LifeWiki:Spaceship Search Status Page: Difference between revisions

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m Add two new tables, known diagonal spaceships by trail width (as Sokwe recommended I should do) and known spaceships by population (since Keith Amling has at present searched exhaustively for c/2's with population ≤ 98, c/3's ≤ 49 and c/4's ≤ 32 and 2c/5's ≤ 31)
Note Matthias Merzenich's explanation of its width measurement convention, add bounds from Keith Amling's new results to the population table (37P4H1V0 proven minimal), no longer regard diagonal symmetries as undefined
Line 1: Line 1:
== Known spaceships by width ==
==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.


The table below gives the minimum orthogonal width of the [[envelope]] for spaceships of the specified type. For types where the minimum width is known, references point to the proof of minimality rather than the discovery of the minimum-width ship. A stamp collection of minimum-width ships is given below the table.
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.


This table assumes horizontal symmetry and does not account for diagonal symmetry for diagonal spaceships.
Symmetry considered is in the line parallel to a spaceship's direction of motion.


{| class="wikitable"
== Known spaceships by width ==
{|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
Line 35: Line 37:
| (1,1)c/4
| (1,1)c/4
| style="background: #80ff80;" | [[Glider|3]]
| style="background: #80ff80;" | [[Glider|3]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | w &le; {{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=19|style=raw}}
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | w &le; {{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=19|style=raw}}
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #80ff80;" | [[Glider|3]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/4
| (2,0)c/4
Line 59: Line 59:
| (1,1)c/5
| (1,1)c/5
| style="background: #80ff80;" | {{LinkCatagolue|xq5_cih1h0czhrpw1035z7ui0h1go04k8z012xp6oc2zy39ng|name=13|style=raw}}<ref name="coe1"/>
| style="background: #80ff80;" | {{LinkCatagolue|xq5_cih1h0czhrpw1035z7ui0h1go04k8z012xp6oc2zy39ng|name=13|style=raw}}<ref name="coe1"/>
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | w &le; [[86P5H1V1|24]]
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | w &le; [[86P5H1V1|24]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/5
| (2,0)c/5
Line 83: Line 81:
| (1,1)c/6
| (1,1)c/6
| style="background: #ffa0a0;" | 10 < w &le; [[Seal|35]]
| style="background: #ffa0a0;" | 10 < w &le; [[Seal|35]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 10 < w &le; [[77P6H1V1|36]]
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 10 < w
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 10 < w &le; [[Seal|35]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/6
| (2,0)c/6
Line 123: Line 119:
| (1,1)c/7
| (1,1)c/7
| style="background: #ffa0a0;" | 9 < w &le; [[Lobster|27]]
| style="background: #ffa0a0;" | 9 < w &le; [[Lobster|27]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 9 < w &le; [[Lobster|27]]
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 9 < w
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/7
| (2,0)c/7
Line 163: Line 157:
| (1,1)c/8
| (1,1)c/8
| style="background: #ffa0a0;" | 7 < w &le; [[Walrus|21]]
| style="background: #ffa0a0;" | 7 < w &le; [[Walrus|21]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 7 < w
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 7 < w
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 7 < w &le; [[Walrus|21]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/8
| (2,0)c/8
Line 186: Line 178:
|-
|-
| (2,2)c/8
| (2,2)c/8
| style="background: #ffa0a0;" | 8 < w &le; {{LinkCatagolue|xq8_o4w8gi5hcgwgz5og0g7gadxj184s6332gkozx8iqxgh2p40ar8aczy3c80h01446zy5223|name=24|style=raw}}
| style="background: #ffa0a0;" | 8 < w &le; {{LinkCatagolue|xq8_o4w8gi5hcgwgz5og0g7gadxj184s6332gkozx8iqxgh2p40ar8aczy3c80h01446zy5223|name=23|style=raw}}
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 8
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 8
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 8
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (3,0)c/8
| (3,0)c/8
Line 227: Line 217:
| (1,1)c/9
| (1,1)c/9
| style="background: #ffa0a0;" | 6
| style="background: #ffa0a0;" | 6
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/9
| (2,0)c/9
Line 251: Line 239:
| (2,2)c/9
| (2,2)c/9
| style="background: #ffa0a0;" | 7
| style="background: #ffa0a0;" | 7
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (3,0)c/9
| (3,0)c/9
Line 291: Line 277:
| (1,1)c/10
| (1,1)c/10
| style="background: #ffa0a0;" | 7
| style="background: #ffa0a0;" | 7
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 7
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 7
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 7
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/10
| (2,0)c/10
Line 315: Line 299:
| (2,2)c/10
| (2,2)c/10
| style="background: #ffa0a0;" | 6
| style="background: #ffa0a0;" | 6
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 6
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 6
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | 6
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (3,0)c/10
| (3,0)c/10
Line 379: Line 361:
| (1,1)c/11
| (1,1)c/11
| style="background: #ffffa0;" | ?
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/11
| (2,0)c/11
Line 403: Line 383:
| (2,2)c/11
| (2,2)c/11
| style="background: #ffffa0;" | ?
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (3,0)c/11
| (3,0)c/11
Line 475: Line 453:
== Known spaceships by height ==
== Known spaceships by height ==


{|class="wikitable"
{|class="wikitable" style="text-align: center"
|-
|-
! Velocity !! minimum height
! Velocity !! minimum height
Line 527: Line 505:
==Known diagonal spaceships by trail width==
==Known diagonal spaceships by trail width==
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.
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"
{|class="wikitable" style="text-align: center"
|-
|-
! Velocity !! Asymmetric !! Symmetric !! Gutter !! Glide-symmetric
! Velocity !! Asymmetric !! Symmetric !! Gutter !! Glide-symmetric
Line 563: Line 541:


