Difference between revisions of "LifeWiki:Spaceship Search Status Page"
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==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-<tt>p</tt> spaceship for <tt>p</tt> 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 == | == 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-diagonal]]s), 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. | |||
{|class="wikitable" | {|class="wikitable" style="text-align: center" | ||
|- | |- | ||
! Velocity !! Asymmetric !! Odd-symmetric !! Even-symmetric !! Gutter !! Odd glide-symmetric !! Even glide-symmetric | ! Velocity !! Asymmetric !! Odd-symmetric !! Even-symmetric !! Gutter !! Odd glide-symmetric !! Even glide-symmetric | ||
|- | |- | ||
| (1,0)c/2 | | (1,0)c/2 | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | [[70P2H1V0.1|21]] | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | [[70P2H1V0.1|21]] | ||
| style="background: #80ff80;" | 28 | | style="background: #80ff80;" | {{LinkCatagolue|xq2_y1c2h19a073370a91h2czg8c2n0v06ugy2gu60v0n2c8gz2201yg1022|name=28|style=raw}} | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | [[70P2H1V0.1|21]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,0)c/3 | | (1,0)c/3 | ||
| style="background: #80ff80;" | 12 | | style="background: #80ff80;" | [[Turtle|12]] | ||
| style="background: #80ff80;" | 15 | | style="background: #80ff80;" | [[Dart|15]] | ||
| style="background: #80ff80;" | 12 | | style="background: #80ff80;" | [[Turtle|12]] | ||
| style="background: #80ff80;" | 17 | | style="background: #80ff80;" | [[Brain|17]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,0)c/4 | | (1,0)c/4 | ||
| style="background: #80ff80;" | 10 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_xap1zxo276z06n6ihzwjp40a2zw3ikn0aizx11shhczcgi28mkb08zxu995222z2c2|name=10|style=raw}} | ||
| style="background: #80ff80;" | 13 | | style="background: #80ff80;" | [[Non-monotonic spaceship 1|13]] | ||
| style="background: #80ff80;" | 16 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_w434y0434z0om7e0mm0e7mozh1kf431134fk1hzdg122e11e221gdzxp74mm47pzx166w661|name=16|style=raw}} | ||
| style="background: #80ff80;" | 17 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_y0671x176zw2359cs0sc9532zw68cvhxhvc86z66br22ge0eg22rb66zy16e606e6|name=17|style=raw}} | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/4 | | (1,1)c/4 | ||
| style="background: #80ff80;" | 3 | | rowspan="2" style="background: #80ff80;" | [[Glider|3]] | ||
| style="background: #c0c0c0;" | - | | style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=7|style=raw}}<ref group="n" name="sep" /> | ||
| style="background: #c0c0c0;" | - | | rowspan="2" style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=7|style=raw}}<ref group="n" name="sep" /> | ||
| style="background: # | | rowspan="2" style="background: #c0c0c0;" | - | ||
| style="background: # | | rowspan="2" style="background: #80ff80;" | [[Glider|3]] | ||
|- | |||
|strict | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_y48444552gkozwg808oc72zcgfzw247|name=18|style=raw}}<ref name="post172628" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=19|style=raw}}<ref name="post172628" /> | |||
|- | |- | ||
| (2,0)c/4 | | (2,0)c/4 | ||
| style="background: #80ff80;" | 5 | | rowspan="2" style="background: #80ff80;" | [[Lightweight spaceship|5]] | ||
| style="background: #80ff80;" | 11 | | rowspan="2" style="background: #80ff80;" | [[X66|11]] | ||
| style="background: #80ff80;" | 12 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_6rucwcur6|name=12|style=raw}}<ref group="n" name="sep" /> | ||
| style="background: #80ff80;" | 11 | | rowspan="2" style="background: #80ff80;" | [[X66|11]] | ||
| style="background: #80ff80;" | 5 | | rowspan="2" style="background: #80ff80;" | [[Lightweight spaceship|5]] | ||
| style="background: #80ff80;" | 12 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_6frcx6frc|name=12|style=raw}}<ref group="n" name="sep" /> | ||
|- | |||
|strict | |||
| style="background: #80ff80;" | [[Hammerhead|20]]<ref name="MM2"/> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_si2rqr3c44s0g0gzw1rhoow10hddb06cq7k4ze9hkhb3ac03o0301zy01|name=16|style=raw}}<ref name="post172628" /> | |||
|- | |- | ||
| (1,0)c/5 | | (1,0)c/5 | ||
| style="background: #80ff80;" | 11 | | style="background: #80ff80;" | {{LinkCatagolue|xq5_w4bn0n96zwo4k4sq0ozy010b29k1zwg4m0hdd5z02ac2c85896zw8pihmdzpkti8p9gzwh90v8z01121i664ozy01siszw25ci2zxgg1fuczw7uqf010n3zwghiik22zhp0d0d0phzwa8gs2zg8g66mh04m2z066w13w2|name=11|style=raw}} | ||
| style="background: #80ff80;" | 19 | | style="background: #80ff80;" | {{LinkCatagolue|xq5_wm2kci1u0u1ick2mzw33274i101i47233zw2dc1v0v0v0v1cd2zxg8a3gv0vg3a8gz6978fgr3x3rgf8796zy21137311|name=19|style=raw}} | ||
| style="background: #80ff80;" | 18 | | style="background: #80ff80;" | {{LinkCatagolue|xq5_0gowe019910ewogz0o8g4797ee7974g8oz0uify6fiuzx7uarewerau7z6eghhd0hcch0dhhge6zwc1m4o2442o4m1czy1uhb44bhuz0ca1gly2lg1acz015054m6uu6m45051zy134011043|name=18|style=raw}} | ||
| style="background: #80ff80;" | 19 | | style="background: #80ff80;" | {{LinkCatagolue|xq5_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|name=19|style=raw}} | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/5 | | (1,1)c/5 | ||
| style="background: #80ff80;" | 13<ref name="coe1"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq5_cih1h0czhrpw1035z7ui0h1go04k8z012xp6oc2zy39ng|name=13|style=raw}}<ref name="coe1"/> | ||
| style="background: # | | style="background: #ffa0a0;" | w ≤ [[86P5H1V1|24]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | w ≤ [[86P5H1V1|24]] | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (2,0)c/5 | | (2,0)c/5 | ||
| style="background: #80ff80;" | 10 | | style="background: #80ff80;" | {{LinkCatagolue|xq5_rhlmggz3gggoar7zxpdm57zwmk8izw1ghe2zwmdb|name=10|style=raw}} | ||
| style="background: #80ff80;" | 15 | | style="background: #80ff80;" | [[44P5H2V0|15]] | ||
| style="background: #80ff80;" | 18 | | style="background: #80ff80;" | [[70P5H2V0|18]] | ||
| style="background: #80ff80;" | 15 | | style="background: #80ff80;" | [[44P5H2V0|15]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,0)c/6 | | (1,0)c/6 | ||
| style="background: #80ff80;" | 12<ref>{{ | | style="background: #80ff80;" | [[409P6H1V0|12]]<ref>{{LinkForumThread|format=ref|p=43495|title=Re: Spaceship Discussion Thread|author=praosylen|date=May 13, 2017}}</ref> | ||
| style="background: #80ff80;" | 19 | | style="background: #80ff80;" | [[600P6H1V0|19]] | ||
| style="background: #80ff80;" | [[Dragon|18]] | | style="background: #80ff80;" | [[Dragon|18]] | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | [[274P6H1V0|21]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/6 | | (1,1)c/6 | ||
| style="background: #ffa0a0;" | 10 | | style="background: #ffa0a0;" | 10 < w ≤ [[Seal|35]] | ||
| style="background: #ffa0a0;" | 10 < w ≤ [[77P6H1V1|36]] | |||
| style="background: # | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 10 < w | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 10 < w ≤ [[Seal|35]] | |||
|- | |- | ||
| (2,0)c/6 | | (2,0)c/6 | ||
| style="background: #80ff80;" | 12 | | style="background: #80ff80;" | {{LinkCatagolue|xq6_0keh2y088y08c04kc0o88bb84ny1s40g0mi0cc8zehkggk691wdca331w66701ddaw378f2w121zx13|name=12|style=raw}}<ref name="MM4"/> | ||
| style="background: #80ff80;" | 17<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq6_y0g81v0v18gzwso4k7ece7k4oszy1l3i4i3lzx2q9fxf9q2zg738c04o0o40c837gz22cc1hgf0fgh1cc22zy24aia4|name=17|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 18<ref name="coe5">{{ | | style="background: #80ff80;" | {{LinkCatagolue|xq6_x42jgbffbgj24zy0gideccedigzy02w4oo4w2zxe6oi1111io6ezy0djoppppojdz4a22ckf0880fkc22a4zy03y43|name=18|style=raw}}<ref name="MM2"/><ref name="coe5">{{LinkForumThread|format=ref|p=29960|title=Re: Spaceship Discussion Thread|author=Tim Coe|date=April 13, 2016}}</ref> | ||
| style="background: #80ff80;" | 19<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq6_8ci02j3ac604a02a83g4350go0ook222o0gwggz7b99aa8cab88cab888bc8b894cy21226d8406ac8b5zedp95l135d1135d111t31d1pi3gggxo4k6bhi06531daz13404cc5360250451c02caw101124441|name=19|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 17 | | style="background: #80ff80;" | {{LinkCatagolue|xq6_wgoihe4wgwkccy2o0gg66io1g3ccza58sc2a2klk2mvs13m90l3223x2kklkkk30s2k8zx395ph02411noq312023d174gg5c060oo3w1zy0121yf1110203|name=17|style=raw}} | ||
| style="background: #80ff80;" | 18<ref name="coe5" /> | | style="background: #80ff80;" | {{LinkCatagolue|xq6_w4a2a8jj8a2a4zy0j4ijji4jzx3313rr3133z08460mussum0648zxdj8gggg8jdzee8c0k666mk0sgeezw301y2221|name=18|style=raw}}<ref name="coe5" /> | ||
|- | |- | ||
| (2,1)c/6 | | (2,1)c/6 | ||
| style="background: #ffa0a0;" | 15<ref name="coe1">{{ | | style="background: #ffa0a0;" | 15<ref name="coe1">{{LinkForumThread|format=ref|p=25972|title=Re: 3c/7 othogonal and 2c/9 diagonal spaceships|author=Tim Coe|date=December 18, 2015}}</ref> < w ≤ [[Sir Robin|31]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 104: | Line 120: | ||
|- | |- | ||
| (3,0)c/6 | | (3,0)c/6 | ||
| style="background: # | | style="background: #80ff80;" | {{LinkCatagolue|xq6_y161cz8ogg3u1p4goe2z0338fho1fg44zy127cog9114k0u0ou2zaig0g8xp0i30vk32zw1278994302631|name=21|style=raw}}<ref name="amling-3c/6-w20-asym"/> | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | {{LinkCatagolue|xq6_y18waj0jaw8zw2qg1ng62026gn1gq2z2cagn21y312ngac2zgg03l4w88088w4l30ggz076gv0r6of0fo6r0vg67zy15fogo0ogof5zy41x1|name=21|style=raw}} | ||
| style="background: #80ff80;" | 28 | | style="background: #80ff80;" | {{LinkCatagolue|xq6_y2ogm6e3z8suj23aqaa98gzo605y01345024ozgrodwgokmhl821z013626qaa2kzy43336|name=28|style=raw}} | ||
| style="background: #80ff80;" | 21 | | style="background: #80ff80;" | {{LinkCatagolue|xq6_y18waj0jaw8zw2qg1ng62026gn1gq2z2cagn21y312ngac2zgg03l4w88088w4l30ggz076gv0r6of0fo6r0vg67zy15fogo0ogof5zy41x1|name=21|style=raw}} | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,0)c/7 | | (1,0)c/7 | ||
