LifeWiki:Spaceship Search Status Page: Difference between revisions

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m add 2c/8 diagonal upper bound of 24 in diagonal width table
Added references to min height table and corrected min diagonal width (2,2)c/8
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| style="background: #80ff80;" | [[64P2H1V0|8]]
| style="background: #80ff80;" | [[64P2H1V0|8]]<ref name="MM-WLS">Checked by Matthias Merzenich using WLS.</ref><ref name="post172210" />
| style="background: #80ff80;" | [[64P2H1V0|8]]
| style="background: #80ff80;" | [[64P2H1V0|8]]
| style="background: #80ff80;" | {{LinkCatagolue|xq2_1fc0s04g0tje28agga82ejt0g40s0cf1zx112731ya137211|name=8|style=raw}}
| style="background: #80ff80;" | {{LinkCatagolue|xq2_1fc0s04g0tje28agga82ejt0g40s0cf1zx112731ya137211|name=8|style=raw}}
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| style="background: #80ff80;" | {{LinkCatagolue|xq3_25c4a8goko06550687099c0264egij2630362jige4620c99078605560okog8a4c52|name=6|style=raw}}
| style="background: #80ff80;" | {{LinkCatagolue|xq3_25c4a8goko06550687099c0264egij2630362jige4620c99078605560okog8a4c52|name=6|style=raw}}<ref name="post172309" />
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| style="background: #80ff80;" | {{LinkCatagolue|xq3_25c4a8goko06550687099c0264egij2630362jige4620c99078605560okog8a4c52|name=6|style=raw}}<ref name="post172309" />
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| style="background: #80ff80;" | {{LinkCatagolue|xq4_02k4772z31h28oz560ao31z2ud62zhhd0gozy11|name=8|style=raw}}<ref name="post172309" />
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| style="background: #ffa0a0;" | 8<ref name="post172309" />
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| style="background: #80ff80;" | [[Lightweight spaceship|6]]<ref name="MM-WLS" /><ref name="post172210" />
| style="background: #80ff80;" | [[MWSS on MWSS 1|7]]<ref name="post172309" />
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6eeed72z05m04ogz0pvij1zqq8447z2v824sz0p699gzkv1423z5lhiiez09v4cogz0a6021z6777be4|name=8|style=raw}}<ref name="post172309" />
| style="background: #80ff80;" | [[MWSS on MWSS 1|7]]<ref name="post172309" />
| style="background: #80ff80;" | [[Lightweight spaceship|6]]
| style="background: #80ff80;" | [[Lightweight spaceship|6]]
| style="background: #80ff80;" | [[MWSS on MWSS 1|7]]
| style="background: #ffa0a0;" | 7<ref name="post172309" />
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6eeed72z05m04ogz0pvij1zqq8447z2v824sz0p699gzkv1423z5lhiiez09v4cogz0a6021z6777be4|name=8|style=raw}}
| style="background: #80ff80;" | [[MWSS on MWSS 1|7]]
| style="background: #80ff80;" | [[Lightweight spaceship|6]]
| style="background: #ffa0a0;" | 7
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| (1,0)c/5
| (1,0)c/5
| style="background: #80ff80;" | [[Spider|8]]
| style="background: #80ff80;" | [[Spider|8]]<ref name="MM-WLS" /><ref name="post172215" />
| style="background: #80ff80;" | [[Spider|8]]
| style="background: #80ff80;" | [[Spider|8]]
| style="background: #80ff80;" | {{LinkCatagolue|xq5_ug1hmgc865da808ad568cgmh1guwug1hmgc865da808ad568cgmh1guz124w6yb6w421w124w6yb6w421|name=8|style=raw}}
| style="background: #80ff80;" | {{LinkCatagolue|xq5_ug1hmgc865da808ad568cgmh1guwug1hmgc865da808ad568cgmh1guz124w6yb6w421w124w6yb6w421|name=8|style=raw}}
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| style="background: #80ff80;" | [[34P5H2V0|11]]
| style="background: #80ff80;" | [[34P5H2V0|11]]<ref name="post178547" />
| style="background: #80ff80;" | {{LinkCatagolue|xq5_2aordd6zwp21so8ogzxhhwhhzwj8g73231z8a3rmmc|name=11|style=raw}}
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| (1,0)c/6
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| style="background: #ffa0a0;" | 9 < h &le; [[56P6H1V0|12]]
| style="background: #ffa0a0;" | 9<ref name="post178547" /> < h &le; [[56P6H1V0|12]]
| style="background: #ffa0a0;" | 9
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| style="background: #ffa0a0;" | 7 < h &le; {{LinkCatagolue|xq6_8k64a213530ckk0c2m4swq3qws484c4swq3qws4m2c0kkc035312a46k8zyc1x71x17y371x17x1|name=9|style=raw}}
| style="background: #ffa0a0;" | 7<ref name="post178547" /> < h &le; {{LinkCatagolue|xq6_8k64a213530ckk0c2m4swq3qws484c4swq3qws4m2c0kkc035312a46k8zyc1x71x17y371x17x1|name=9|style=raw}}
| style="background: #ffa0a0;" | 7
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| (3,0)c/6
| (3,0)c/6
| style="background: #ffa0a0;" | 9 < h &le; [[86P6H3V0|13]]
| style="background: #ffa0a0;" | 9<ref name="MM-WLS" /> < h &le; [[86P6H3V0|13]]
| style="background: #ffa0a0;" | 9
| style="background: #ffa0a0;" | 9
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| style="background: #ffa0a0;" | 8 < h &le; [[Loafer|10]]
| style="background: #ffa0a0;" | 8<ref name="MM-WLS" /> < h &le; [[Loafer|10]]
| style="background: #ffa0a0;" | 8
| style="background: #ffa0a0;" | 8
| style="background: #ffa0a0;" | 8
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| style="background: #ffa0a0;" | 8 < h &le; [[Weekender|12]]
| style="background: #ffa0a0;" | 8<ref name="MM-WLS" /> < h &le; [[Weekender|12]]
| style="background: #ffa0a0;" | 8
| style="background: #ffa0a0;" | 8
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| style="background: #ffa0a0;" | 7 < h &le; [[Soba|42]]
| style="background: #ffa0a0;" | 7<ref name="MM-WLS" /> < h &le; [[Soba|42]]
| style="background: #ffa0a0;" | 7
| style="background: #ffa0a0;" | 7
| style="background: #ffa0a0;" | 7
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All results checked by Matthias Merzenich using WLS.