==Known spaceships by population==
==Known spaceships by population==
{| 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
Line 584: Line 562:
|-
|-
| (1,0)c/4
| (1,0)c/4
| style="background: #ffa0a0;" | 32<ref name="amling-c/4-pop-le-32" /> < p &le; [[37P4H1V0|37]]
| style="background: #80ff80;" | [[37P4H1V0|37]]<ref name="amling-c/4-pop-le-37" />
| style="background: #ffa0a0;" | 32<ref name="amling-c/4-pop-le-32" /> < p &le; [[Non-monotonic spaceship 1|66]]
| style="background: #ffa0a0;" | 37<ref name="amling-c/4-pop-le-37" /> < p &le; [[Non-monotonic spaceship 1|66]]
| style="background: #ffa0a0;" | 32<ref name="amling-c/4-pop-le-32" /> < p &le; {{LinkCatagolue|xq4_w434y0434z0om7e0mm0e7mozh1kf431134fk1hzdg122e11e221gdzxp74mm47pzx166w661|name=108|style=raw}}
| style="background: #ffa0a0;" | 37<ref name="amling-c/4-pop-le-37" /> < p &le; {{LinkCatagolue|xq4_w434y0434z0om7e0mm0e7mozh1kf431134fk1hzdg122e11e221gdzxp74mm47pzx166w661|name=108|style=raw}}
| style="background: #ffa0a0;" | 32<ref name="amling-c/4-pop-le-32" /> < p &le; {{LinkCatagolue|xq4_y0671x176zw2359cs0sc9532zw68cvhxhvc86z66br22ge0eg22rb66zy16e606e6|name=88|style=raw}}
| style="background: #ffa0a0;" | 37<ref name="amling-c/4-pop-le-37" /> < p &le; {{LinkCatagolue|xq4_y0671x176zw2359cs0sc9532zw68cvhxhvc86z66br22ge0eg22rb66zy16e606e6|name=88|style=raw}}
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
Line 593: Line 571:
| (1,1)c/4
| (1,1)c/4
| style="background: #80ff80;" | [[Glider|5]]
| style="background: #80ff80;" | [[Glider|5]]
| style="background: #c0c0c0;" | -<!--9 < p for all of these, if they are to stop being undefined eventually-->
|colspan="2"; style="background: #ffa0a0;" | 9<ref name="amling-(1,1)c/4-pop-le-9"  /> < p &le; {{LinkCatagolue|xq4_y48444552gkozwg808oc72zcgfzw247|name=37|style=raw}}
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | 9<ref name="amling-(1,1)c/4-pop-le-9"  /> < p &le; {{LinkCatagolue|xq4_y184ltgz8ok0bd225dmo8ggzy6o9mp39703zy56c2|name=50|style=raw}}
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #80ff80;" | [[Glider|5]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/4
| (2,0)c/4
Line 617: Line 593:
| (1,1)c/5
| (1,1)c/5
| style="background: #ffa0a0;" | p &le; [[58P5H1V1|58]]
| style="background: #ffa0a0;" | p &le; [[58P5H1V1|58]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | p &le; [[58P5H1V1|58]]
| style="background: #c0c0c0;" | -
| style="background: #ffa0a0;" | p &le; [[58P5H1V1|58]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/5
| (2,0)c/5
Line 641: Line 615:
| (1,1)c/6
| (1,1)c/6
| style="background: #ffa0a0;" | p &le; [[77P6H1V1|77]]
| style="background: #ffa0a0;" | p &le; [[77P6H1V1|77]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | p &le; [[77P6H1V1|77]]
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | p &le; [[Seal|170]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/6
| (2,0)c/6
Line 664: Line 636:
|-
|-
| (3,0)c/6
| (3,0)c/6
| style="background: #ffa0a0;" | p &le; [[86P6H3V0|86]]
| style="background: #ffa0a0;" | 25<ref name="amling-3c/6-pop-le-25" /> < p &le; [[86P6H3V0|86]]
| style="background: #ffa0a0;" | p &le; [[86P6H3V0|86]]
| style="background: #ffa0a0;" | 25<ref name="amling-3c/6-pop-le-25" /> < p &le; [[86P6H3V0|86]]
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq6_y2ogm6e3z8suj23aqaa98gzo605y01345024ozgrodwgokmhl821z013626qaa2kzy43336|patternname=104|style=raw}}
| style="background: #ffa0a0;" | 25<ref name="amling-3c/6-pop-le-25" /> < p &le; {{LinkCatagolue|xq6_y2ogm6e3z8suj23aqaa98gzo605y01345024ozgrodwgokmhl821z013626qaa2kzy43336|patternname=104|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq6_y18waj0jaw8zw2qg1ng62026gn1gq2z2cagn21y312ngac2zgg03l4w88088w4l30ggz076gv0r6of0fo6r0vg67zy15fogo0ogof5zy41x1|name=154|style=raw}}
| style="background: #ffa0a0;" | 25<ref name="amling-3c/6-pop-le-25" /> < p &le; {{LinkCatagolue|xq6_y18waj0jaw8zw2qg1ng62026gn1gq2z2cagn21y312ngac2zgg03l4w88088w4l30ggz076gv0r6of0fo6r0vg67zy15fogo0ogof5zy41x1|name=154|style=raw}}
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
Line 681: Line 653:
| (1,1)c/7
| (1,1)c/7
| style="background: #ffa0a0;" | p &le; [[Lobster|83]]
| style="background: #ffa0a0;" | p &le; [[Lobster|83]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | p &le; [[Lobster|83]]
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/7
| (2,0)c/7
Line 698: Line 668:
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #ffa0a0;" |  
| style="background: #ffffa0;" | ?
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #ffa0a0;" | p &le; [[232P7H3V0|232]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
Line 705: Line 675:
| (1,1)c/8
| (1,1)c/8
| style="background: #ffa0a0;" | p &le; [[Walrus|68]]
| style="background: #ffa0a0;" | p &le; [[Walrus|68]]
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffa0a0;" | p &le; [[Walrus|68]]
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (2,0)c/8
| (2,0)c/8
| style="background: #ffa0a0;" |  
| style="background: #ffffa0;" | ?
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_1263hoc6coh3621zxo60l2l06ozwvw2o0o2wvz0o0rjpxpjr0ozcfhi3108013ihfczxduik9kiud|name=121|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_1263hoc6coh3621zxo60l2l06ozwvw2o0o2wvz0o0rjpxpjr0ozcfhi3108013ihfczxduik9kiud|name=121|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_671y8176z111uu0o4w4o0uu111z8g8334mi66im4338g8z01xshraarhsx1zy22ahha2zy2cqbbqczy2ip88piz0djk7w1221w7kjdzwd11464w46411dz5dod5y45dod5zops108k8w8k801spoz01084173oo3714801zy0hphy0hph|name=242|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_671y8176z111uu0o4w4o0uu111z8g8334mi66im4338g8z01xshraarhsx1zy22ahha2zy2cqbbqczy2ip88piz0djk7w1221w7kjdzwd11464w46411dz5dod5y45dod5zops108k8w8k801spoz01084173oo3714801zy0hphy0hph|name=242|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_o0r54kc606ck45r0ozx8d5gg0gg5d8zwg0gm11011mg0gz0gre539e0e935ergz3o539k4x4k935o3zw249c1v0v1c942zy1so707oszy0gq2x2qgzw4o22oxo22o4zwoog57x75goozgo888h5o0o5h888ogzx33hph0hph33|name=232|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_o0r54kc606ck45r0ozx8d5gg0gg5d8zwg0gm11011mg0gz0gre539e0e935ergz3o539k4x4k935o3zw249c1v0v1c942zy1so707oszy0gq2x2qgzw4o22oxo22o4zwoog57x75goozgo888h5o0o5h888ogzx33hph0hph33|name=232|style=raw}}
| style="background: #ffa0a0;" | p &le; [[74P8H2V0|74]]
| style="background: #ffa0a0;" | p &le; [[74P8H2V0|74]]
| style="background: #ffa0a0;" |  
| style="background: #ffffa0;" | ?
|-
|-
| (2,2)c/8
| (2,2)c/8
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_o4w8gi5hcgwgz5og0g7gadxj184s6332gkozx8iqxgh2p40ar8aczy3c80h01446zy5223|name=90|style=raw}}
| style="background: #ffa0a0;" | p &le; {{LinkCatagolue|xq8_o4w8gi5hcgwgz5og0g7gadxj184s6332gkozx8iqxgh2p40ar8aczy3c80h01446zy5223|name=90|style=raw}}
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
|colspan="2"; style="background: #ffffa0;" | ?
| style="background: #c0c0c0;" | -
| style="background: #c0c0c0;" | -
|-
|-
| (4,0)c/8
| (4,0)c/8
Line 845: Line 811:
|date  = November 12, 2023
|date  = November 12, 2023
}}</ref>
}}</ref>
<ref name="amling-c/4-pop-le-32">{{LinkForumThread
<ref name="amling-c/4-pop-le-37">{{LinkForumThread
|format = ref
|format = ref
|title  = Re: LLSSS min pop search results spam
|title  = Re: LLSSS min pop search results spam
|p      = 171172
|p      = 171705
|author = Keith Amling
|author = Keith Amling
|date  = November 15, 2023
|date  = November 22, 2023
}}</ref><!--maybe p171321 reveals &le; 35 disproven but he didn't explicitly say-->
}}</ref><!--maybe p171321 reveals &le; 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
<ref name="amling-2c/5-pop-le-31">{{LinkForumThread
|format = ref
|format = ref
Line 858: Line 831:
|author = Keith Amling
|author = Keith Amling
|date  = November 15, 2023
|date  = November 15, 2023
}}</ref>
<ref name="amling-3c/6-pop-le-25">{{LinkForumThread
|format = ref
|title  = Re: LLSSS min pop search results spam
|p      = 171721
|author = Keith Amling
|date  = November 22, 2023
}}</ref>
}}</ref>
</references>
</references>

