2,0)c/5 ships up to a population of 35 cells (2 ships: 30P5H2V0 and 34P5H2V0)[65]
  • All (2,0)c/5 odd-symmetric ships up to a population of 57 cells (2 ships: 44P5H2V0 and this ship)[80]
  • All (2,0)c/5 even-symmetric ships up to a population of 74 cells (3 strict ships: 70P5H2V0, this ship, and this ship)[81]
  • All (2,0)c/5 ships up to width 12 (1 width-10 ship; infinitely many width-11 ships; infinitely many width-12 ships)[75]
  • All (2,0)c/5 odd-symmetric ships up to width 17 (1 width-15 ship; infinitely many width-17 ships)[75]
  • All (2,0)c/5 even-symmetric ships up to width 20 (1 ship)[75]
  • All (2,0)c/5 gutter-symmetric ships up to width 21 (1 width-15 ship; 1 width-19 ship; infinitely many width-21 ships)[75]
  • All (4,0)c/10 odd-symmetric ships up to width 15 (3 period-10 ships)[2]

c/6 orthogonal

  • All (1,0)c/6 even-symmetric ships up to width 18 (1 ship)[75]

2c/7 orthogonal

c/10 orthogonal

  • All (1,0)c/10 even-symmetric ships up to width 12 (1 width-10 ship; infinitely many width-12 ships)[2]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Note that this is not recognised as a single contiguous spaceship by apgsearch's object separation.