| style="background: #80ff80;" | 10<ref name="coe8">{{ | | style="background: #80ff80;" | [[Loafer|10]]<ref name="coe8">{{LinkForumThread|format=ref|p=31878|title=Re: Spaceship Discussion Thread|author=Tim Coe|date=June 11, 2016}}</ref><ref name="MM1"/> | ||
| style="background: #80ff80;" | 19<ref name="MM1"/> | | style="background: #80ff80;" | [[339P7H1V0|19]]<ref name="MM1"/> | ||
| style="background: #80ff80;" | 22<ref>{{ | | style="background: #80ff80;" | {{LinkCatagolue|xq7_26871wn3y03nw17862zy12596y06952|name=22|style=raw}}<ref>{{LinkForumThread|format=ref|p=44351|title=Re: Spaceship Discussion Thread|author=Matthias Merzenich|date=June 14, 2017}}</ref><ref group="n" name="sep" /> | ||
| style="background: #80ff80;" | 21<ref name="coe8"/><ref name="MM1"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq7_26871wn3x3nw17862zy12596x6952|name=21|style=raw}}<ref name="coe8"/><ref name="MM1"/><ref group="n" name="sep" /> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/7 | | (1,1)c/7 | ||
| style="background: #ffa0a0;" | 9 | | style="background: #ffa0a0;" | 9 < w ≤ [[Lobster|27]] | ||
| style="background: # | | style="background: #ffa0a0;" | 9 < w ≤ [[Lobster|27]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 9 < w | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (2,0)c/7 | | (2,0)c/7 | ||
| style="background: #ffa0a0;" | 11<ref>{{ | | style="background: #ffa0a0;" | 11<ref>{{LinkForumThread|format=ref|p=57129|title=Re: Spaceship Discussion Thread|author=Tomas Rokicki|date=March 1, 2018}}</ref><ref name="MM6"/> | ||
| style="background: #80ff80;" | 23<ref name="MM2"/> | | style="background: #80ff80;" | [[Scholar|23]]<ref name="MM2"/> | ||
| style="background: #80ff80;" | 18 | | style="background: #80ff80;" | [[Weekender|18]] | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 23<ref name="MM6"/> < w ≤ [[186P7H2V0|33]] | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 144: | Line 160: | ||
|- | |- | ||
| (3,0)c/7 | | (3,0)c/7 | ||
| style="background: #ffa0a0;" | 14<ref name="coe6">{{ | | style="background: #ffa0a0;" | 14<ref name="coe6">{{LinkForumThread|format=ref|p=30124|title=Re: Spaceship Discussion Thread|author=Tim Coe|date=April 17, 2016}}</ref> | ||
| style="background: #80ff80;" | 29<ref name="pt1">Checked by Paul Tooke with gfind</ref> | | style="background: #80ff80;" | [[Spaghetti monster|29]]<ref name="pt1">Checked by Paul Tooke with gfind</ref> | ||
| style="background: #ffa0a0;" | 28<ref name="coe6"/> | | style="background: #ffa0a0;" | 28<ref name="coe6"/> | ||
| style="background: #80ff80;" | 31<ref name="coe6"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq7_y1o0ab6gggxggg6ba0ozxstk15l4lhdxdhl4l51ktszy2o860oioxoio068ozoke0738a42j0430340j24a8370ekoz0108oox37dexed73xoo801z0jb995sogy7gos599bjz122212a0gl2y32lg0a212221zy3tv2c8gxg8c2vtzy3k0cv3y13vc0kzy3380102s0s201083zy3h1210670760121hzy2hd5y75dh|name=31|style=raw}}<ref name="coe6"/><ref name="chen-3c/7-w31gutter"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,0)c/8 | | (1,0)c/8 | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 10<ref name="Sokwe-c/8-w10g"/> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 19<ref name="Sokwe-c/8-w10odd"/> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 20<ref name="Sokwe-c/8-w10even"/> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 21<ref name="Sokwe-c/8-w10g"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/8 | | (1,1)c/8 | ||
| style="background: #ffa0a0;" | 7 | | style="background: #ffa0a0;" | 7 < w ≤ [[Walrus|21]] | ||
| style="background: #ffa0a0;" | 7 < w | |||
| style="background: # | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 7 < w | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 7 < w ≤ [[Walrus|21]] | |||
|- | |- | ||
| (2,0)c/8 | | (2,0)c/8 | ||
| style="background: #ffa0a0;" | 9<ref name="MM2"/> | | style="background: #ffa0a0;" | 9<ref name="MM2"/> | ||
| style="background: #80ff80;" | 15<ref name="coe7">{{ | | style="background: #80ff80;" | {{LinkCatagolue|xq8_1263hoc6coh3621zxo60l2l06ozwvw2o0o2wvz0o0rjpxpjr0ozcfhi3108013ihfczxduik9kiud|name=15|style=raw}}<ref name="MM2"/><ref name="coe7">{{LinkForumThread|format=ref|p=30299|title=Re: Spaceship Discussion Thread|author=Tim Coe|date=April 21, 2016}}</ref> | ||
| style="background: # | | style="background: #80ff80;" | {{LinkCatagolue|xq8_671y8176z111uu0o4w4o0uu111z8g8334mi66im4338g8z01xshraarhsx1zy22ahha2zy2cqbbqczy2ip88piz0djk7w1221w7kjdzwd11464w46411dz5dod5y45dod5zops108k8w8k801spoz01084173oo3714801zy0hphy0hph|name=18|style=raw}}<ref name="MM2"/><ref name="coe7"/> | ||
| style="background: #80ff80;" | 17<ref name=" | | style="background: #80ff80;" | {{LinkCatagolue|xq8_o0r54kc606ck45r0ozx8d5gg0gg5d8zwg0gm11011mg0gz0gre539e0e935ergz3o539k4x4k935o3zw249c1v0v1c942zy1so707oszy0gq2x2qgzw4o22oxo22o4zwoog57x75goozgo888h5o0o5h888ogzx33hph0hph33|name=17|style=raw}}<ref name="MM2"/><ref name="coe7"/> | ||
| style="background: #80ff80;" | 13 | | style="background: #80ff80;" | {{LinkCatagolue|xq8_xk3k0k3kzwe0698960ez0bt08o8o80tbzxhs505shzw855o0o558z06746bsb6476zxoo464soz0258bn1061zwgwfc010gzor1304cgg6d43z01w302|name=13|style=raw}} | ||
| style="background: #ffa0a0;" | 14 | | style="background: #ffa0a0;" | 14 | ||
|- | |- | ||
Line 184: | Line 200: | ||
|- | |- | ||
| (2,2)c/8 | | (2,2)c/8 | ||
| style="background: #ffa0a0;" | 8 < w ≤ {{LinkCatagolue|xq8_o4w8gi5hcgwgz5og0g7gadxj184s6332gkozx8iqxgh2p40ar8aczy3c80h01446zy5223|name=24|style=raw}} | |||
| style="background: #ffa0a0;" | 8 | | style="background: #ffa0a0;" | 8 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffa0a0;" | 8 | ||
| style="background: # | | style="background: #ffa0a0;" | 8 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
Line 208: | Line 224: | ||
|- | |- | ||
| (4,0)c/8 | | (4,0)c/8 | ||
| style="background: #80ff80;" | 11<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq8_e9885e88wgs046gy34eb766cg22aazsigg83cd47307q0ne3qsma4e68mmuw177w33244zym11|name=11|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 17<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq8_go8ggc2ghhioc4s1116agooz0hrawr4weeaxhhaaxhz13211681hh93647gggca133|name=17|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 20<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq8_v112oy2o211vz01wo1a44a1ow1zwo6k5t44t5k6oz0d1c32i33i23c1dzy0g895598gzx258owo852|name=20|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 19<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq8_x6996y16996zy0337pe0ep733zmgg118bio0oib811ggmz2fgmhihu202uhihmgf2zx36m1gxg1m63zxsv046101640vszwighc2y12chgizw78jnmio0oimnj87z0o40ho6ec0ce6oh04ozw12a421x124a21zks4g9k1fd0df1k9g4skz112cg22ue0eu22gc211zy06f1mc0cm1f6zy0988po0op889zxg8c2qf0fq2c8gz258pdd1y11ddp852zwe8950oxo0598ezy08um6x6mu8zy034461016443|name=19|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 17 | | style="background: #80ff80;" | {{LinkCatagolue|xq8_wgu113484311ugz0cdp1x2x1pdcz344240o444o042443zx3nqi212iqn3z0su944im3mi449uszy1ehh9d18azwg442mkg02hhqzwbg8531y032cz0oo0go8636cwq7z0132x420111|name=17|style=raw}} | ||
| style="background: #80ff80;" | 20<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq8_0sur6y66ruszw11w1rcsscr1w11zxo421i5w5i124oz0u1uur2y22ruu1uz24852y625842z251888g0oooo0g888152z8f7k4m641w146m4k7f8zy058heowoeh85z0oo2703sox474ba8zw22|name=20|style=raw}}<ref name="MM2"/> | ||
|- | |- | ||
| (1,0)c/9 | | (1,0)c/9 | ||
| style="background: #ffa0a0;" | 8<ref name="AforAmpere1">{{ | | style="background: #ffa0a0;" | 8<ref name="AforAmpere1">{{LinkForumThread|format=ref|p=52707|title=Re: Spaceship Discussion Thread|author=AforAmpere|date=November 5, 2017}}</ref> | ||
| style="background: #ffa0a0;" | 15<ref name="AforAmpere1"/> | | style="background: #ffa0a0;" | 15<ref name="AforAmpere1"/> | ||
| style="background: #ffa0a0;" | 16<ref name="AforAmpere1"/> | | style="background: #ffa0a0;" | 16<ref name="AforAmpere1"/> | ||
| style="background: #ffa0a0;" | 15<ref name=" | | style="background: #ffa0a0;" | 15<ref name="praosylen3"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/9 | | (1,1)c/9 | ||
| style="background: #ffa0a0;" | 6 | |||
| style="background: #ffa0a0;" | 6 | | style="background: #ffa0a0;" | 6 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffa0a0;" | 6 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (2,0)c/9 | | (2,0)c/9 | ||
| style="background: #ffa0a0;" | 8<ref name=" | | style="background: #ffa0a0;" | 8<ref name="praosylen4">{{LinkForumThread|format=ref|p=38767|title=Re: Spaceship Discussion Thread|author=praosylen|date=December 28, 2016}}</ref> | ||
| style="background: #ffa0a0;" | 15<ref name=" | | style="background: #ffa0a0;" | 15<ref name="praosylen2">{{LinkForumThread|format=ref|p=38682|title=Re: Spaceship Discussion Thread|author=praosylen|date=December 25, 2016}}</ref> | ||
| style="background: #ffa0a0;" | 16<ref name=" | | style="background: #ffa0a0;" | 16<ref name="praosylen3">{{LinkForumThread|format=ref|p=38728|title=Re: Spaceship Discussion Thread|author=praosylen|date=December 27, 2016}}</ref> | ||
| style="background: #ffa0a0;" | 17<ref name=" | | style="background: #ffa0a0;" | 17<ref name="praosylen4"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 248: | Line 264: | ||
|- | |- | ||
| (2,2)c/9 | | (2,2)c/9 | ||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | | style="background: #ffa0a0;" | 7 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffa0a0;" | 7 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 257: | Line 273: | ||
| (3,0)c/9 | | (3,0)c/9 | ||
| style="background: #ffa0a0;" | 11<ref name="MM3"/> | | style="background: #ffa0a0;" | 11<ref name="MM3"/> | ||
| style="background: #80ff80;" | 17<ref name="MM2"/> | | style="background: #80ff80;" | [[117P9H3V0|17]]<ref name="MM2"/> | ||
| style="background: #ffa0a0;" | 16<ref name="MM4"/> | | style="background: #ffa0a0;" | 16<ref name="MM4"/> | ||