{{EmbedViewer
{{EmbedViewer
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| (2,2)c/8
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| style="background: #ffa0a0;" | w &le; {{LinkCatagolue|xq8_xeuoqpk880ggz8oo03b8qf1013j044gzx1hsxai862w11ko084oozy36186088gy4iguggzy78hn4gx8ggop111f04aa08zyb1120elnsw562wgw11cegzyh368gx123y39dczyk1050a8cccc8a8b0k0b088zyr3311211ehd231ggbuiozyz540ogp3o80kg1ac0gzyzx11win09g0k04jggo488zyzy622i01hhhtf04tot4zyzy81038qqu0cgw16e08g8czyzyiad0me3hw3rofgzyzyi1220o163fa48811acggwoozyzyn1x35224y0106g1e608ggzyzyt8lff0oo0ogi2a0811zyzyx21ko803ep843120b88bsozyzyzy31v544s4hce01050koozyzyzy311wfdb0gy21472zyzyzy91730ac4|name=24|style=raw}}
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|author = Matthias Merzenich
|author = Matthias Merzenich
|date  = February 19, 2024
|date  = February 19, 2024
}}</ref>
<ref name="post178547">{{LinkForumThread
|format = ref
|title  = Re: LLSSS min height search results
|p      = 178547
|author = Matthias Merzenich
|date  = February 20, 2024
}}</ref>
<ref name="post172210">{{LinkForumThread
|format = ref
|title  = Re: LLSSS min height search results
|p      = 172210
|author = Keith Amling
|date  = November 29, 2023
}}</ref>
<ref name="post172215">{{LinkForumThread
|format = ref
|title  = Re: LLSSS min height search results
|p      = 172215
|author = Keith Amling
|date  = November 29, 2023
}}</ref>
}}</ref>
</references>
</references>