Revision as of 17:14, 22 November 2023

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

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 w ≤ 19 w ≤ 19 3
(2,0)c/4 5 11 12[n 1] 11 5 12[n 1]
(1,0)c/5 11 19 18 19 - -
(1,1)c/5 13[1] w ≤ 24 w ≤ 24 -
(2,0)c/5 10 15 18 15 - -
(1,0)c/6 12[2] 19 18 21 - -
(1,1)c/6 10 < w ≤ 35 10 < w ≤ 36 10 < w 10 < w ≤ 35
(2,0)c/6 12[3] 17[4] 18[4][5] 19[4] 17 18[5]
(2,1)c/6 15 < w ≤ 31[1] - - - - -
(3,0)c/6 21[6] 21 28 21 - -
(1,0)c/7 10[7][8] 19[8] 22[9][n 1] 21[7][8][n 1] - -
(1,1)c/7 9 < w ≤ 27 9 < w ≤ 27 9 < w -
(2,0)c/7 11[10][11] 23[4] 18 23 < w ≤ 33[11] - -
(2,1)c/7 11[12] - - - - -
(3,0)c/7 14[13] 29[14] 28[13] 31[13][15] - -
(1,0)c/8 10[16] 19[17] 20[18] 21[16] - -
(1,1)c/8 7 < w ≤ 21 7 < w 7 < w 7 < w ≤ 21
(2,0)c/8 9[4] 15[4][19] 18[4][19] 17[4][19] 13 14
(2,1)c/8 8 - - - - -
(2,2)c/8 8 < w ≤ 23 8 8 8
(3,0)c/8 11[12] 21[12] 22[20] 23[12] - -
(3,1)c/8 12[12] - - - - -
(4,0)c/8 12[4] 17[4] 20[4] 19[4] 17 20[4]
(1,0)c/9 8[21] 15[21] 16[21] 15[22] - -
(1,1)c/9 6 ? ? -
(2,0)c/9 8[23] 15[24] 16[22] 17[23] - -
(2,1)c/9 7 - - - - -
(2,2)c/9 7 ? ? -
(3,0)c/9 11[25] 17[4] 16[3] 17[4] - -
(3,1)c/9 8 - - - - -
(4,0)c/9 11[13] 21[13] 22[26] 23[13] - -
(1,0)c/10 6[27] 11[27] 10 13[27] - -
(1,1)c/10 7 7 7 7
(2,0)c/10 6 < w ≤ 15 11 < w ≤ 19 12 13 < w ≤ 21 13[26] 14[26]
(2,1)c/10 6 - - - - -
(2,2)c/10 6 6 6 6
(3,0)c/10 9[28] 17[29] 18[28] 17[30] - -
(3,1)c/10 7 - - - - -
(3,2)c/10 8 - - - - -
(4,0)c/10 10[3] 15[4] 22[31] 21[4] 15[32] 16[32]
(4,1)c/10 8 - - - - -
(5,0)c/10 11[3] 19[4] 22[3] 19[4] - -
(1,0)c/11 6[33] 11[34] 12[34] 11[33] - -
(1,1)c/11 ? ? ? -
(2,0)c/11 6[27] 11[27] 12[27] 13[27] - -
(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[35] 17[35] 18[35] 19[35] - -
(4,1)c/11 ? - - - - -
(5,0)c/11 10[35] 19[35] 20[35] 21[35] - -
(2,0)c/12 ? w ≤ 63 ? ? 9[36] ?
x = 1360, y = 676, rule = B3/S23 5b2o50b2o44b2o102b3ob3o193b3ob3o249b3o2b4o2b3o220b3ob3o245b3o153b3o4b 3o$4b2o51bobo42b2o102bo2bobo2bo191bo2bobo2bo247bo3bob4obo3bo218bo2bobo 2bo243bo2bo153bo2bo3bo2bo$6bo50bo45bo2bo98bo3bobo3bo189bo3bobo3bo245bo 6bo2bo6bo216bo3bobo3bo245bo153bo6bo$60bo42b2obo98bo9bo189bo9bo245bo3b 2o6b2o3bo216bo9bo245bo153bo6bo$59bobo41b2o3bo98bo5bo193bo5bo249bo12bo 220bo5bo244bobo155bobo4bobo$59bobo142bobo7bobo187bobo7bobo243bobo14bob o214bobo7bobo$59bo46bobob2o91b2obob2ob2obob2o185b2obob2ob2obob2o241b2o bob2o8b2obob2o212b2obob2ob2obob2o$59bo44bobo3bo91bobobo2bobo2bobobo 183bobobo2bobo2bobobo239bobobob2o8b2obobobo210bobobo2bobo2bobobo$55bo 3bo35bo8b3o2bo91b2obo4bobo4bob2o181b2obo4bobo4bob2o237b2o3bo2bo8bo2bo 3b2o208b2obo4bobo4bob2o$54b3obo35b5o6b2o93bo3bob2obobob2obo3bo179bo3bo b2obobob2obo3bo235bo3bobo2b2o6b2o2bobo3bo206bo3bob2obobob2obo3bo$53b2o 39bo2b2o2b2o101bo4bo2b3obo187bob3o3b3obo242bo20bo213bo4bobo4bo$52b2o 48b2o96b2o3bo2bo2b2o2bo3b2o179b2o3bo2b2ob2o2bo3b2o235b2o24b2o206b2o3bo 2bo3bo2bo3b2o$53bo42b2o2b4o111b2o187b2o9b2o$44b3o357bo11bo$44bo8bo44bo bo302bobo9bobo$45bo2b5o49bo299bo15bo$47bo52b2o302bo11bo$48b2o50bo300b 