| style="background: #ffa0a0;" | 17<ref name="MM2"/> | | style="background: #ffa0a0;" | 17<ref name="MM2"/> | ||
Line 274: | Line 290: | ||
| style="background: #ffa0a0;" | 11<ref name="coe6"/> | | style="background: #ffa0a0;" | 11<ref name="coe6"/> | ||
| style="background: #ffa0a0;" | 21<ref name="coe6"/> | | style="background: #ffa0a0;" | 21<ref name="coe6"/> | ||
| style="background: #ffa0a0;" | 22<ref name="coe4">{{ | | style="background: #ffa0a0;" | 22<ref name="coe4">{{LinkForumThread|format=ref|p=28770|title=Re: Spaceship Discussion Thread|author=Tim Coe|date=March 1, 2016}}</ref> | ||
| style="background: #ffa0a0;" | 23<ref name="coe6"/> | | style="background: #ffa0a0;" | 23<ref name="coe6"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 280: | Line 296: | ||
|- | |- | ||
| (1,0)c/10 | | (1,0)c/10 | ||
| style="background: #ffa0a0;" | 6<ref name=" | | style="background: #ffa0a0;" | 6<ref name="praosylen5">{{LinkForumThread|format=ref|p=39024|title=Re: Spaceship Discussion Thread|author=praosylen|date=January 5, 2017}}</ref> | ||
| style="background: #ffa0a0;" | 11<ref name=" | | style="background: #ffa0a0;" | 11<ref name="praosylen5"/> | ||
| style="background: #80ff80;" | 10 | | style="background: #80ff80;" | [[Copperhead|10]] | ||
| style="background: #ffa0a0;" | 13<ref name=" | | style="background: #ffa0a0;" | 13<ref name="praosylen5"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/10 | | (1,1)c/10 | ||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | | style="background: #ffa0a0;" | 7 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffa0a0;" | 7 | ||
|- | |- | ||
| (2,0)c/10 | | (2,0)c/10 | ||
| style="background: #ffa0a0;" | 6 | | style="background: #ffa0a0;" | 6 < w ≤ {{LinkCatagolue|xq10_w4bn0n96zwo4k4sq0ozy010b29k1zwg4m0hdd5z02ac2c85896zw8pihmdzpkti8p9gzwh90v8z01121i664ozy01siszw25ci2zy1hfeczxgh48clgzw4ca9o089gzxpq21gqbdzwgk1gt52z0802g441z0dc13ae1352z0e620szwg840o3ozwgjjo303oz01237rg841zx84i12uszxss9f431zg1pdz197zwbb64a0ezy0ehmzwfo04tkz2h3o50nzw131275zy12pjg|name=11|style=raw}} | ||
| style="background: #ffa0a0;" | 11 | | style="background: #ffa0a0;" | 11 < w ≤ [[160P10H2V0|19]] | ||
| style="background: #ffa0a0;" | 12 | | style="background: #ffa0a0;" | 12 < w ≤ {{LinkCatagolue|xq10_wgg088c0770c880ggzwhhgorg3113groghhz0ov0vey4ev0vozw143w2m88m2w341z0kkci2mmgccgmm2ickkzx31tcooddooct13zy1os1uoou1sozwok0mj2y02jm0kozw4427922222297244zy2eua22auezy2f116611fzy0op1i3w3i1pozxv211h1441h112vz08o8hpf601106fph8o8zwgs880339933088sgzy23hoccoh3zy3l6w6lzy1e731w137ezwg88oo374473oo88gzxtx6rkkr6xtzxghg8k0220k8ghgzx3v301c88c103v3zy1jg88gg88gjzy0mekh3ii3hkemzw9p08prpwprp80p9zx2t93tg11gt39t2zy0gpkl8w8lkpgz0cc404ccy0cc404ccz6h58w312w213w85h6zx4ffoy2off4zy2beeweebzy1gi589985igzy13968w8693zxgggo948849ogggzw3011dqswsqd1103z0997y8799zx5774k4w4k4775zws2gm1b0uu0b1mg2szx8paw4664wap8zy153q4w4q35zwg84442766724448gzw5482f9ghhg9f2845zy24a9119a4|name=20|style=raw}} | ||
| style="background: #ffa0a0;" | 13 | | style="background: #ffa0a0;" | 13 < w ≤ {{LinkCatagolue|xq10_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|name=19|style=raw}} | ||
| style="background: #ffa0a0;" | 13<ref name="coe4"/> | | style="background: #ffa0a0;" | 13<ref name="coe4"/> < w ≤ {{LinkCatagolue|xq10_xc19gy1c19gzy033y333zwm2kci1u0u1ick2mzw33274i101i47233zw2dc1v0v0v0v1cd2zxg8a3gv0vg3a8gz6978fgr3x3rgf8796zy21137311|name=19|style=raw}} | ||
| style="background: #ffa0a0;" | 14<ref name="coe4"/> | | style="background: #ffa0a0;" | 14<ref name="coe4"/> < w ≤ {{LinkCatagolue|xq10_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|name=20|style=raw}} | ||
|- | |- | ||
| (2,1)c/10 | | (2,1)c/10 | ||
Line 312: | Line 328: | ||
|- | |- | ||
| (2,2)c/10 | | (2,2)c/10 | ||
| style="background: #ffa0a0;" | 6 | |||
| style="background: #ffa0a0;" | 6 | | style="background: #ffa0a0;" | 6 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffa0a0;" | 6 | ||
| style="background: # | | style="background: #ffa0a0;" | 6 | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (3,0)c/10 | | (3,0)c/10 | ||
| style="background: #ffa0a0;" | 9<ref name="AforAmpere2">{{ | | style="background: #ffa0a0;" | 9<ref name="AforAmpere2">{{LinkForumThread|format=ref|p=52865|title=Re: Spaceship Discussion Thread|author=AforAmpere|date=November 13, 2017}}</ref> | ||
| style="background: #ffa0a0;" | 17<ref>{{ | | style="background: #ffa0a0;" | 17<ref>{{LinkForumThread|format=ref|p=53546|title=Re: Spaceship Discussion Thread|author=AforAmpere|date=December 10, 2017}}</ref> | ||
| style="background: #ffa0a0;" | 18<ref name="AforAmpere2"/> | | style="background: #ffa0a0;" | 18<ref name="AforAmpere2"/> | ||
| style="background: #ffa0a0;" | 17<ref>{{ | | style="background: #ffa0a0;" | 17<ref>{{LinkForumThread|format=ref|p=51306|title=Re: Spaceship Discussion Thread|author=AforAmpere|date=November 5, 2017}}</ref> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 344: | Line 360: | ||
|- | |- | ||
| (4,0)c/10 | | (4,0)c/10 | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 10<ref name="MM4"/> | ||
| style="background: #80ff80;" | 15<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq10_o4c4onrqoh8y1g8c8k4088y1gzha0ay4err0l4rhwrh0haelh4vz34643trb3h2y1126254022y11|name=15|style=raw}}<ref name="MM2"/> | ||
| style="background: # | | style="background: #80ff80;" | {{LinkCatagolue|xq10_eaiebb8c82gkwo4rfgt4w6696zx11303hoj1ed1w411zxggo0oh3pgemgw4ggzea9eqq262815w34ru1n4wccic|name=22|style=raw}}<ref name="MM5"/> | ||
| style="background: #80ff80;" | 21<ref name="MM2"/> | | style="background: #80ff80;" | {{LinkCatagolue|xq10_wgwfhj4o0o4jhfwgzbvo33w1iv0vi1w33ovbzy162q2h0h2q26zy31b303b1zy33470743|name=21|style=raw}}<ref name="MM2"/> | ||
| style="background: #80ff80;" | 15<ref name="coe3">{{ | | style="background: #80ff80;" | {{LinkCatagolue|xq10_ggcmhe404ehmcggz8pjmy3mjp8zy0p81s1ohzx8nnw745|name=15|style=raw}}<ref name="coe3">{{LinkForumThread|format=ref|p=27167|title=Re: 3c/7 othogonal and 2c/9 diagonal spaceships|author=Tim Coe|date=February 1, 2016}}</ref> | ||
| style="background: #ffa0a0;" | 16<ref name="coe3"/> | | style="background: #ffa0a0;" | 16<ref name="coe3"/> | ||
|- | |- | ||
Line 360: | Line 376: | ||
|- | |- | ||
| (5,0)c/10 | | (5,0)c/10 | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 11<ref name="MM4"/> | ||
| style="background: #ffa0a0;" | 19<ref name="MM2"/> | | style="background: #ffa0a0;" | 19<ref name="MM2"/> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 22<ref name="MM4"/> | ||
| style="background: #ffa0a0;" | 19<ref name="MM2"/> | | style="background: #ffa0a0;" | 19<ref name="MM2"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 368: | Line 384: | ||
|- | |- | ||
| (1,0)c/11 | | (1,0)c/11 | ||
| style="background: #ffa0a0;" | 6<ref name=" | | style="background: #ffa0a0;" | 6<ref name="praosylen1">{{LinkForumThread|format=ref|p=38671|title=Re: Spaceship Discussion Thread|author=praosylen|date=December 25, 2016}}</ref> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 11<ref name="lordlouckster1">{{LinkForumThread|format = ref|title = Re: Spaceship Discussion Thread|p = 148225|author = lordlouckster|date = July 13, 2022}}</ref> | ||
| style="background: #ffa0a0;" | | | style="background: #ffa0a0;" | 12<ref name="lordlouckster1"/> | ||
| style="background: #ffa0a0;" | 11<ref name=" | | style="background: #ffa0a0;" | 11<ref name="praosylen1"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (1,1)c/11 | | (1,1)c/11 | ||
| style="background: #ffffa0;" | ? | |||
| style="background: #ffffa0;" | ? | | style="background: #ffffa0;" | ? | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffffa0;" | ? | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (2,0)c/11 | | (2,0)c/11 | ||
| style="background: #ffa0a0;" | 6<ref name=" | | style="background: #ffa0a0;" | 6<ref name="praosylen5"/> | ||
| style="background: #ffa0a0;" | 11<ref name=" | | style="background: #ffa0a0;" | 11<ref name="praosylen5"/> | ||
| style="background: #ffa0a0;" | 12<ref name=" | | style="background: #ffa0a0;" | 12<ref name="praosylen5"/> | ||
| style="background: #ffa0a0;" | 13<ref name=" | | style="background: #ffa0a0;" | 13<ref name="praosylen5"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 400: | Line 416: | ||
|- | |- | ||
| (2,2)c/11 | | (2,2)c/11 | ||
| style="background: #ffffa0;" | ? | |||
| style="background: #ffffa0;" | ? | | style="background: #ffffa0;" | ? | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: # | | style="background: #ffffa0;" | ? | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 432: | Line 448: | ||
|- | |- | ||
| (4,0)c/11 | | (4,0)c/11 | ||
| style="background: #ffa0a0;" | 9 | | style="background: #ffa0a0;" | 9<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 17<ref name =" | | style="background: #ffa0a0;" | 17<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 18<ref name=" | | style="background: #ffa0a0;" | 18<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 19<ref name=" | | style="background: #ffa0a0;" | 19<ref name="MM7"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
Line 448: | Line 464: | ||
|- | |- | ||
| (5,0)c/11 | | (5,0)c/11 | ||
| style="background: #ffa0a0;" | 10 | | style="background: #ffa0a0;" | 10<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 19<ref name =" | | style="background: #ffa0a0;" | 19<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 20<ref name=" | | style="background: #ffa0a0;" | 20<ref name="MM7"/> | ||
| style="background: #ffa0a0;" | 21<ref name=" | | style="background: #ffa0a0;" | 21<ref name="MM7"/> | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
| style="background: #c0c0c0;" | - | | style="background: #c0c0c0;" | - | ||
|- | |- | ||
| (2,0)c/12 | | (2,0)c/12 | ||