Revision as of 12:53, 20 February 2024

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] w ≤ 24 - 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 10 < w ≤ 36 - 10 < w - 10 < 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 9 < w ≤ 27 - 9 < w - -
(2,0)c/7 11[11][12] 23[2] 18 23[12] < w ≤ 33 - -
(2,1)c/7 11[13] - - - - -
(3,0)c/7 14[14] 29[15] 28[14] 31[14][16] - -
(1,0)c/8 10[17] 19[18] 20[19] 21[17] - -
(1,1)c/8 7 < w ≤ 21 7 < w - 7 < w - 7 < w ≤ 21
(2,0)c/8 9[2] 15[2][20] 18[2][20] 17[2][20] 13 14
(2,1)c/8 8 - - - - -
(2,2)c/8 8 < w ≤ 24 8 - 8 8 -
(3,0)c/8 11[13] 21[13] 22[21] 23[13] - -
(3,1)c/8 12[13] - - - - -
(4,0)c/8 11[2] 17[2] 20[2] 19[2] 17 20[2]
(1,0)c/9 8[22] 15[22] 16[22] 15[23] - -
(1,1)c/9 6 ? - ? - -
(2,0)c/9 8[24] 15[25] 16[23] 17[24] - -
(2,1)c/9 7 - - - - -
(2,2)c/9 7 ? - ? - -
(3,0)c/9 11[26] 17[2] 16[5] 17[2] - -
(3,1)c/9 8 - - - - -
(4,0)c/9 11[14] 21[14] 22[27] 23[14] - -
(1,0)c/10 6[28] 11[28] 10 13[28] - -
(1,1)c/10 7 7 - 7 - 7
(2,0)c/10 6 < w ≤ 11 11 < w ≤ 19 12 < w ≤ 20 13 < w ≤ 19 13[27] < w ≤ 19 14[27] < w ≤ 20
(2,1)c/10 6 - - - - -
(2,2)c/10 6 6 - 6 6 -
(3,0)c/10 9[29] 17[30] 18[29] 17[31] - -
(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 6[28] 11[28] 12[28] 13[28] - -
(2,1)c/11 ? - - - - -
(2,2)c/11 ? ? - ? - -
(3,0)c/11 6 11 12 13 - -
(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] - -
(2,0)c/12 w ≤ 63 ? ? ? 9[37] ?
x = 1360, y = 676, rule = B3/S23 5b2o50b2o44b2o102b3ob3o193b3ob3o249b3o2b4o2b3o220b3ob3o245b3o153b3o4b 3o$4b2o51bobo42b2o102bo2bobo2bo191bo2bobo2bo247bo3bob4obo3bo218bo2bobo 2bo243bo2bo153bo2bo3bo2bo$6bo50bo45bo2bo98bo3bobo3bo189bo3bobo3bo245bo 6bo2bo6bo216bo3bobo3bo245bo153bo6bo$60bo42b2obo98bo9bo189bo9bo245bo3b 2o6b2o3bo216bo9bo245bo153bo6bo$59bobo41b2o3bo98bo5bo193bo5bo249bo12bo 220bo5bo244bobo155bobo4bobo$59bobo142bobo7bobo187bobo7bobo243bobo14bob o214bobo7bobo$59bo46bobob2o91b2obob2ob2obob2o185b2obob2ob2obob2o241b2o bob2o8b2obob2o212b2obob2ob2obob2o$59bo44bobo3bo91bobobo2bobo2bobobo 183bobobo2bobo2bobobo239bobobob2o8b2obobobo210bobobo2bobo2bobobo$55bo 3bo35bo8b3o2bo91b2obo4bobo4bob2o181b2obo4bobo4bob2o237b2o3bo2bo8bo2bo 3b2o208b2obo4bobo4bob2o$54b3obo35b5o6b2o93bo3bob2obobob2obo3bo179bo3bo b2obobob2obo3bo235bo3bobo2b2o6b2o2bobo3bo206bo3bob2obobob2obo3bo$53b2o 39bo2b2o2b2o101bo4bo2b3obo187bob3o3b3obo242bo20bo213bo4bobo4bo$52b2o 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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[38][39] 8 8 8 - -
(1,0)c/3 5[38][39] 6[40] 7[40] 6[40] - -
(1,0)c/4 8[38][39][40] 9[40] 8[40] 9[40] - -
(2,0)c/4 6[38][39] 7[40] 8[40] 7[40] 6 7[40]
(1,0)c/5 8[38][41] 8 8 8 - -
(2,0)c/5 11[42] 11 10 11 - -
(1,0)c/6 9[42] < h ≤ 12 9 9 9 - -
(2,0)c/6 7[42] < h ≤ 9 7 7 7 7 7
(3,0)c/6 9[38] < h ≤ 13 9 9 9 - -
(1,0)c/7 8[38] < h ≤ 10 8 8 8 - -
(2,0)c/7 8[38] < h ≤ 12 8 8 8 - -
(3,0)c/7 7[38] < h ≤ 42 7 7 7 - -
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[43] 15[43]
(1,1)c/5 15 27 27 -
(1,1)c/6 w ≤ 26 w ≤ 33 w ≤ 55 26[43]
(1,1)c/7 w ≤ 31 w ≤ 31 w ≤ 65 -
(1,1)c/8 w ≤ 24 w ≤ 51 w ≤ 51 w ≤ 24
(2,2)c/8 w ≤ 24
Minimum height
Velocity Asymmetric Symmetric (strict) Gutter (strict) Glide-symmetric (strict)
(1,1)c/4 5[44] 13[44] 14[44] 5[44]
(1,1)c/5 12[1] 12[1] 12[1] -
(1,1)c/6 12[45] 12[45] 11[45] 11[45]