2obo11bob2o$400bo3b2o9b2o3bo$401bo2bo11bo2bo$406b2o5b2o735bo158b2o$ 403b2obo7bob2o731bobo153b2obo2bob2o$406bob2ob2obo733bo3bo152b2o6b2o$ 406bob2ob2obo734b3o153bobo4bobo$405bo3bobo3bo891b2o2b2o$407bo5bo733b2o 3b2o152b2ob2ob2o$405bo9bo728b2o3bobo3b2o151bo2bo$406bob2ob2obo729b2o3b obo3b2o149bo6bo$403b2obob2ob2obob2o724b2o5bobo5b2o147bo6bo$404bobobobo bobobo729b2obobob2o$210bo190b2obobo7bobob2o249b2o222b3o9b3o234bo6bobo 6bo147b8o$209b3obo187b2o3bo7bo3b2o245b2obo2bob2o217bobob2o5b2obobo236b 2o2bobo2b2o149b2o6b2o$205b3obob2obo186b3obo9bob3o245b2o6b2o217bobobo7b obobo234bo2bobo3bobo2bo$204bobo4bo3bo184b2o17b2o244bobo4bobo218bob2ob 2ob2ob2obo235b2o11b2o151b2o$204bob4obo3bo451b2o2b2o224bobobobo239b2o 11b2o150bo2bo$205bo2b2obo454b2ob2ob2o221bobobobobobo240bo7bo$213bo454b 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421bobo4bobo32bo4bo222bo3bobo3bo$7bo235bo463bo4bo182b2o7b2o31bobobobo$ 8b2o201bo32bobo457bobo6bobo179b5ob5o31bo5bo$209b3o454bo6bo218b2o3bobob obo3b2o28b2o3b2o$208bo2bo453b3ob2ob3o218b4o2bobo2b4o30b2ob2o$205b3o3bo 453b3ob2ob3o223bo3bo35b2ob2o$208b3o453bo2bo4bo2bo261bo5bo$208b2o2b2o 450b2o3b2o3b2o221b2o3b2o$205bobo2bo3bo448b2obob4obob2o217b3o7b3o435b3o 10b3o$208b2o4bo451bobo2bobo220b2o9b2o435bo2bo8bo2bo$207bobob2o452b3o4b 3o222b2o3b2o438bo14bo$207bo458bo6bo224bo3bo439bo3bo6bo3bo$207b3o453bob o8bobo220b2o3b2o438bo3bo6bo3bo$206bo2bo453bobo3b2o3bobo218bo2bo3bo2bo 437bo3bo4bo3bo$206bo2bo456b3o2b3o221bo2bo3bo2bo442bo2bo$663bo4bo2bo4bo 217bo11bo442b2o$207b2ob2o451bo4bo2bo4bo219b2o5b2o441bobo2bobo$206bo2b 3o452bo10bo670bo6bo$207bo200bo3bo33b3o3b3o211b2o4b2o222b2o5b2o243bo3bo 32bo5bo155b2o2b2o$209b2o197bo3bo33bo2bobo2bo212bob2obo224bo5bo244bo3bo 31b3o3b3o152b2o6b2o$206b2obob2o194bobobobo31bo3bobo3bo211b6o474bobobob o29b2obo3bob2o150b3obo2bob3o$209bo2bo234bobobobo212bo6bo223b2o3b2o279b 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o2bobo2bo26b2o3bo3bo3b2o144b2o16b2o$1149bobo30bo11bo149b2o8b2o$1146bo 2bobo2bo31b2ob2o153b3o6b3o$1145b2ob2ob2ob2o28b3o2bo155b3o4b3o$1145b4ob ob4o29b3ob3o155bo4bo$1149b3o32b2o2b4o153bo2bo2bo2bo$1150bo195bobo2bobo $669b2o32bo12bo177bo11bo30bo5bo240b2o157b2obo6bob2o$669b2o31bobo10bobo 174b2obobo5bobob2o27b3o3b3o205bo33b2o5bo152bo2bo4bo2b2o$667bob2obo28b 2ob2o8b2ob2o176bob2o3b2obo29bo2bo3bo2bo203b4o31b2o3b2obo149bobo3bo3bo 3b2o$665b3o4b3o26b2o14b2o173b2obo3bobo3bob2o25b3o7b3o200b2o3b2o29b2o4b o2b2o147b2o5bo$662b2o12b2o25bo12bo175b3o2bobobobo2b3o26bobo5bobo201b2o 3b2o30bo2b3o2b2o148bo4bo$662b2o2bob4obo2b2o25b4o6b4o180bobobobo33b2o3b 2o202bob3o2bo31bo5b3o148b2obo$666bobo2bobo29bo2b2o4b2o2bo177bo2bobobob o2bo26bo4bo3bo4bo197bo2b2o2bo30bo5bo2b2o$704b2o2bo2bo2b2o179bobobobobo bo32bo3bo203bo2bo2bo29bobo4bo2b2o$665b2o6b2o30b2ob4ob2o180b3obobob3o 27b2o3bo3bo3b2o199b2o33b5o5b3o$662b6o4b6o28bobo2bobo179bo2b3o3b3o2bo 27bo2bo3bo2bo203bo33b2o$208bo38bo162bo36bo5bo208bobo10bobo29bo4bo185b 2ob2o34bo5bo205bo2bo29bo$207b5o34bobo161bo35b3o3b3o207bob2o8b2obo215b 2o11b2o241bo32b3o2b3o$206bo3bobo32b2ob2o160bo34bo2bo3bo2bo206bob2o8b2o bo28bo6bo179b2o11b2o241b2o35bo2bo4bo$206bobobobo32bo2b2o156bo3bo3bo29b 