| style="background: #ffffa0;" | | | style="background: #ffffa0;" | w ≤ {{LinkCatagolue|xq12_yj13922y022931zymo7q99q7ozyggg0nj611tuut116jn0ggzyi1y0gc44cgy01z03m0m3y03m0m3y8223322y93m0m3y03m0m3zw3gn3aaaa3ng3y7o035w530oy83gn3aaaa3ng3zwu97y279uy812222221y9u97y279uz22qggy2ggq220248oe2yb2eo842022qggy2ggq22zxq03q22q30qy526csssssssssssc62y5q03q22q30qzxdidy0didybe2i2eybdidy0didzyk8g40cscsc04g8zyjg0omb86068bmo0gzyj1247y37421zyk4ao9f9o9f9oa4zykg8kg0o5o0gk8gzyk12jg12121gj21zyj11cn4mo0om4nc11zyjgo0g61x16g0ogzyhegcd16b6g0g6b61dcgezyhc4g122e0a0a0e221g4czyh124epni2h0h2inpe421zyjg8mti47074itm8gzyg8u125g11gg0gg11g521u8zyj1h9o8pp0pp8o9h1zyj12t60uu0uu06t21zymora202arozyi80a191vg0gv191a08zyh18d6oy5o6d81zyk1gp4y14pg1zyhgg07g24gxg42g70ggzyh1210121y11210121|name=63|style=raw}} | ||
| style="background: #ffffa0;" | ? | | style="background: #ffffa0;" | ? | ||
| style="background: #ffffa0;" | ? | | style="background: #ffffa0;" | ? | ||
Line 464: | Line 480: | ||
|} | |} | ||
{{EmbedViewer | |||
|pname = knownspaceshipsbywidth | |||
|position = center | |||
|caption = Spaceships by width | |||
|viewerconfig = #C [[ WIDTH 800 HEIGHT 600 ]] | |||
}} | |||
== Known spaceships by height == | == Known spaceships by height == | ||
{|class="wikitable" | {|class="wikitable" style="text-align: center" | ||
|- | |- | ||
! Velocity !! | ! Velocity !! Asymmetric || Odd-symmetric (strict) || Even-symmetric (strict) || Gutter (strict) || Odd glide-symmetric (strict) || Even glide-symmetric (strict) | ||
|- | |- | ||
| (1,0)c/2 | | (1,0)c/2 | ||
| style="background: #80ff80;" | 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;" | {{LinkCatagolue|xq2_1fc0s04g0tje28agga82ejt0g40s0cf1zx112731ya137211|name=8|style=raw}} | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq2_32mmgozg0igke72z1n2q1z0qgm1z0hjrgz0a889be4z0lhhpd72z0ostz0l0m8zoeklozwkgine4zc46601|name=8|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (1,0)c/3 | | (1,0)c/3 | ||
| style="background: #80ff80;" | 5 | | style="background: #80ff80;" | [[25P3H1V0.1|5]]<ref name="MM-WLS" /><ref name="post172210" /> | ||
| style="background: #80ff80;" | {{LinkCatagolue|xq3_25c4a8goko06550687099c0264egij2630362jige4620c99078605560okog8a4c52|name=6|style=raw}}<ref name="post172309" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq3_2554ca0so07bgg0s4me08ewfjkk0gg0kkjfwe80em4s0ggb70os0ac4552zyc13y711y731|name=7|style=raw}}<ref name="post172309" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq3_25c4a8goko06550687099c0264egij2630362jige4620c99078605560okog8a4c52|name=6|style=raw}}<ref name="post172309" /> | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (1,0)c/4 | | (1,0)c/4 | ||
| style="background: #80ff80;" | 8 | | style="background: #80ff80;" | {{LinkCatagolue|xq4_02k4772z31h28oz560ao31z2ud62zhhd0gozy11|name=8|style=raw}}<ref name="MM-WLS" /><ref name="post172210" /><ref name="post172309" /> | ||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_7094uz0go83h2zg3n4698z3cf9h1ggzwcth4g8zy0dabzxgr5tzw3bo2ghzs3v988z0su26p1zw11s84ze0927|name=9|style=raw}}<ref name="post172309" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_ksoxso0s950473228c8sw66w8gy3ee88eey3g8w66ws8c822374059s0osxoskz122556yd6431077acee23261w16232eeca7701346yd655221|name=10|style=raw}}<ref name="post178496" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_7094uz0go83h2zg3n4698z3cf9h1ggzwcth4g8zy0dabzxgr5tzw3bo2ghzs3v988z0su26p1zw11s84ze0927|name=9|style=raw}}<ref name="post172309" /> | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (2,0)c/4 | | (2,0)c/4 | ||
| style="background: #80ff80;" | 6 | | 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: #ffa0a0;" | 7<ref name="post172309" /> | |||
|- | |- | ||
| (1,0)c/5 | | (1,0)c/5 | ||
| style="background: #80ff80;" | 8 | | style="background: #80ff80;" | [[Spider|8]]<ref name="MM-WLS" /><ref name="post172215" /> | ||
| style="background: #80ff80;" | [[Spider|8]] | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq5_ug1hmgc865da808ad568cgmh1guwug1hmgc865da808ad568cgmh1guz124w6yb6w421w124w6yb6w421|name=8|style=raw}} | |||
| style="background: #80ff80;" | [[Spider|8]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (2,0)c/5 | | (2,0)c/5 | ||
| style="background: #80ff80;" | 11 | | style="background: #80ff80;" | [[34P5H2V0|11]]<ref name="post178547" /> | ||
| style="background: #80ff80;" | {{LinkCatagolue|xq5_2aordd6zwp21so8ogzxhhwhhzwj8g73231z8a3rmmc|name=11|style=raw}} | |||
| style="background: #ffa0a0;" | 10 | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq5_2aordd6zwp21so8ogzxhhwhhzwj8g73231z8a3rmmc|name=11|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (1,0)c/6 | | (1,0)c/6 | ||
| style="background: #ffa0a0;" | 9<ref name="post178547" /> < h ≤ [[56P6H1V0|12]] | |||
| style="background: #ffa0a0;" | 9 | | style="background: #ffa0a0;" | 9 | ||
| style="background: #ffa0a0;" | 9 | |||
| style="background: #ffa0a0;" | 9 | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (2,0)c/6 | | (2,0)c/6 | ||
| style="background: #ffa0a0;" | 7<ref name="post178722" /> < h ≤ {{LinkCatagolue|xq6_8k64a213530ckk0c2m4swq3qws484c4swq3qws4m2c0kkc035312a46k8zyc1x71x17y371x17x1|name=9|style=raw}} | |||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | | style="background: #ffa0a0;" | 7 | ||
|- | |- | ||
| (3,0)c/6 | | (3,0)c/6 | ||
| style="background: #ffa0a0;" | 9<ref name="MM-WLS" /> < h ≤ [[86P6H3V0|13]] | |||
| style="background: #ffa0a0;" | 9 | | style="background: #ffa0a0;" | 9 | ||
| style="background: #ffa0a0;" | 9 | |||
| style="background: #ffa0a0;" | 9 | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (1,0)c/7 | | (1,0)c/7 | ||
| style="background: #ffa0a0;" | 8<ref name="post178547" /> < h ≤ [[Loafer|10]] | |||
| style="background: #ffa0a0;" | 8 | | style="background: #ffa0a0;" | 8 | ||
| style="background: #ffa0a0;" | 8 | |||
| style="background: #ffa0a0;" | 8 | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (2,0)c/7 | | (2,0)c/7 | ||
| style="background: #ffa0a0;" | 8<ref name="MM-WLS" /> < h ≤ [[Weekender|12]] | |||
| style="background: #ffa0a0;" | 8 | |||
| style="background: #ffa0a0;" | 8 | |||
| style="background: #ffa0a0;" | 8 | | style="background: #ffa0a0;" | 8 | ||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |- | ||
| (3,0)c/7 | | (3,0)c/7 | ||
| style="background: #ffa0a0;" | 7<ref name="MM-WLS" /> < h ≤ [[Soba|42]] | |||
| style="background: #ffa0a0;" | 7 | | style="background: #ffa0a0;" | 7 | ||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #ffa0a0;" | 7 | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|} | |||
{{EmbedViewer | |||
|pname = knownspaceshipsbyheight | |||
|viewerconfig = #C [[ WIDTH 800 HEIGHT 600 ]] | |||
|position = center | |||
|caption = Spaceships by height | |||
}} | |||
==Known diagonal spaceships by diagonal width and height== | |||
These are measured in [[half-diagonal]]s, as the width of the intersection of a 1-cell-wide orthogonal ray with the cells that turn on during the spaceship's motion. | |||
{|class="wikitable" style="text-align: center" | |||
|+ style="text-align: left;" | Minimum width | |||
|- | |||
! Velocity !! Asymmetric !! Symmetric !! Gutter !! Glide-symmetric | |||
|- | |||
| (1,1)c/4 | |||
| rowspan="2" style="background: #80ff80;" | [[Glider|4]] | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=11|style=raw}} | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=11|style=raw}} | |||
| rowspan="2" style="background: #80ff80;" | [[Glider|4]] | |||
|- | |||
|strict | |||
| style="background: #80ff80;" | [[big glider|15]]<ref name="post172047" /> | |||
| style="background: #80ff80;" | [[big glider|15]]<ref name="post172047" /> | |||
|- | |||
| (1,1)c/5 | |||
| style="background: #80ff80;" | [[67P5H1V1|15]] | |||
| style="background: #80ff80;" | [[86P5H1V1|27]] | |||
| style="background: #80ff80;" | [[86P5H1V1|27]] | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/6 | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq6_yzyj8mh15zyzy3g4484qba82am42f3zyzgg0c661aeoghgy2hi9gzyz1f6y31043g88rr8zysgg888077y7o9m42zyng0cu44mb4aa3cc0c4220a6022zyhgc26g044896013f8v0o8g761zyeo0e9842113xs8406753zya868g1gg402amocc87646czy3g8g224vgwgslh89h0174czy234c52og9854ke4p8152z08oo0464me6whjimz71x843o1x133zy1711|name=26|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq6_y2gowge9e1114zx462hg065d112b0448zkaae1fg32y2rc54ug06608z304w11ch05hujhy13wa6q8c8zy7cc011pg8y2374nozy91w14f1bbego0gggewbggzyl4404o2hg06k644448g0gsozyr2v01401xgg1o01zys12k8wgmm1p4550774zys1332y0dctwco9720cc8zyzy46ew4qkc0ggzyzyb669dew666ggozyzydee0ggx11113iigzyzyf23fowgg8o6518fggwgkk8zyzyi1w35446owo44mb16kk4ss6zyzyoo0s6bp2hzyzyp1wgvcd|name=33|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq6_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|name=55|style=raw}} | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq6_yzyj8mh15zyzy3g4484qba82am42f3zyzgg0c661aeoghgy2hi9gzyz1f6y31043g88rr8zysgg888077y7o9m42zyng0cu44mb4aa3cc0c4220a6022zyhgc26g044896013f8v0o8g761zyeo0e9842113xs8406753zya868g1gg402amocc87646czy3g8g224vgwgslh89h0174czy234c52og9854ke4p8152z08oo0464me6whjimz71x843o1x133zy1711|name=26|style=raw}}<ref name="post172047" /> | |||
|- | |||
| (1,1)c/7 | |||
| style="background: #ffa0a0;" | w ≤ [[Lobster|31]] | |||
| style="background: #ffa0a0;" | w ≤ [[Lobster|31]] | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq7_y4oo04jmzy7751zy1ce32621y3g0oo08ogz033360gn6oogw4uhw111cc1xgcoz6670ggh104so0331y5330sm6zy033y011y6goc8o84zyeccco11soy1go4w647jg532zydoosx660jj20cc72y111zyhee2x77|name=65|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/8 | |||
| style="background: #ffa0a0;" | w ≤ [[Walrus|24]] | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_ybg811hk03r688zy9f90gfto403ewgo80oozy1o88oy211115xi8y111zsw2hc4csqv0gy337pzcsh894c98w80g873244zx3y0c6zy4333|name=51|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_ybg811hk03r688zy9f90gfto403ewgo80oozy1o88oy211115xi8y111zsw2hc4csqv0gy337pzcsh894c98w80g873244zx3y0c6zy4333|name=51|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ [[Walrus|24]] | |||
|- | |||