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.[46]

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 64[47] 64[47] 66[47] 70[47] - -
(1,0)c/3 25[48] 34[48] 44[48] 50[48] - -
strict 52[49]
(1,0)c/4 37[50] 46[51] 58[52] 46[51] - -
(1,1)c/4 5 10[53] - 10[53] - 5
strict 9[53] < p ≤ 37 9[53] < p ≤ 50
(2,0)c/4 9 18 18 18 9 18
strict 20[49][54] 34[55] < p ≤ 48 20[49][54] p ≤ 32
(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[56] 44[57] 31[56] < p ≤ 60 44[57] - -
strict 31[56] < p ≤ 70
(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 49 cells[48]
  • All (1,0)c/3 odd-symmetric ships up to a population of 67 cells (26 strict ships)[62]
  • All (1,0)c/3 even-symmetric ships up to a population of 86 cells (29 strict ships)[63]
  • All (1,0)c/3 ships up to width 13[64]
  • All (1,0)c/3 ships up to height 6 (5 ships)[40]
  • All (1,0)c/3 odd-symmetric ships up to width 19 (1 width-15 ship; infinitely many width-17+ ships)[64]
  • All (1,0)c/3 even-symmetric ships up to width 20 (1 width-12 ship; infinitely many width-14+ ships)[64]
  • All (1,0)c/3 gutter-symmetric ships up to width 21 (1 width-17 ship; infinitely many width-19+ ships)[64]
  • 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 9 cells (1 ship)[65]
  • All (1,1)c/4 symmetric ships in an 18x18 bounding box (1 strict ship)[1]
  • All (1,1)c/4 gutter-symmetric ships in a 19x19 bounding box (1 strict ship)[1]
  • All (1,1)c/4 ships up to diagonal height 12 (1 ship)[44]
  • All (1,1)c/4 ships up to diagonal width 13 (4 ships)[43]
  • All (1,1)c/4 ships up to orthogonal width 10 (5 ships)[43]
  • All (1,1)c/4 ships up to single-phase orthogonal width 9 (15 ships)[43]

c/5 orthogonal

  • All (1,0)c/5 ships up to height 8[66]
  • All (1,0)c/5 even-symmetric ships up to width 18[64]
  • All (1,0)c/5 gutter-symmetric ships up to width 19[64]

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)[40]
  • All (1,1)c/5 symmetric ships up to diagonal width 27 (2 ships: 86P5H1V1 and this ship)[67]
  • All (1,1)c/5 gutter-symmetric ships up to diagonal width 29 (1 ship)[40]