3o7b3o204b2ob2o8b2ob2o25b2ob2o2b2ob2o178b3o7b3o242b2o32b3o4b2o2bo$207b 2ob2o32b3o156bobob2obob2obobo27bobo5bobo205b2obo10bob2o26bo8bo177b2o2b o7bo2b2o237bo7bo26bo2b2o6bobo$208b3o31b2o4b2o152b2obobob3obobob2o28b2o 3b2o208bobo10bobo27b2o6b2o177bobobo7bobobo236b3o6bobo28bobo5b2o$242b4o 155bo3bo9bo3bo23bo4bo3bo4bo206bo2b2o2b2o2bo469bobo5bo2bo23bo7bo5bo$ 208b3o29bo5b2o153bobobob2o3b2obobobo28bo3bo210bo4bo2bo4bo217bo11bo242b 2o2b3o33bo$209bob2o29b3obo158b2obo3bob2o27b2o3bo3bo3b2o211b2o222bobob 2o3b2obobo236b2o4bo3bo35bobo$204b3o3b2o33bo156b2obo9bob2o26bo2bo3bo2bo 212bo2bo225b2o3b2o240b2o5b2o29b2o$204b3o36bobo159b2o2bobo2b2o31bo5bo 445bobo243bo2bo$205bob3o31bobo161bobobobobobo248b4o4b4o218bobob2ob2obo bo241bobo$207bo32bobo164bobobobo247b3o2b2ob2ob2o2b3o217b2obobob2o$207b 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206bo3b2o313bo9bo131bo4bo119b2ob2o6b2ob2o$205bo6b2o232b3o3b3o70bo9bo 257bob2obo2bob2obo$204bo2bo2b4o229b2o11b2o67bo3b3o3bo260bobo2bobo93bo 5bo27bo17bo23b3o9b3o$205b2o2bo3bo229b2o4bobo4b2o69bo2bo2bo134b4o121b2o bobo2bobob2o89bobo3bobo26bo17bo23bo2bo7bo2bo$210bo235bobo3bobo72bobobo bo135b2o122b2o3b4o3b2o88bo2bo3bo2bo24bobo15bobo21b2o13b2o$445b2o7b2o 71bo5bo260bo3bo2bo3bo90b2o5b2o26bo17bo20b2obo3bo5bo3bob2o$446bobo3bobo 69bo2bo5bo2bo258bo2bo2bo2bo126bo17bo23b3ob2o3b2ob3o$445bo2bo3bo2bo67b 2o11b2o255b4o6b4o85bo5bo3bo5bo21bo4bo9bo4bo18bo21bo$445bobobobobobo70b 2o5b2o256b2o2bo8bo2b2o82bobo3bo5bo3bobo25b2o7b2o24bobob5o3b5obobo$444b 3o7b3o65bob2ob2o3b2ob2obo251bo3bo10bo3bo80bo2bo3b2o3b2o3bo2bo18b2o4bob 2o3b2obo4b2o18bo3bo2b2o3b2o2bo3bo$444b3o7b3o65bo5b2ob2o5bo251bo4bo8bo 4bo80bo2b2o3bo3bo3b2o2bo26b2o3b2o26bo3b3o7b3o3bo$444b3o7b3o70bo5bo256b o4b2o6b2o4bo129bobo28bo4bo9bo4bo$445b2o7b2o70bo2bobo2bo256b2o2bo8bo2b 2o122b3o3bobobobo3b3o24b3o7b3o$445b2o7b2o71bobobobo257b2obo10bob2o128b 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489bobo484b2o5b2o$488bo3bo479bob2o9b2obo$489b3o$974b3o7b3o$487b2o3b2o 479b3o9b3o$484b2o3bobo3b2o475bo3b4ob4o3bo$484b2o3bobo3b2o477b4obobob4o $482b2o5bobo5b2o474b2obo2bobo2bob2o$486b2obobob2o478b2obo2bobo2bob2o$ 482bo6bobo6bo477bob2ob2obo$485b2o2bobo2b2o482bo3bo$483bo2bobo3bobo2bo 479bo5bo$483b2o11b2o$483b2o11b2o474b3o11b3o$486bo7bo478bo13bo$486b3o3b 3o478bo13bo$488bo3bo478bobo13bobo$485b2obo3bob2o476bo15bo$487b2o3b2o$ 487bobobobo2$487bo2bo2bo$488b2ob2o$487b2o3b2o2$486bo2b3o2bo$485b11o$ 485b2obo3bob2o$311bo5bo$310b3o3b3o$309b2obo2b2obo$309b3o3b3o$310b2o4b 2o$315bo$311bobob2obo$311bo2bobo$315bo$314b2o$312bo2bo$312bo625bo3bo 73b3o3b3o$312bo3bo621bo3bo73bo2bobo2bo$311b5obo619bobobobo71bo3bobo3bo $311bob2o2b2o698bobobobo$310bo5b3o617bo7bo72bo5bo$314bo618bob2o2bobo2b 2obo69b2o3b2o$311bo3bo617bobo2b2ob2o2bobo70b2ob2o$310bo3bo617bob2obobo bobob2obo69b2ob2o$310bo2b2o702bo5bo$309bo628bo3bo70b3o9b3o$310bo2bo 213bo5bo33b3ob3o438bo2b2o7b2o2bo$311bobo212b3o3b3o31bo2bobo2bo359b2ob 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75bo5bo$526bobo3bobo28b4o7b4o358b2obobob2o72bo5bo$528b2ob2o29b2o4b2ob 