| (2,2)c/8 | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_xeuoqpk880ggz8oo03b8qf1013j044gzx1hsxai862w11ko084oozy36186088gy4iguggzy78hn4gx8ggop111f04aa08zyb1120elnsw562y111cegzyh368gy99dczyk1050a8cccc8a8b0k0b088zyr3311211ehd231ggbuiozyz540ogp3o80kg1ac0gzyzx11win09g0k04jggo488zyzy622i01hhhtf04tot4zyzy81038qqu0cgw16e08g8czyzyiad0me3hw3rofgzyzyi1220o163fa48811acggwoozyzyn1x35224y0106g1e608ggzyzyt8lff0oo0ogi2a0811zyzyx21ko803ep843120b88bsozyzyzy31v544s4hce01050koozyzyzy311wfdb0gy21472zyzyzy91730ac4|name=24|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_yzyzy8gg088kpqogwo0ozyzyzy4g440j3101fq8b30op8zyzyz0oo480ok11w268iaxsh1y4gx88zyzyxggugiy4g8806816y2ogg0c3j0opphzyzyr80aa40f111pogg8xg4nh8y28ii4g80o02746c7r412zyzyngec11y1265wsnle0211xgm1c4686y0126040g676zyzykcd9y9g863y1g8oahg8y4c8403201zyzyg880b0k0b8a8cccc8a0501w88423132j1h76wssggk0cd2zyzyboiubgg132dhe1121133y2sh41y313wiai33zyzy5g0ca1gk08o3pgo045y7jf0v7gy3gg0c0501zyzx884oggj40k0g90niw11y4o088kk4r838220so0c2111zyz4tot40fthhh10i22y86ea0goow360d011zytc8g80e61wgc0uqq8301y4o0j823ap38web271zypgfor3wh3em0day6go0k5pw1si0aggg6421zygoowggca11884af361o0221y6jba3036m477k8zyagg806e1g601y042253x1y1gg0618jqp20goo477d0501zyb1180a2igo0oo0ffl8y5gh0oaud2whj4qgzy3osb88b021348pe308ok12y14qsosw9610610ob7455z0ook05010ech4s445v1y5co412mmy38c321z2741y2g0bdfw11xgy0g8s46a380e028pp466zy24ca0371y2oo8phhv13w1a601w6c2zyag2m7410112cd82gvg99zya13y2gg0k0511zyg36233|name=51|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_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|name=51|style=raw}} | |||
| style="background: #ffa0a0;" | w ≤ {{LinkCatagolue|xq8_2338iggy1gok8zx12d897x3f81psogk4zx8kem64cy613fbo4011uozy210i7vgy634622w6ko8oczy41w77ie82qcy566g0gzy7688oo09o0g0cc0gy131zye8f5y0231|name=35|style=raw}} | |||
|} | |||
{|class="wikitable" style="text-align: center" | |||
|+ style="text-align: left;" | Minimum height | |||
|- | |||
! Velocity !! Asymmetric !! Symmetric (strict) !! Gutter (strict) !! Glide-symmetric (strict) | |||
|- | |||
| (1,1)c/4 | |||
| style="background: #80ff80;" | [[Glider|5]]<ref name="post178496" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_y48444552gkozwg808oc72zcgfzw247|name=13|style=raw}}<ref name="post178496" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_g8i17z10fg0gogy1gzy33364o21jzy5110131t4xgcozya33wee40gwkc8zyh33jgggo0gzyj11x2n98g532zyp1w176s8zyv2444kk8153|name=14|style=raw}}<ref name="post178496" /> | |||
| style="background: #80ff80;" | [[Glider|5]]<ref name="post178496" /> | |||
|- | |||
| (1,1)c/5 | |||
| style="background: #80ff80;" | [[58P5H1V1|12]]<ref name="post172628" /> | |||
| style="background: #80ff80;" | [[58P5H1V1|12]]<ref name="post172628" /> | |||
| style="background: #80ff80;" | [[58P5H1V1|12]]<ref name="post172628" /> | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
|- | |||
| (1,1)c/6 | |||
| style="background: #80ff80;" | [[77P6H1V1|12]]<ref name="post4365" /> | |||
| style="background: #80ff80;" | [[77P6H1V1|12]]<ref name="post4365" /> | |||
| style="background: #ffa0a0;" | 11<ref name="post4365" /> | |||
| style="background: #ffa0a0;" | 11<ref name="post4365" /> | |||
|- | |||
|} | |||
==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 {{LinkCatagolue|xq4_6frcxcrf6|name=a LWSS pair|style=raw}} 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.<ref>{{LinkForumThread|f=2|t=3604|format=ref|title=Systematic survey of small patterns|author=Nick Gotts|date=November 28, 2018}}</ref> | |||
{|class="wikitable" style="text-align: center" | |||
|- | |||
! Velocity !! Asymmetric !! Odd-symmetric !! Even-symmetric !! Gutter !! Odd glide-symmetric !! Even glide-symmetric | |||
|- | |||
| (1,0)c/2 | |||
| style="background: #80ff80;" | [[64P2H1V0|64]]<ref name="amling-c/2-pop-le-98" /> | |||
| style="background: #80ff80;" | [[64P2H1V0|64]]<ref name="amling-c/2-pop-le-98" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq2_1fc0s04g0tje28agga82ejt0g40s0cf1zx112731ya137211|name=66|style=raw}}<ref name="amling-c/2-pop-le-98" /> | |||
| style="background: #80ff80;" | [[70P2H1V0.1|70]]<ref name="amling-c/2-pop-le-98" /> | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,0)c/3 | |||
|rowspan="2" style="background: #80ff80;" | [[25P3H1V0.1|2]][[25P3H1V0.2|5]]<ref name="amling-c/3-pop-le-49" /> | |||
|rowspan="2" style="background: #80ff80;" | [[Dart|34]]<ref name="amling-c/3-pop-le-49" /> | |||
|rowspan="2" style="background: #80ff80;" | [[Turtle|44]]<ref name="amling-c/3-pop-le-49" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq3_16614e8o4aa82cc202cc28aa4o8e41661|name=50|style=raw}}<ref name="amling-c/3-pop-le-49" /> | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
|- | |||
|strict | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq3_xr3v488zcori2gzxnkzocc704zw3d1sg88zx333|name=52|style=raw}}<ref name="amling-c/3-odd-pop-le-52" /> | |||
|- | |||
| (1,0)c/4 | |||
| style="background: #80ff80;" | [[37P4H1V0|37]]<ref name="amling-c/4-pop-le-37" /> | |||
| style="background: #80ff80;" | [[46P4H1V0|46]]<ref name="post172207" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_13ho8gyeg8oh31zw134dh1i0s0s8w8s0s0i1hd431zy74b8228b4|name=58|style=raw}}<ref name="post172249" /> | |||
| style="background: #80ff80;" | [[46P4H1V0|46]]<ref name="post172207" /> | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/4 | |||
|rowspan="2" style="background: #80ff80;" | [[Glider|5]] | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=10|style=raw}}<ref name="amling-(1,1)c/4-pop-le-9" /> | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_o8g351z1|name=10|style=raw}}<ref name="amling-(1,1)c/4-pop-le-9" /> | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
|rowspan="2" style="background: #80ff80;" | [[Glider|5]] | |||
|- | |||
|strict | |||
| style="background: #ffa0a0;" | 9<ref name="amling-(1,1)c/4-pop-le-9" /> < p ≤ {{LinkCatagolue|xq4_y48444552gkozwg808oc72zcgfzw247|name=37|style=raw}} | |||
| style="background: #ffa0a0;" | 9<ref name="amling-(1,1)c/4-pop-le-9" /> < p ≤ {{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=50|style=raw}} | |||
|- | |||
|(2,0)c/4 | |||
|rowspan="2" style="background: #80ff80;" | [[Lightweight spaceship|9]] | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6frcxcrf6|name=18|style=raw}} | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6rucwcur6|name=18|style=raw}} | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6frcxcrf6|name=18|style=raw}} | |||
|rowspan="2" style="background: #80ff80;" | [[Lightweight spaceship|9]] | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq4_6frcx6frc|name=18|style=raw}} | |||
|- | |||
|strict | |||
| style="background: #80ff80;" | [[MWSS on MWSS 1|20]]<ref name="amling-c/3-odd-pop-le-52" /><ref name="NiemiecCounts" /> | |||
| style="background: #ffa0a0;" | 34<ref name="post172601" /> < p ≤ {{LinkCatagolue|xq4_e9885zxe994o10czy3g9fzx79921803z7911a|name=48|style=raw}} | |||
| style="background: #80ff80;" | [[MWSS on MWSS 1|20]]<ref name="amling-c/3-odd-pop-le-52" /><ref name="NiemiecCounts" /> | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq4_suuw5b61ruuz1363y11363|name=32|style=raw}} | |||
|- | |||
| (1,0)c/5 | |||
| style="background: #ffa0a0;" | p ≤ [[Spider|58]] | |||
| style="background: #ffa0a0;" | p ≤ [[Spider|58]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq5_ug1hmgc865da808ad568cgmh1guwug1hmgc865da808ad568cgmh1guz124w6yb6w421w124w6yb6w421|name=116|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[Spider|58]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/5 | |||
| style="background: #ffa0a0;" | p ≤ [[58P5H1V1|58]] | |||
| style="background: #ffa0a0;" | p ≤ [[58P5H1V1|58]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffa0a0;" | p ≤ [[58P5H1V1|58]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (2,0)c/5 | |||
|rowspan="2" style="background: #80ff80;" | [[30P5H2V0|30]]<ref name="amling-2c/5-pop-le-31" /> | |||
|rowspan="2" style="background: #80ff80;" | [[44P5H2V0|44]]<ref name="post177064" /> | |||
| style="background: #80ff80;" | {{LinkCatagolue|xq5_0gggwmdhdmggwggmdhdmwgggz2h9nx1x22w22x1xn9h2|name=60|style=raw}}<ref name="post181787" /> | |||
|rowspan="2" style="background: #80ff80;" | [[44P5H2V0|44]]<ref name="post177064" /> | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
|rowspan="2" style="background: #c0c0c0;" | - | |||
|- | |||
|strict | |||
| style="background: #ffa0a0;" |60<ref name="post181787" /> < p ≤ [[70P5H2V0|70]] | |||
|- | |||
| (1,0)c/6 | |||
| style="background: #ffa0a0;" | p ≤ [[56P6H1V0|56]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_eaqqrexcswscxerqqaexeaqqrexcswscxerqqaezy2c330a66a033cybc330a66a033czy331y213yd31y213|name=112|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[56P6H1V0|56]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_eaqqrexcswscxerqqaexeaqqrexcswscxerqqaezy2c330a66a033cybc330a66a033czy331y213yd31y213|name=112|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/6 | |||
| style="background: #ffa0a0;" | p ≤ [[77P6H1V1|77]] | |||
| style="background: #ffa0a0;" | p ≤ [[77P6H1V1|77]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_yzyoos296zyzyioo638011zyzyagggweeee442zyzy7skitc74cc6zyzy4sssw8f6zyzw8c4j30971zywg84m66zyrgo4ic011zylggc6g033zyissst984zyao84rpf8ooczy7ooo11hvczy1go8660jf3z0g8cccw1z1221|name=154|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffa0a0;" | p ≤ [[Seal|170]] | |||
|- | |||
| (2,0)c/6 | |||
| style="background: #ffa0a0;" | p ≤ [[72P6H2V0|72]] | |||
| style="background: #ffa0a0;" | p ≤ [[72P6H2V0|72]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_0g0ggchp92c608gggo8e6mgz1s612vy42648s3ep1ssszg7cg8vy48c427oejg777z010116hji86c0211132ecd1|name=128|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[72P6H2V0|72]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_8k64a213530ckk0c2m4swq3qws484c4swq3qws4m2c0kkc035312a46k8zyc1x71x17y371x17x1|name=110|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_w4a2a8jj8a2a4zy0j4ijji4jzx3313rr3133z08460mussum0648zxdj8gggg8jdzee8c0k666mk0sgeezw301y2221|name=129|style=raw}} | |||
|- | |||
| (2,1)c/6 | |||
| style="background: #ffa0a0;" | p ≤ [[Sir Robin|282]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (3,0)c/6 | |||
| style="background: #ffa0a0;" | p ≤ [[86P6H3V0|86]] | |||