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 Matthias Merzenich (March 17, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. ↑ 3.0 3.1 Tim Coe (December 18, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  4. ↑ praosylen (May 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. ↑ 5.0 5.1 5.2 5.3 5.4 Matthias Merzenich (April 14, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  6. ↑ 6.0 6.1 6.2 6.3 Tim Coe (April 13, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. ↑ Keith Amling (January 18, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. ↑ 8.0 8.1 Tim Coe (June 11, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. ↑ 9.0 9.1 9.2 Matthias Merzenich (December 24, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  10. ↑ Matthias Merzenich (June 14, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  11. ↑ Tomas Rokicki (March 1, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  12. ↑ 12.0 12.1 Matthias Merzenich (April 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  13. ↑ shuich01 (May 28, 2025). Re: Spaceship Discussion Thread, in which the first w25gutter 2c/7 was discovered with LSSS (may not be shortest possible)
  14. ↑ 14.0 14.1 14.2 14.3 14.4 Checked with knight2.c
  15. ↑ 15.0 15.1 15.2 15.3 15.4 Tim Coe (April 17, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  16. ↑ Checked by Paul Tooke with gfind
  17. ↑ Dylan Chen (January 10, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  18. ↑ 18.0 18.1 Matthias Merzenich (November 29, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  19. ↑ Matthias Merzenich (February 25, 2020). Re: Help me finish this c/8 search (discussion thread) at the ConwayLife.com forums
  20. ↑ Matthias Merzenich (December 22, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  21. ↑ 21.0 21.1 21.2 Tim Coe (April 21, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  22. ↑ Tanner Jacobi (December 3, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  23. ↑ 23.0 23.1 23.2 AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  24. ↑ 24.0 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 Alex Greason (September 7, 2025). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  25. ↑ Matthias Merzenich (March 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  26. ↑ Exa (December 7, 2024). Message in #cgol on the Conwaylife Lounge Discord server, in which 4c/9 w24e was disproven with qfind
  27. ↑ Exa (December 6, 2024). Message in #cgol on the Conwaylife Lounge Discord server, in which 4c/9 w24e was disproven with qfind
  28. ↑ 28.0 28.1 28.2 28.3 28.4 28.5 praosylen (January 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  29. ↑ 29.0 29.1 Tim Coe (March 1, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  30. ↑ 30.0 30.1 AforAmpere (November 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  31. ↑ AforAmpere (December 10, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  32. ↑ Matthias Merzenich (April 19, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  33. ↑ 33.0 33.1 Tim Coe (February 1, 2016). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  34. ↑ 34.0 34.1 praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  35. ↑ 35.0 35.1 lordlouckster (July 13, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  36. ↑ 36.0 36.1 36.2 36.3 36.4 36.5 36.6 36.7 Matthias Merzenich (May 5, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  37. ↑ 37.0 37.1 37.2 37.3 asymmetric, odd, even and gutter lower bounds by DroneBetter using qfind
  38. ↑ Ivan Fomichev using gfind under OS X 10.9.5, verified by DroneBetter using rlifesrc in 8.36 hours
  39. ↑ 39.0 39.1 39.2 39.3 39.4 39.5 39.6 Checked by Matthias Merzenich using WLS.
  40. ↑ 40.0 40.1 40.2 40.3 Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  41. ↑ 41.00 41.01 41.02 41.03 41.04 41.05 41.06 41.07 41.08 41.09 41.10 41.11 41.12 41.13 41.14 Matthias Merzenich (December 1, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  42. ↑ 42.0 42.1 42.2 42.3 42.4 42.5 Matthias Merzenich (February 19, 2024). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  43. ↑ Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  44. ↑ 44.0 44.1 44.2 Matthias Merzenich (February 20, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  45. ↑ Keith Amling (October 31, 2025). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  46. ↑ Matthias Merzenich (February 22, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  47. ↑ verified by DroneBetter in 5.7 hours with rlifesrc
  48. ↑ 48.0 48.1 48.2 48.3 48.4 48.5 Matthias Merzenich (November 27, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  49. ↑ 49.0 49.1 49.2 49.3 Matthias Merzenich (March 28, 2011). Re: New small c/6 diagonal ship. (discussion thread) at the ConwayLife.com forums
  50. ↑ Nick Gotts (November 28, 2018). Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
  51. ↑ 51.0 51.1 51.2 51.3 Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  52. ↑ 52.0 52.1 52.2 52.3 52.4 Keith Amling (November 12, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  53. ↑ 53.0 53.1 53.2 Keith Amling (December 1, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  54. ↑ 54.0 54.1 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  55. ↑ 55.0 55.1 Keith Amling (November 29, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  56. ↑ 56.0 56.1 Keith Amling (November 30, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  57. ↑ 57.0 57.1 Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  58. ↑ 58.0 58.1 58.2 58.3 Matthias Merzenich (October 5, 2025). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  59. ↑ 59.0 59.1 59.2 "Life Object Counts". Mark Niemiec. Retrieved on December 9, 2023.
  60. ↑ 60.0 60.1 Keith Amling (February 4, 2025). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  61. ↑ 61.0 61.1 Keith Amling (February 5, 2025). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  62. ↑ Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  63. ↑ 63.0 63.1 Keith Amling (February 1, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  64. ↑ Keith Amling (April 4, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  65. ↑ 65.0 65.1 Keith Amling (November 1, 2025). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  66. ↑ Keith Amling (January 15, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  67. ↑ Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  68. ↑ Keith Amling (February 4, 2025). Re: amling search program principles discussion / brain dump (discussion thread) at the ConwayLife.com forums
  69. ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  70. ↑ 70.0 70.1 Matthias Merzenich (March 22, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  71. ↑ Matthias Merzenich (May 7, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  72. ↑ Keith Amling (February 6, 2025). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  73. ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  74. ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  75. ↑ 75.00 75.01 75.02 75.03 75.04 75.05 75.06 75.07 75.08 75.09 75.10 75.11 75.12 75.13 75.14 "knightt results". Matthias Merzenich. Retrieved on February 17, 2024.
  76. ↑ Keith Amling (March 2, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  77. ↑ Matthias Merzenich (October 13, 2025). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  78. ↑ Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  79. ↑ Matthias Merzenich (November 28, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  80. ↑ Keith Amling (April 3, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  81. ↑ Keith Amling (November 10, 2025). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  82. ↑ Matthias Merzenich (March 21, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
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