2o4b2o357b2obobob2o$528b2ob2o33bob2ob2obo360bo3bobo3bo68b3ob2ob2ob3o$ 565b5ob5o358b3ob2ob2ob3o66bo3b2o3b2o3bo$530bo34b2o7b2o358b2o9b2o65bo2b o2bo3bo2bo2bo$530bo38bobo362b3o7b3o65b2o3b2o3b2o3b2o$528bobobo35b2ob2o 361bo2bo5bo2bo65bob5o3b5obo$527b2o3b2o33bobobobo358b2o3b2o3b2o3b2o69b 2ob2o$566b2obobob2o358b2ob3o3b3ob2o64b5o7b5o$525bo9bo29bo3bobo3bo358bo 2bo5bo2bo64b4ob2o5b2ob4o$525bo9bo399bo2bo3bo2bo65b3o3b2o3b2o3b3o$526bo 7bo30b2ob2ob2ob2o359b2ob2ob2ob2o70bob2ob2obo$528bo3bo404bobobobo74b2ob 2o$566bo3bo3bo358bobo2bo3bo2bobo67bobo5bobo$565bo4bo4bo357bo2bo7bo2bo 66bob2o5b2obo$564bo11bo360bo5bo69b2o2bo5bo2b2o$563b2obo7bob2o434b2o13b 2o$562bobob2o5b2obobo357bobo3bobo70bo2b2ob2o2bo$561b2obobob2ob2obobob 2o358bo3bo69b2o4b2ob2o4b2o$560bo3bobo2bobo2bobo3bo355bobo3bobo73bo3bo$ 569bobo363bo2bo3bo2bo69b4o3b4o$560b2ob2ob2obobob2ob2ob2o355bo7bo69bo4b obo4bo$569bobo365bo5bo70bob2obobob2obo$561bo3bo9bo3bo433b2ob2obobob2ob 2o$932b2o2b2o5b2o2b2o63b3o11b3o$562b3o11b3o353b3o3bo3bo3b3o65bo11bo$ 935b4o3b4o68bo11bo$934bo4bobo4bo65b3o11b3o$564b2o9b2o358bo2bo3bo2bo69b 3o5b3o$564bob2o5b2obo358bo9bo70b2o5b2o$568bo3bo$563b2obob2ob2obob2o 437b3o5b3o$567bobobobo441b2o7b2o$569bobo445bo5bo$565b2o2bobo2b2o440b2o bobob2o$565b2o2bobo2b2o439bo9bo$564bo2bobobobo2bo438bo3bobo3bo$567bobo bobo$567bobobobo441b3o5b3o$567bobobobo440bo11bo$566bo2bobo2bo440bobo5b obo$562b2o2b3o3b3o2b2o434bo2bobo3bobo2bo$561bo2bo11bo2bo433b4obo3bob4o $562b2o13b2o433bo3bob2ob2obo3bo$1012bo2b2o7b2o2bo$1011b2obo3b2ob2o3bob 2o$561bo17bo434bob2obobob2obo$561bo17bo431b5obo5bob5o$1011bo6bo3bo6bo$ 1016bo7bo$1015bo2bo3bo2bo$1019bobo$1019bobo$1016b2obobob2o$1016bo2bobo 2bo$1016bo2bobo2bo2$1015b2o7b2o$1015b2o7b2o$1015b2o7b2o3$1014bo2bo5bo 2bo46$1016bo7bo32b3ob3o$1015b3o5b3o30bo2bobo2bo$1015bo2bo3bo2bo29bo3bo bo3bo$1016b2obobob2o30bo9bo$1012bo3b2obobob2o3bo28bo5bo$1011bobo5bobo 5bobo24bobo7bobo$1010b2ob2o3b2ob2o3b2ob2o22b2obob2ob2obob2o$1011bo7bob o7bo22bobobo2bobo2bobobo$1011bo7bobo7bo21b2obo4bobo4bob2o$1011bo2bo3b 2ob2o3bo2bo20bo3bob2obobob2obo3bo$1012bo15bo25bob3o3b3obo$1016b3o3b3o 25b2o3bo2b2ob2o2bo3b2o$1014b2obo5bob2o27b2o9b2o$1017bo5bo30bo11bo$ 1017b2o3b2o29bobo9bobo$1018b2ob2o29bo15bo$1054bo11bo$1015bo3bobo3bo25b 2obo11bob2o$1050bo3b2o9b2o3bo$1017bobobobo27bo2bo11bo2bo$1017bobobobo 32b2o5b2o$1018b2ob2o30b2ob2o5b2ob2o$1018bo3bo30b4obo3bob4o$1052b2o4bo 3bo4b2o$1056bo2bobo2bo$1057bobobobo$1054b2obobobobob2o$1054bo4bobo4bo$ 1056bo7bo$1053b2obob2ob2obob2o$1056bo7bo$1054bobobo3bobobo2$1055bobo5b obo$1055bobo5bobo$1054b2ob2o3b2ob2o2$1052b2obo2bo3bo2bob2o$1052b2obo9b ob2o$1052bob2ob2o3b2ob2obo$1051b2obo4bobo4bob2o$1056bo7bo$1051b3o4b2ob 2o4b3o3$1051b2o15b2o$1051bo2b2o9b2o2bo$1054bob2o5b2obo$1050b2o6bo3bo6b 2o$1053b2obob2ob2obob2o$1057bobobobo$1059bobo$1055b2o2bobo2b2o$1055b2o 2bobo2b2o$1054bo2bobobobo2bo$1057bobobobo$1057bobobobo$1057bobobobo$ 1056bo2bobo2bo$1052b2o2b3o3b3o2b2o$1051bo2bo11bo2bo$1052b2o13b2o3$ 1051bo17bo$1051bo17bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by width
(click above to open LifeViewer)
RLE: here Plaintext: here