| style="background: #ffa0a0;" | p ≤ [[86P6H3V0|86]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_y2ogm6e3z8suj23aqaa98gzo605y01345024ozgrodwgokmhl821z013626qaa2kzy43336|patternname=104|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq6_y2c2h17071h2cz0g8c2v0ng2u0u2gn0v2c8gz4a20ia03r1x1r30ai02a4zwgkm83y538mkgzy14y74|name=108|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,0)c/7 | |||
| rowspan="2" style="background: #ffa0a0;" | p ≤ [[Loafer|20]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_3nw17862026871wn3z6952y72596|name=40|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_26871wn3y03nw17862zy12596y06952|name=40|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_26871wn3x3nw17862zy12596x6952|name=40|style=raw}} | |||
| rowspan="2" style="background: #c0c0c0;" | - | |||
| rowspan="2" style="background: #c0c0c0;" | - | |||
|- | |||
|strict | |||
| style="background: #ffa0a0;" |p ≤ [[taco|90]] | |||
| style="background: #ffa0a0;" |p ≤ {{LinkCatagolue|xq7_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|name=684|style=raw}} | |||
| style="background: #ffa0a0;" |p ≤ [[taco|90]] | |||
|- | |||
| (1,1)c/7 | |||
| style="background: #ffa0a0;" | p ≤ [[Lobster|83]] | |||
| style="background: #ffa0a0;" | p ≤ [[Lobster|83]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_y4oo04jmzy7751zy1ce32621y3g0oo08ogz033360gn6oogw4uhw111cc1xgcoz6670ggh104so0331y5330sm6zy033y011y6goc8o84zyeccco11soy1go4w647jg532zydoosx660jj20cc72y111zyhee2x77|name=166|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (2,0)c/7 | |||
| style="background: #ffa0a0;" | p ≤ [[Weekender|36]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_7dfxg88gxfd7x7dfxg88gxfd7zw123u2222u321y3123u2222u321|name=72|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[Weekender|36]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq7_7dfxg88gxfd7x7dfxg88gxfd7zw123u2222u321y3123u2222u321|name=72|style=raw}} | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (3,0)c/7 | |||
| style="background: #ffa0a0;" | p ≤ [[232P7H3V0|232]] | |||
| style="background: #ffa0a0;" | p ≤ [[232P7H3V0|232]] | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #ffa0a0;" | p ≤ [[232P7H3V0|232]] | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (1,1)c/8 | |||
| style="background: #ffa0a0;" | p ≤ [[Walrus|68]] | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffa0a0;" | p ≤ [[Walrus|68]] | |||
|- | |||
| (2,0)c/8 | |||
| style="background: #ffa0a0;" | p ≤ [[74P8H2V0|74]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_1263hoc6coh3621zxo60l2l06ozwvw2o0o2wvz0o0rjpxpjr0ozcfhi3108013ihfczxduik9kiud|name=121|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_x6atw3becy4ceb3wta6zgcxcqcqcxcgwgcxcqcqcxcgz02e4m1u0u1m4e2y02e4m1u0u1m4e2zxiigmgmgiiy4iigmgmgiizy11x1y81x1|name=148|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_x6atw3becy3ceb3wta6zgcxcqcqcxcg0gcxcqcqcxcgz02e4m1u0u1m4e2x2e4m1u0u1m4e2zxiigmgmgiiy3iigmgmgiizy11x1y71x1|name=148|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[74P8H2V0|74]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_x6atw3becy46atw3beczgcxcqcqcxcgwgcxcqcqcxcgz02e4m1u0u1m4e2y02e4m1u0u1m4e2zxiigmgmgiiy4iigmgmgiizy11x1y81x1|name=148|style=raw}} | |||
|- | |||
| (2,2)c/8 | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_x67xecgy6ggz84gevjrgu810223wsp631118aczx3otoy46408gzy2oic6332gko0111zy0c81hzy2223|name=89|style=raw}} | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #c0c0c0;" | - | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #ffffa0;" | ? | |||
| style="background: #c0c0c0;" | - | |||
|- | |||
| (4,0)c/8 | |||
| style="background: #ffa0a0;" | p ≤ [[31P8H4V0|31]] | |||
| style="background: #ffa0a0;" | p ≤ [[58P8H4V0|58]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_0ooc4rbhe644w446ehbr4cooz6d73x7frcy0crf7x37d6|name=62|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ [[58P8H4V0|58]] | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_027de6eozgocss5bor7266z0hhy0rz13677kq3rsz08smece3|name=62|style=raw}} | |||
| style="background: #ffa0a0;" | p ≤ {{LinkCatagolue|xq8_0sighgazy1egq40ooz79111895zsiggg2ikzy1e1b4z0791h1a|name=62|style=raw}} | |||
|} | |} | ||
==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=== | |||
* All (1,0)c/2 ships up to a population of 127 cells<ref name="post175793" /> (total number of ships only; complete stamp collection up to 80 cells<ref name="post171031" />) | |||
* All (2,0)c/4 ships up to a population of 25 cells (28 ships)<ref name="NiemiecCounts" /> | |||
* All (2,0)c/4 odd-symmetric ships up to a population of 35 cells (3 strict ships: [[MWSS on MWSS 1]], [[HWSS on HWSS 1]], [[Big A]], and [[X66]])<ref name="post172601" /> | |||
* All (2,0)c/4 ships up to width 11 (7 ships)<ref name="post126570" /> | |||
* All (2,0)c/4 ships up to height 7 (strings of interacting [[lightweight spaceship|lightweight]] and [[middleweight spaceship|middleweight]] spaceships only)<ref name="post172309" /> | |||
* All (2,0)c/4 odd-symmetric ships up to width 15 (6 strict ships: [[MWSS on MWSS 1]], [[HWSS on HWSS 1]], [[X66]], and three [[hivenudger]] variants)<ref name="MM2"/> | |||
* All (2,0)c/4 gutter-symmetric ships up to width 17 (3 strict ships: [[MWSS on MWSS 1]], [[HWSS on HWSS 1]], and [[X66]])<ref name="MM2"/> | |||
* All (2,0)c/4 ships up to width 13 with a population of 50 or fewer cells<ref name="post59813" /> | |||
* All (4,0)c/8 ships up to width 11 ({{LinkCatagolue|xq8_e9885e88wgs046gy34eb766cg22aazsigg83cd47307q0ne3qsma4e68mmuw177w33244zym11|name=1 period-8 ship|style=raw}})<ref name="post126570" /> | |||
===c/3 orthogonal=== | |||
* All (1,0)c/3 ships up to a population of 49 cells<ref name="amling-c/3-pop-le-49" /> | |||
* All (1,0)c/3 odd-symmetric ships up to a population of 67 cells (26 strict ships)<ref name="post172607" /> | |||
* All (1,0)c/3 even-symmetric ships up to a population of 86 cells (29 strict ships)<ref name="post172640" /> | |||
* All (1,0)c/3 ships up to width 13<ref name="knightt-results" /> | |||
* All (1,0)c/3 ships up to height 6 (5 ships)<ref name="post172309" /> | |||
* All (1,0)c/3 odd-symmetric ships up to width 19 ([[dart|1 width-15 ship]]; infinitely many width-17+ ships)<ref name="knightt-results" /> | |||
* All (1,0)c/3 even-symmetric ships up to width 20 ([[turtle|1 width-12 ship]]; infinitely many width-14+ ships)<ref name="knightt-results" /> | |||
* All (1,0)c/3 gutter-symmetric ships up to width 21 ([[brain|1 width-17 ship]]; infinitely many width-19+ ships)<ref name="knightt-results" /> | |||
* All (2,0)c/6 even-symmetric ships up to width 18<ref name="coe5" /> | |||
* All (2,0)c/6 even-glide-symmetric ships up to width 18<ref name="coe5" /> | |||
===c/4 orthogonal=== | |||
* All (1,0)c/4 ships up to a population of 37 cells ([[37P4H1V0|1 ship]])<ref name="amling-c/4-pop-le-37" /> | |||
* All (1,0)c/4 odd-symmetric ships up to a population of 61 cells (4 ships: [[46P4H1V0]], {{LinkCatagolue|xq4_7094uz4ee2dd0kg0gzxs0kk08mk1zgoo0oo0k4142zg19hu2z30201|name=this 59-cell ship|style=raw}}, {{LinkCatagolue|xq4_y2oo7t0t7ooz2qgx8t2rgr2t8xgq2z122166y5661221|name=this 61-cell ship|style=raw}}, and {{LinkCatagolue|xq4_mp6z5992gozy016u8c44czy1pv5c99dz844g36zr7pz01|name=this 61-cell ship|style=raw}})<ref name="post179535" /> | |||
* All (1,0)c/4 even-symmetric ships up to a population of 58 cells ({{LinkCatagolue|xq4_13ho8gyeg8oh31zw134dh1i0s0s8w8s0s0i1hd431zy74b8228b4|name=1 ship|style=raw}})<ref name="post172249" /> | |||
* All (1,0)c/4 ships up to width 11<ref name="knightt-results" /> | |||
* All (1,0)c/4 ships up to height 8 ({{LinkCatagolue|xq4_02k4772z31h28oz560ao31z2ud62zhhd0gozy11|name=1 ship|style=raw}})<ref name="post172309" /> | |||
* All (1,0)c/4 odd-symmetric ships up to width 17<ref name="knightt-results" /> | |||
* All (1,0)c/4 even-symmetric ships up to width 18 (2 width-16 ships: {{LinkCatagolue|xq4_w434y0434z0om7e0mm0e7mozh1kf431134fk1hzdg122e11e221gdzxp74mm47pzx166w661|name=this ship|style=raw}} and {{LinkCatagolue|xq4_wb1o4w4o1bzw7ssowoss7zy1cccczw821dccd128zxddugguddz1tb201dd102bt1zefhsiswsishfezw2e033330e2zw373y0373|name=the same ship with a tagalong|style=raw}}; infinitely many width-18 ships)<ref name="knightt-results" /> | |||
* All (1,0)c/4 gutter-symmetric ships up to width 19<ref name="knightt-results" /> | |||
===c/4 diagonal=== | |||
* All (1,1)c/4 ships up to a population of 9 cells ([[glider|1 ship]])<ref name="post171151" /> | |||
* All (1,1)c/4 symmetric ships in an {{times|18|18}} bounding box ({{LinkCatagolue|xq4_y48444552gkozwg808oc72zcgfzw247|name=1 strict ship|style=raw}})<ref name="post172628" /> | |||
* All (1,1)c/4 gutter-symmetric ships in a {{times|19|19}} bounding box ({{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=1 strict ship|style=raw}})<ref name="post172628" /> | |||
* All (1,1)c/4 ships up to diagonal height 12 ([[glider|1 ship]])<ref name="post178496" /> | |||
* All (1,1)c/4 ships up to diagonal width 13 (4 ships)<ref name="post172047" /> | |||
* All (1,1)c/4 ships up to orthogonal width 10 (5 ships)<ref name="post172047" /> | |||
* All (1,1)c/4 ships up to single-phase orthogonal width 9 (15 ships)<ref name="post172047" /> | |||
===c/5 orthogonal=== | |||
* All (1,0)c/5 ships up to height 8<ref name="post172604" /> | |||
* All (1,0)c/5 even-symmetric ships up to width 18<ref name="knightt-results" /> | |||
* All (1,0)c/5 gutter-symmetric ships up to width 19<ref name="knightt-results" /> | |||
===c/5 diagonal=== | |||
* All (1,1)c/5 ships up to diagonal height 12 ([[58P5H1V1|1 ship]])<ref name="post172628" /> | |||
* All (1,1)c/5 ships up to diagonal width 16 ([[67P5H1V1|1 ship]])<ref name="post172309" /> | |||
* All (1,1)c/5 symmetric ships up to diagonal width 27 (2 ships: [[86P5H1V1]] and {{LinkCatagolue|xq5_yjggn6kzyf8k0cdh7qzyabm4ooot1sy01aik6st0764zy6ait0h0h1ogxtt506495zy4dv8e4spg3aaxb596c8z0ggo0407321ok8urao35161zoh11xggg511zx64w33|name=this ship|style=raw}})<ref name="post172133" /> | |||