2c/5 orthogonal

  • All (2,0)c/5 ships up to a population of 31 cells (1 ship)[56]
  • All (2,0)c/5 odd-symmetric ships up to a population of 44 cells (1 ship)[57]
  • All (2,0)c/5 ships up to width 12 (1 width-10 ship; infinitely many width-11 ships; infinitely many width-12 ships)[64]
  • All (2,0)c/5 odd-symmetric ships up to width 17 (1 width-15 ship; infinitely many width-17 ships)[64]
  • All (2,0)c/5 even-symmetric ships up to width 20 (1 ship)[64]
  • 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)[64]
  • 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)[64]

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. ↑ 13.0 13.1 13.2 13.3 13.4 Checked with knight2.c
  14. ↑ 14.0 14.1 14.2 14.3 14.4 14.5 Tim Coe (April 17, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  15. ↑ Checked by Paul Tooke with gfind
  16. ↑ Dylan Chen (January 10, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  17. ↑ 17.0 17.1 Matthias Merzenich (November 29, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  18. ↑ Matthias Merzenich (February 25, 2020). Re: Help me finish this c/8 search (discussion thread) at the ConwayLife.com forums
  19. ↑ Matthias Merzenich (December 22, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  20. ↑ 20.0 20.1 20.2 Tim Coe (April 21, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  21. ↑ Tanner Jacobi (December 3, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  22. ↑ 22.0 22.1 22.2 AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  23. ↑ 23.0 23.1 praosylen (December 27, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  24. ↑ 24.0 24.1 praosylen (December 28, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  25. ↑ praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  26. ↑ Matthias Merzenich (March 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  27. ↑ 27.0 27.1 27.2 Tim Coe (March 1, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  28. ↑ 28.0 28.1 28.2 28.3 28.4 28.5 28.6 praosylen (January 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  29. ↑ 29.0 29.1 AforAmpere (November 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  30. ↑ AforAmpere (December 10, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  31. ↑ AforAmpere (November 5, 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. ↑ Ivan Fomichev using gfind under OS X 10.9.5
  38. ↑ 38.0 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 Checked by Matthias Merzenich using WLS.
  39. ↑ 39.0 39.1 39.2 39.3 Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  40. ↑ 40.00 40.01 40.02 40.03 40.04 40.05 40.06 40.07 40.08 40.09 40.10 40.11 40.12 40.13 40.14 40.15 Matthias Merzenich (December 1, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  41. ↑ Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  42. ↑ 42.0 42.1 42.2 Matthias Merzenich (February 20, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  43. ↑ 43.0 43.1 43.2 43.3 43.4 43.5 Matthias Merzenich (November 27, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  44. ↑ 44.0 44.1 44.2 44.3 44.4 Matthias Merzenich (February 19, 2024). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  45. ↑ 45.0 45.1 45.2 45.3 Matthias Merzenich (March 28, 2011). Re: New small c/6 diagonal ship. (discussion thread) at the ConwayLife.com forums
  46. ↑ Nick Gotts (November 28, 2018). Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
  47. ↑ 47.0 47.1 47.2 47.3 Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  48. ↑ 48.0 48.1 48.2 48.3 48.4 Keith Amling (November 12, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  49. ↑ 49.0 49.1 49.2 Keith Amling (December 1, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  50. ↑ 50.0 50.1 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  51. ↑ 51.0 51.1 51.2 Keith Amling (November 29, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  52. ↑ 52.0 52.1 Keith Amling (November 30, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  53. ↑ 53.0 53.1 53.2 53.3 Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  54. ↑ 54.0 54.1 54.2 "Life Object Counts". Mark Niemiec. Retrieved on December 9, 2023.
  55. ↑ 55.0 55.1 Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  56. ↑ 56.0 56.1 56.2 56.3 Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  57. ↑ 57.0 57.1 57.2 Keith Amling (February 1, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  58. ↑ Keith Amling (January 15, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  59. ↑ Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  60. ↑ 60.0 60.1 Matthias Merzenich (March 22, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  61. ↑ Matthias Merzenich (May 7, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  62. ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  63. ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  64. ↑ 64.00 64.01 64.02 64.03 64.04 64.05 64.06 64.07 64.08 64.09 64.10 64.11 64.12 64.13 64.14 "knightt results". Matthias Merzenich. Retrieved on February 17, 2024.
  65. ↑ Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  66. ↑ Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  67. ↑ Matthias Merzenich (November 28, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  68. ↑ Matthias Merzenich (March 21, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
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