Known spaceships by height

Velocity minimum height
(1,0)c/2 8
(1,0)c/3 5
(1,0)c/4 8
(2,0)c/4 6
(1,0)c/5 8
(2,0)c/5 11
(1,0)c/6 9 < h ≤ 12
(2,0)c/6 7 < h ≤ 9
(3,0)c/6 9 < h ≤ 13
(1,0)c/7 8 < h ≤ 10
(2,0)c/7 8 < h ≤ 12
(3,0)c/7 7 < h ≤ 42

All results checked by Matthias Merzenich using WLS.

x = 65, y = 70, rule = B3/S23 6bo17bo$5b3o15b3o$3b2ob3o13b3ob2o$4bo2bob2o4bo4b2obo2bo$b2obo4bobob2ob 2obobo4bob2o$b2obobo2bobo7bobo2bobob2o$bo8b3obobob3o8bo$2o7b2o9b2o7b2o 13$15bo$8b2ob3ob3o$8b2o4bo2b2ob2o$7bo2bob2o3bo2b2o$19bo2bo16$3bo53bo$ 3bo7b3o11b3o28b3o$2bobo4b2o5b3o36b2obo$9b5ob5o4bo2bo27b3o$7bobo2bo2bo 3bo5bo30b2o$3b6o3bo2b2o4b6o$4b2o6bobo2b2o3bo$14bo6bo13$11bo7bo33bo$5b 2obobob2o3b2obobob2o26b3o$2b3obob3o9b3obob3o22bo3bo$2bo3bobo5bobo5bobo 3bo22b2ob2o5bo$6b2o6bobo6b2o36b2o$3b2o9bobo9b2o22b4obo5bob2o$3b2ob2o 15b2ob2o23bo2bo2b3o2bo$7bo15bo33b3o$61bo$61bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by height
(click above to open LifeViewer)
RLE: here Plaintext: here

Known diagonal spaceships by trail width

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 w ≤ 15 w ≤ 15 4
(1,1)c/5 w ≤ 15 w ≤ 27 w ≤ 27 -
(1,1)c/6 w ≤ 15 w ≤ 33 w ≤ 28
(1,1)c/7 w ≤ 31 w ≤ 31
(1,1)c/8 w ≤ 24 w ≤ 24

Known spaceships by population

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 64[37] 64[37] 66[37] 70[37] - -
(1,0)c/3 25[38] 34[38] 44[38] 49[38] < p ≤ 52 - -
(1,0)c/4 37[39] 37[39] < p ≤ 66 37[39] < p ≤ 108 37[39] < p ≤ 88 - -
(1,1)c/4 5 9[40] < p ≤ 37 9[40] < p ≤ 50 5
(2,0)c/4 9 18 18 18 9 18
(1,0)c/5 p ≤ 58 p ≤ 58 p ≤ 122 p ≤ 58 - -
(1,1)c/5 p ≤ 58 p ≤ 58 p ≤ 58 -
(2,0)c/5 30[41] 31[41] < p ≤ 44 31[41] < p ≤ 70 31[41] < p ≤ 44 - -
(1,0)c/6 p ≤ 56 p ≤ 274 p ≤ 56 p ≤ 274 - -
(1,1)c/6 p ≤ 77 p ≤ 77 ? 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 25[42] < p ≤ 86 25[42] < p ≤ 86 25[42] < p ≤ 104 25[42] < p ≤ 154 - -
(1,0)c/7 3 < p ≤ 20 3 < p ≤ 40[8] 3 < p ≤ 40 3 < p ≤ 40 - -
(1,1)c/7 p ≤ 83 p ≤ 83 ? -
(2,0)c/7 p ≤ 36 p ≤ 186 p ≤ 36 p ≤ 186 - -
(3,0)c/7 p ≤ 232 p ≤ 232 ? p ≤ 232 - -
(1,1)c/8 p ≤ 68 ? ? p ≤ 68
(2,0)c/8 ? p ≤ 121 p ≤ 242 p ≤ 232 p ≤ 74 ?
(2,2)c/8 p ≤ 90 ? ? ?
(4,0)c/8 p ≤ 31 p ≤ 91 p ≤ 110 p ≤ 448 p ≤ 198 p ≤ 199

See also

Notes

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

References

  1. ↑ 1.0 1.1 Tim Coe (December 18, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  2. ↑ praosylen (May 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. ↑ 3.0 3.1 3.2 3.3 3.4 Matthias Merzenich (April 14, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. ↑ 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 Matthias Merzenich (March 17, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. ↑ 5.0 5.1 Tim Coe (April 13, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  6. ↑ Keith Amling (January 18, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. ↑ 7.0 7.1 Tim Coe (June 11, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. ↑ 8.0 8.1 8.2 8.3 Matthias Merzenich (December 24, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. ↑ Matthias Merzenich (June 14, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  10. ↑ Tomas Rokicki (March 1, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  11. ↑ 11.0 11.1 Matthias Merzenich (April 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  12. ↑ 12.0 12.1 12.2 12.3 12.4 Checked with knight2.c
  13. ↑ 13.0 13.1 13.2 13.3 13.4 13.5 Tim Coe (April 17, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  14. ↑ Checked by Paul Tooke with gfind
  15. ↑ Dylan Chen (January 10, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  16. ↑ 16.0 16.1 Matthias Merzenich (November 29, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  17. ↑ Matthias Merzenich (February 25, 2020). Re: Help me finish this c/8 search (discussion thread) at the ConwayLife.com forums
  18. ↑ Matthias Merzenich (December 22, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  19. ↑ 19.0 19.1 19.2 Tim Coe (April 21, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  20. ↑ Tanner Jacobi (December 3, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  21. ↑ 21.0 21.1 21.2 AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  22. ↑ 22.0 22.1 praosylen (December 27, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  23. ↑ 23.0 23.1 praosylen (December 28, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  24. ↑ praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  25. ↑ Matthias Merzenich (March 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  26. ↑ 26.0 26.1 26.2 Tim Coe (March 1, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  27. ↑ 27.0 27.1 27.2 27.3 27.4 27.5 27.6 praosylen (January 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  28. ↑ 28.0 28.1 AforAmpere (November 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  29. ↑ AforAmpere (December 10, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  30. ↑ AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  31. ↑ Matthias Merzenich (April 19, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  32. ↑ 32.0 32.1 Tim Coe (February 1, 2016). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  33. ↑ 33.0 33.1 praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  34. ↑ 34.0 34.1 lordlouckster (July 13, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  35. ↑ 35.0 35.1 35.2 35.3 35.4 35.5 35.6 35.7 Matthias Merzenich (May 5, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  36. ↑ Ivan Fomichev using gfind under OS X 10.9.5
  37. ↑ 37.0 37.1 37.2 37.3 Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  38. ↑ 38.0 38.1 38.2 38.3 Keith Amling (November 12, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  39. ↑ 39.0 39.1 39.2 39.3 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  40. ↑ 40.0 40.1 Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  41. ↑ 41.0 41.1 41.2 41.3 Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  42. ↑ 42.0 42.1 42.2 42.3 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
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