* All (1,1)c/5 gutter-symmetric ships up to diagonal width 29 ([[86P5H1V1|1 ship]])<ref name="post172309" /> | |||
===2c/5 orthogonal=== | |||
* All (2,0)c/5 ships up to a population of 31 cells ([[30P5H2V0|1 ship]])<ref name="amling-2c/5-pop-le-31" /> | |||
* 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 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 even-symmetric ships up to width 20 ([[70P5H2V0|1 ship]])<ref name="knightt-results" /> | |||
* All (2,0)c/5 gutter-symmetric ships up to width 21 ([[44P5H2V0|1 width-15 ship]]; {{LinkCatagolue|xq5_gv9r4oy3o4r9vgz11cv011gxg110vc11zw2m5j9rg0gr9j5m2zwecl52pxp25lcez066kpc9gxg9cpk66zxhd8l11011l8dhz06v1f0eic0cie0f1v6zx152y3251|name=1 width-19 ship|style=raw}}; infinitely many width-21 ships)<ref name="knightt-results" /> | |||
* All (4,0)c/10 odd-symmetric ships up to width 15 (3 period-10 ships)<ref name="MM2"/> | |||
===c/6 orthogonal=== | |||
* All (1,0)c/6 even-symmetric ships up to width 18 ([[dragon|1 ship]])<ref name="knightt-results" /> | |||
===2c/7 orthogonal=== | |||
* All (2,0)c/7 even-symmetric ships up to width 22 (2 ships: [[weekender]] and {{LinkCatagolue|xq7_wcufecxggxcefuczy0111agmhhmga111zxcigc01y010cgiczy044c8y28c44zy2n08888880nzwgski1y41iksgz37aqikja066660ajkiqa73zw3kmk203y0302kmk3zy0245umowomu542zy124119kk91142zxo4kkiey0eikk4ozy02c87y278c2zx6f78y487f6z02dlg2ty4t2gld2zw730ooy4oo037|name=weekender + tagalong|style=raw}})<ref name="post126432" /> | |||
===c/10 orthogonal=== | |||
* All (1,0)c/10 even-symmetric ships up to width 12 ([[copperhead|1 width-10 ship]]; infinitely many width-12 ships)<ref name="MM2"/> | |||
== See also == | == See also == | ||
* [[List of spaceships]] | |||
* [[User:Sokwe/Spaceship searches]] | |||
== Notes== | |||
<references group="n"> | |||
<ref name="sep">Note that this is not recognised as a single contiguous spaceship by [[apgsearch]]'s object separation.</ref> | |||
</references> | |||
== References == | == References == | ||
<references> | <references> | ||
Line 876: | Line 990: | ||
|p = 127999 | |p = 127999 | ||
|author = Matthias Merzenich | |author = Matthias Merzenich | ||
|date = April 10, 2021 | |date = April 14, 2021 | ||
}}</ref> | |||
<ref name="MM5">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 128542 | |||
|author = Matthias Merzenich | |||
|date = April 19, 2021 | |||
}}</ref> | |||
<ref name="MM6">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 129058 | |||
|author = Matthias Merzenich | |||
|date = April 26, 2021 | |||
}}</ref> | |||
<ref name="MM7">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 129655 | |||
|author = Matthias Merzenich | |||
|date = May 5, 2021 | |||
}}</ref> | |||
<ref name="Sokwe-c/8-w10g">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 138201 | |||
|author = Matthias Merzenich | |||
|date = November 29, 2021 | |||
}}</ref> | |||
<ref name="Sokwe-c/8-w10odd">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Help me finish this c/8 search | |||
|p = 90290 | |||
|author = Matthias Merzenich | |||
|date = February 25, 2020 | |||
}}</ref> | |||
<ref name="Sokwe-c/8-w10even">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 155106 | |||
|author = Matthias Merzenich | |||
|date = December 22, 2022 | |||
}}</ref> | |||
<ref name="amling-3c/6-w20-asym">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 156124 | |||
|author = Keith Amling | |||
|date = January 18, 2023 | |||
}}</ref> | |||
<ref name="chen-3c/7-w31gutter">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 118727 | |||
|author = Dylan Chen | |||
|date = January 10, 2021 | |||
}}</ref> | |||
<ref name="amling-c/2-pop-le-98">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = p171152 | |||
|author = Keith Amling | |||
|date = November 14, 2023 | |||
}}</ref> | |||
<ref name="amling-c/3-pop-le-49">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 171012 | |||
|author = Keith Amling | |||
|date = November 12, 2023 | |||
}}</ref> | |||
<ref name="amling-c/4-pop-le-37">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 171705 | |||
|author = Keith Amling | |||
|date = November 22, 2023 | |||
}}</ref><!--maybe p171321 reveals ≤ 35 disproven but he didn't explicitly say--> | |||
<ref name="amling-(1,1)c/4-pop-le-9">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 171151 | |||
|author = Keith Amling | |||
|date = November 13, 2023 | |||
}}</ref> | |||
<ref name="amling-2c/5-pop-le-31">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 171254 | |||
|author = Keith Amling | |||
|date = November 15, 2023 | |||
}}</ref> | |||
<ref name="post172047">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 172047 | |||
|author = Matthias Merzenich | |||
|date = November 27, 2023 | |||
}}</ref> | |||
<ref name="post126432">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 126432 | |||
|author = Matthias Merzenich | |||
|date = March 21, 2021 | |||
}}</ref> | |||
<ref name="post126570">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 126570 | |||
|author = Matthias Merzenich | |||
|date = March 22, 2021 | |||
}}</ref> | |||
<ref name="post172207">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172207 | |||
|author = Keith Amling | |||
|date = November 29, 2023 | |||
}}</ref> | |||
<ref name="post172249">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172249 | |||
|author = Keith Amling | |||
|date = November 30, 2023 | |||
}}</ref> | |||
<ref name="amling-c/3-odd-pop-le-52">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172310 | |||
|author = Keith Amling | |||
|date = December 1, 2023 | |||
}}</ref> | |||
<ref name="post172309">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 172309 | |||
|author = Matthias Merzenich | |||
|date = December 1, 2023 | |||
}}</ref> | |||
<ref name="post172604">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 172604 | |||
|author = Matthias Merzenich | |||
|date = December 6, 2023 | |||
}}</ref> | |||
<ref name="post172601">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172601 | |||
|author = Keith Amling | |||
|date = December 6, 2023 | |||
}}</ref> | |||
<ref name="post172607">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172607 | |||
|author = Keith Amling | |||
|date = December 6, 2023 | |||
}}</ref> | |||
<ref name="post172628">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 172628 | |||
|author = Matthias Merzenich | |||
|date = December 6, 2023 | |||
}}</ref> | |||
<ref name="post172640">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 172640 | |||
|author = Keith Amling | |||
|date = December 6, 2023 | |||
}}</ref> | |||
<ref name="NiemiecCounts"> | |||
{{cite web | |||
|url=https://conwaylife.com/ref/mniemiec/objcount.htm | |||
|title=Life Object Counts | |||
|publisher=Mark Niemiec | |||
|accessdate=December 9, 2023}}</ref> | |||
<ref name="post175793">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 175793 | |||
|author = Keith Amling | |||
|date = January 15, 2024 | |||
}}</ref> | |||
<ref name="post171031">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 171031 | |||
|author = Keith Amling | |||
|date = November 13, 2023 | |||
}}</ref> | |||
<ref name="post177064">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 177064 | |||
|author = Keith Amling | |||
|date = February 1, 2024 | |||
}}</ref> | |||
<ref name="knightt-results"> | |||
{{cite web | |||
|url=https://github.com/Matthias-Merzenich/knightt-results | |||
|title=knightt results | |||
|publisher=Matthias Merzenich | |||
|accessdate=February 17, 2024}}</ref> | |||
<ref name="post172133">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 172133 | |||
|author = Matthias Merzenich | |||
|date = November 28, 2023 | |||
}}</ref> | |||
<ref name="post171151">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 171151 | |||
|author = Keith Amling | |||
|date = November 14, 2023 | |||
}}</ref> | |||
<ref name="post59813">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 59813 | |||
|author = Matthias Merzenich | |||
|date = May 7, 2018 | |||
}}</ref> | |||
<ref name="post4365">{{LinkForumThread | |||
|format = ref | |||
|title = Re: New small c/6 diagonal ship. | |||
|p = 4365 | |||
|author = Matthias Merzenich | |||
|date = March 28, 2011 | |||
}}</ref> | |||
<ref name="post178496">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Spaceship Discussion Thread | |||
|p = 178496 | |||
|author = Matthias Merzenich | |||
|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 name="post178722">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min height search results | |||
|p = 178722 | |||
|author = Matthias Merzenich | |||
|date = February 22, 2024 | |||
}}</ref> | |||
<ref name="post179535">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 179535 | |||
|author = Keith Amling | |||
|date = March 2, 2024 | |||
}}</ref> | |||
<ref name="post181755">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 181755 | |||
|author = Keith Amling | |||
|date = April 3, 2024 | |||
}}</ref> | |||
<ref name="post181787">{{LinkForumThread | |||
|format = ref | |||
|title = Re: LLSSS min pop search results spam | |||
|p = 181787 | |||
|author = Keith Amling | |||
|date = April 4, 2024 | |||
}}</ref> | }}</ref> | ||
</references> | </references> |
Latest revision as of 08:37, 4 April 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 | 6 | - | 6 | - | - |
(2,0)c/9 | 8[24] | 15[25] | 16[23] | 17[24] | - | - |
(2,1)c/9 | 7 | - | - | - | - | - |
(2,2)c/9 | 7 | 7 | - | 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] | ? |
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] | 10[41] | 9[40] | - | - |
(2,0)c/4 | 6[38][39] | 7[40] | 8[40] | 7[40] | 6 | 7[40] |
(1,0)c/5 | 8[38][42] | 8 | 8 | 8 | - | - |
(2,0)c/5 | 11[43] | 11 | 10 | 11 | - | - |
(1,0)c/6 | 9[43] < h ≤ 12 | 9 | 9 | 9 | - | - |
(2,0)c/6 | 7[44] < h ≤ 9 | 7 | 7 | 7 | 7 | 7 |
(3,0)c/6 | 9[38] < h ≤ 13 | 9 | 9 | 9 | - | - |
(1,0)c/7 | 8[43] < 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 | - | - |
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.
Velocity | Asymmetric | Symmetric | Gutter | Glide-symmetric |
---|---|---|---|---|
(1,1)c/4 | 4 | 11 | 11 | 4 |
strict | 15[45] | 15[45] | ||
(1,1)c/5 | 15 | 27 | 27 | - |
(1,1)c/6 | w ≤ 26 | w ≤ 33 | w ≤ 55 | 26[45] |
(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 | w ≤ 51 | w ≤ 51 | w ≤ 35 |
Velocity | Asymmetric | Symmetric (strict) | Gutter (strict) | Glide-symmetric (strict) |
---|---|---|---|---|
(1,1)c/4 | 5[41] | 13[41] | 14[41] | 5[41] |
(1,1)c/5 | 12[1] | 12[1] | 12[1] | - |
(1,1)c/6 | 12[46] | 12[46] | 11[46] | 11[46] |
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.[47]
Velocity | Asymmetric | Odd-symmetric | Even-symmetric | Gutter | Odd glide-symmetric | Even glide-symmetric |
---|---|---|---|---|---|---|
(1,0)c/2 | 64[48] | 64[48] | 66[48] | 70[48] | - | - |
(1,0)c/3 | 25[49] | 34[49] | 44[49] | 50[49] | - | - |
strict | 52[50] | |||||
(1,0)c/4 | 37[51] | 46[52] | 58[53] | 46[52] | - | - |
(1,1)c/4 | 5 | 10[54] | - | 10[54] | - | 5 |
strict | 9[54] < p ≤ 37 | 9[54] < p ≤ 50 | ||||
(2,0)c/4 | 9 | 18 | 18 | 18 | 9 | 18 |
strict | 20[50][55] | 34[56] < p ≤ 48 | 20[50][55] | 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[57] | 44[58] | 60[59] | 44[58] | - | - |
strict | 60[59] < 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
- All (1,0)c/2 ships up to a population of 127 cells[60] (total number of ships only; complete stamp collection up to 80 cells[61])
- All (2,0)c/4 ships up to a population of 25 cells (28 ships)[55]
- All (2,0)c/4 odd-symmetric ships up to a population of 35 cells (3 strict ships: MWSS on MWSS 1, HWSS on HWSS 1, Big A, and X66)[56]
- All (2,0)c/4 ships up to width 11 (7 ships)[62]
- All (2,0)c/4 ships up to height 7 (strings of interacting lightweight and middleweight spaceships only)[40]
- All (2,0)c/4 odd-symmetric ships up to width 15 (6 strict ships: MWSS on MWSS 1, HWSS on HWSS 1, X66, and three hivenudger variants)[2]
- All (2,0)c/4 gutter-symmetric ships up to width 17 (3 strict ships: MWSS on MWSS 1, HWSS on HWSS 1, and X66)[2]
- All (2,0)c/4 ships up to width 13 with a population of 50 or fewer cells[63]
- All (4,0)c/8 ships up to width 11 (1 period-8 ship)[62]
c/3 orthogonal
- All (1,0)c/3 ships up to a population of 49 cells[49]
- All (1,0)c/3 odd-symmetric ships up to a population of 67 cells (26 strict ships)[64]
- All (1,0)c/3 even-symmetric ships up to a population of 86 cells (29 strict ships)[65]
- All (1,0)c/3 ships up to width 13[66]
- 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)[66]
- All (1,0)c/3 even-symmetric ships up to width 20 (1 width-12 ship; infinitely many width-14+ ships)[66]
- All (1,0)c/3 gutter-symmetric ships up to width 21 (1 width-17 ship; infinitely many width-19+ ships)[66]
- 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
- All (1,0)c/4 ships up to a population of 37 cells (1 ship)[51]
- All (1,0)c/4 odd-symmetric ships up to a population of 61 cells (4 ships: 46P4H1V0, this 59-cell ship, this 61-cell ship, and this 61-cell ship)[67]
- All (1,0)c/4 even-symmetric ships up to a population of 58 cells (1 ship)[53]
- All (1,0)c/4 ships up to width 11[66]
- All (1,0)c/4 ships up to height 8 (1 ship)[40]
- All (1,0)c/4 odd-symmetric ships up to width 17[66]
- All (1,0)c/4 even-symmetric ships up to width 18 (2 width-16 ships: this ship and the same ship with a tagalong; infinitely many width-18 ships)[66]
- All (1,0)c/4 gutter-symmetric ships up to width 19[66]
c/4 diagonal
- All (1,1)c/4 ships up to a population of 9 cells (1 ship)[68]
- 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)[41]
- All (1,1)c/4 ships up to diagonal width 13 (4 ships)[45]
- All (1,1)c/4 ships up to orthogonal width 10 (5 ships)[45]
- All (1,1)c/4 ships up to single-phase orthogonal width 9 (15 ships)[45]
c/5 orthogonal
- All (1,0)c/5 ships up to height 8[69]
- All (1,0)c/5 even-symmetric ships up to width 18[66]
- All (1,0)c/5 gutter-symmetric ships up to width 19[66]
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)[70]
- 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)[57]
- All (2,0)c/5 odd-symmetric ships up to a population of 57 cells (2 ships: 44P5H2V0 and this ship)[71]
- All (2,0)c/5 ships up to width 12 (1 width-10 ship; infinitely many width-11 ships; infinitely many width-12 ships)[66]
- All (2,0)c/5 odd-symmetric ships up to width 17 (1 width-15 ship; infinitely many width-17 ships)[66]
- All (2,0)c/5 even-symmetric ships up to width 20 (1 ship)[66]
- 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)[66]
- All (4,0)c/10 odd-symmetric ships up to width 15 (3 period-10 ships)[2]
c/6 orthogonal
2c/7 orthogonal
- All (2,0)c/7 even-symmetric ships up to width 22 (2 ships: weekender and weekender + tagalong)[72]
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
References
- ↑ 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
- ↑ 2.00 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
- ↑ 3.0 3.1 Tim Coe (December 18, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
- ↑ praosylen (May 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 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
- ↑ 6.0 6.1 6.2 6.3 Tim Coe (April 13, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (January 18, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 8.0 8.1 Tim Coe (June 11, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 9.0 9.1 9.2 Matthias Merzenich (December 24, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (June 14, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Tomas Rokicki (March 1, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 12.0 12.1 Matthias Merzenich (April 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 13.0 13.1 13.2 13.3 13.4 Checked with knight2.c
- ↑ 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
- ↑ Checked by Paul Tooke with gfind
- ↑ Dylan Chen (January 10, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 17.0 17.1 Matthias Merzenich (November 29, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (February 25, 2020). Re: Help me finish this c/8 search (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (December 22, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 20.0 20.1 20.2 Tim Coe (April 21, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Tanner Jacobi (December 3, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
- ↑ 22.0 22.1 22.2 AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 23.0 23.1 praosylen (December 27, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 24.0 24.1 praosylen (December 28, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (March 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 27.0 27.1 27.2 Tim Coe (March 1, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 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
- ↑ 29.0 29.1 AforAmpere (November 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ AforAmpere (December 10, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (April 19, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 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
- ↑ 34.0 34.1 praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 35.0 35.1 lordlouckster (July 13, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 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
- ↑ Ivan Fomichev using gfind under OS X 10.9.5
- ↑ 38.0 38.1 38.2 38.3 38.4 38.5 38.6 38.7 Checked by Matthias Merzenich using WLS.
- ↑ 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
- ↑ 40.00 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 Matthias Merzenich (December 1, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 41.0 41.1 41.2 41.3 41.4 41.5 Matthias Merzenich (February 19, 2024). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
- ↑ 43.0 43.1 43.2 Matthias Merzenich (February 20, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (February 22, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
- ↑ 45.0 45.1 45.2 45.3 45.4 45.5 Matthias Merzenich (November 27, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 46.0 46.1 46.2 46.3 Matthias Merzenich (March 28, 2011). Re: New small c/6 diagonal ship. (discussion thread) at the ConwayLife.com forums
- ↑ Nick Gotts (November 28, 2018). Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
- ↑ 48.0 48.1 48.2 48.3 Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 49.0 49.1 49.2 49.3 49.4 Keith Amling (November 12, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 50.0 50.1 50.2 Keith Amling (December 1, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 51.0 51.1 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 52.0 52.1 Keith Amling (November 29, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 53.0 53.1 Keith Amling (November 30, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 54.0 54.1 54.2 54.3 Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 55.0 55.1 55.2 "Life Object Counts". Mark Niemiec. Retrieved on December 9, 2023.
- ↑ 56.0 56.1 Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 57.0 57.1 Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 58.0 58.1 Keith Amling (February 1, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 59.0 59.1 Keith Amling (April 4, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (January 15, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 62.0 62.1 Matthias Merzenich (March 22, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (May 7, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ 66.00 66.01 66.02 66.03 66.04 66.05 66.06 66.07 66.08 66.09 66.10 66.11 66.12 66.13 66.14 "knightt results". Matthias Merzenich. Retrieved on February 17, 2024.
- ↑ Keith Amling (March 2, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (November 28, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (April 3, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (March 21, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums